- What is the main purpose of a single fixed pulley that is bolted to an overhead beam?
- It doubles the force the worker applies to the load
- It changes the direction of the pulling force without reducing the effort needed
- It eliminates the weight of the load entirely
- It stores energy so the load lifts itself
Correct answer: It changes the direction of the pulling force without reducing the effort needed
A single fixed pulley changes the direction of the pulling force without reducing the effort needed. It lets a worker pull down to raise a load up, but because only one rope supports the load, the force required still equals the load's full weight.
- A single movable pulley supports a 200-pound load on two rope strands. Ignoring friction, how much force is needed to hold the load?
- 400 pounds
- 200 pounds
- 50 pounds
- 100 pounds
Correct answer: 100 pounds
About 100 pounds is needed. A single movable pulley is supported by two strands, giving a mechanical advantage of two, so the holding force is half the 200-pound load.
- A block-and-tackle has four rope strands directly supporting the movable block. What is its ideal mechanical advantage?
Correct answer: 4
The ideal mechanical advantage is four. The mechanical advantage of a pulley system equals the number of strands directly supporting the movable block, and here four strands carry the load.
- In a class 1 lever, where is the fulcrum located?
- Between the effort and the load
- At the same end as the load
- At the same end as the effort
- Outside the bar entirely
Correct answer: Between the effort and the load
In a class 1 lever the fulcrum sits between the effort and the load. A seesaw or a pair of scissors is the classic example, with the pivot in the middle and force and load on opposite sides.
- A worker uses a 6-foot pry bar with the fulcrum 1 foot from the load and effort applied at the far end. What is the mechanical advantage of this lever?
Correct answer: 5
The mechanical advantage is five. The effort arm is 5 feet (6-foot bar minus the 1 foot to the fulcrum) and the load arm is 1 foot, so dividing the effort arm by the load arm gives five.
- A 30-pound weight sits 4 feet from a fulcrum. How far on the other side must a 60-pound weight be placed to balance the lever?
Correct answer: 2 feet
The 60-pound weight must be 2 feet away. Balance requires equal torque on each side; 30 pounds times 4 feet equals 120, so the 60-pound weight needs a distance of 120 divided by 60, which is 2 feet.
- Two workers carry a load on a pole resting on their shoulders. To make the worker on the left bear more of the weight, where should the load be slid?
- Toward the worker on the left
- Toward the worker on the right
- Exactly to the middle of the pole
- It makes no difference where the load sits
Correct answer: Toward the worker on the left
Sliding the load toward the worker on the left makes that worker bear more weight. The closer support carries the larger share because the load's torque about the far support increases as it moves nearer the left shoulder.
- Which simple machine arrangement requires the LEAST effort to lift a heavy crate, assuming no friction?
- A single fixed pulley
- A single movable pulley
- A block-and-tackle with four supporting strands
- Lifting the crate straight up by hand
Correct answer: A block-and-tackle with four supporting strands
The block-and-tackle with four supporting strands requires the least effort. Its mechanical advantage of four means the worker pulls with only a quarter of the load's weight, while a fixed pulley offers no advantage and a single movable pulley offers only two.
- A wheelbarrow is an example of which class of lever?
- Class 1, with the fulcrum in the middle
- Class 2, with the load between the fulcrum and the effort
- Class 3, with the effort between the fulcrum and the load
- It is not a lever at all
Correct answer: Class 2, with the load between the fulcrum and the effort
A wheelbarrow is a class 2 lever, with the load between the fulcrum and the effort. The wheel acts as the fulcrum, the dirt in the bin is the load, and the lifting hands at the handles provide the effort.
- A lever balances a 100-pound load using only 25 pounds of effort. What does this tell you about the two arms of the lever?
- The effort arm is one-quarter the length of the load arm
- The effort arm is four times the length of the load arm
- Both arms are exactly equal in length
- The load arm is four times the length of the effort arm
Correct answer: The effort arm is four times the length of the load arm
The effort arm is four times the length of the load arm. A mechanical advantage of four (100 divided by 25) means the effort acts over four times the distance from the fulcrum that the load does.
- Using a single fixed pulley, a worker must apply how much force to lift a 75-pound bucket, ignoring friction?
- About 150 pounds
- About 75 pounds
- About 37 pounds
- About 25 pounds
Correct answer: About 75 pounds
About 75 pounds of force is needed. A fixed pulley only redirects the rope and gives a mechanical advantage of one, so the effort equals the full weight of the bucket.
- When a movable pulley is added to a system, the trade-off for using less force to lift a load is that the worker must:
- Pull a much greater length of rope
- Pull with greater force than before
- Lift the load at a faster speed
- Use a heavier rope to hold the same weight
Correct answer: Pull a much greater length of rope
The worker must pull a much greater length of rope. A movable pulley halves the needed force, but to raise the load a given height the rope must be pulled twice as far, because force and distance trade off in any simple machine.
- A seesaw has a child weighing 80 pounds sitting 3 feet from the pivot. A second child weighing 40 pounds sits on the other side. How far from the pivot must the lighter child sit to balance it?
Correct answer: 6 feet
The 40-pound child must sit 6 feet from the pivot. Balancing torque requires 80 pounds times 3 feet to equal 40 pounds times the unknown distance, so 240 divided by 40 gives 6 feet.
- Why does using a longer wrench handle make it easier to loosen a tight bolt?
- The longer handle increases torque by lengthening the effort arm
- The longer handle reduces the weight of the bolt
- The longer handle changes the direction of the applied force
- The longer handle decreases the friction inside the threads
Correct answer: The longer handle increases torque by lengthening the effort arm
The longer handle increases torque by lengthening the effort arm. Because torque equals force times the distance from the pivot, applying the same hand force farther from the bolt produces more turning effect.
- A fishing rod, where the hand near the reel lifts a fish while the other hand acts as the pivot, is an example of which lever class, and what is its trade-off?
- Class 1; it reverses the direction of motion
- Class 2; it multiplies force at the cost of distance
- Class 3; it multiplies speed and distance at the cost of force
- Class 3; it multiplies force at the cost of speed
Correct answer: Class 3; it multiplies speed and distance at the cost of force
A fishing rod is a class 3 lever that multiplies speed and distance at the cost of force. With the effort applied between the fulcrum and the load, the user must pull harder than the load weighs but moves the fish a longer distance quickly.
- A pulley system has a rope running from the worker's hand, up over a fixed pulley, down around a movable pulley, and back up to a fixed anchor. How many strands support the movable pulley, and what is the mechanical advantage?
- One strand; mechanical advantage of one
- Two strands; mechanical advantage of two
- Three strands; mechanical advantage of three
- Four strands; mechanical advantage of four
Correct answer: Two strands; mechanical advantage of two
Two strands support the movable pulley, giving a mechanical advantage of two. Only the rope segments that go directly to the movable block count; the strand redirected over the fixed pulley is the effort end and the anchored segment is one supporting strand, totaling two on the movable block.
- According to Pascal's Law, when pressure is applied to a confined fluid, how is that pressure transmitted throughout the fluid?
- Equally and undiminished in all directions
- Only in the direction the force was applied
- Mostly downward because of the fluid's weight
- More strongly near the walls of the container
Correct answer: Equally and undiminished in all directions
Pressure applied to a confined fluid is transmitted equally and undiminished in all directions. This is the heart of Pascal's Law and is what allows a small input force on one piston to be felt fully across a larger piston elsewhere in the system.
- In a hydraulic press, a small input piston is pushed to lift a heavy load resting on a large output piston. What allows a small force to lift the much heavier load?
- The fluid loses pressure as it travels to the large piston
- The same fluid pressure acts over the larger area of the output piston, producing more force
- The large piston is lighter than the small piston
- The fluid speeds up and gains energy on the way to the load
Correct answer: The same fluid pressure acts over the larger area of the output piston, producing more force
The same fluid pressure acts over the larger area of the output piston, producing more force. Because pressure equals force divided by area, an equal pressure spread across a bigger area yields a proportionally greater output force, which is how the press multiplies the small input.
- A hydraulic press has an input piston with an area of 2 square inches and an output piston with an area of 10 square inches. If 50 pounds is applied to the input piston, how much force is produced at the output piston?
- 50 pounds
- 100 pounds
- 250 pounds
- 500 pounds
Correct answer: 250 pounds
The output force is 250 pounds. The input produces a pressure of 50 pounds over 2 square inches, or 25 pounds per square inch, and that same pressure acting on the 10-square-inch output piston gives 25 times 10, which equals 250 pounds.
- Two connected hydraulic cylinders are filled with oil. The output piston has four times the area of the input piston. What is the mechanical advantage of this hydraulic system?
Correct answer: 4
The mechanical advantage is four. In a hydraulic system the mechanical advantage equals the ratio of the output piston area to the input piston area, so a four-times-larger output piston multiplies the input force by four.
- How does the pressure at the bottom of a deep tank of water compare to the pressure near the top of the same tank?
- The pressure is greater at the bottom
- The pressure is greater near the top
- The pressure is the same everywhere in the tank
- Pressure depends only on the width of the tank
Correct answer: The pressure is greater at the bottom
The pressure is greater at the bottom. Fluid pressure increases with depth because the deeper fluid must support the weight of all the water stacked above it, so the lowest point bears the most pressure.
- An object is fully submerged in water and the buoyant force pushing up on it is greater than its weight. What will the object do?
- Sink steadily to the bottom
- Float upward to the surface
- Stay perfectly still at its depth
- Spin in place without moving up or down
Correct answer: Float upward to the surface
The object will float upward to the surface. When the upward buoyant force exceeds the object's downward weight, the net force is upward, causing the object to rise until it floats.
- What determines the size of the buoyant force acting on an object placed in a fluid?
- The color of the object
- The weight of the fluid the object displaces
- The temperature of the surrounding air
- The height from which the object was dropped
Correct answer: The weight of the fluid the object displaces
The buoyant force equals the weight of the fluid the object displaces. An object that pushes aside more fluid experiences a larger upward force, which is why wide hollow shapes float more readily than dense compact ones.
- A sealed hydraulic line connects several cylinders of different sizes. If a worker increases the push on one cylinder, what happens to the pressure measured in the other cylinders?
- It drops to zero in the farthest cylinder
- It rises by the same amount in every connected cylinder
- It rises only in the largest cylinder
- It stays unchanged because the cylinders differ in size
Correct answer: It rises by the same amount in every connected cylinder
The pressure rises by the same amount in every connected cylinder. By Pascal's Law a pressure change in a confined fluid is transmitted equally throughout, so all connected cylinders register the same increase regardless of their size.
- In a hydraulic jack, the input piston is pushed down 12 inches to raise the heavy output piston only 2 inches. What does this difference in travel distance tell you?
- The jack is leaking fluid and losing motion
- The output piston moves less but lifts with greater force
- The input piston is heavier than the output piston
- The fluid is being compressed to store energy
Correct answer: The output piston moves less but lifts with greater force
The output piston moves less but lifts with greater force. A hydraulic system trades distance for force just like other machines, so the large piston moves a shorter distance while exerting a force much greater than the input.
- A solid steel block and a hollow steel boat hull have the same total weight. Why does the hull float while the solid block sinks?
- The hull spreads its weight over a shape that displaces more water, increasing buoyant force
- Steel always floats when it is shaped into a boat
- The block is heavier than the hull despite equal weights
- Floating depends only on how the object is lowered into the water
Correct answer: The hull spreads its weight over a shape that displaces more water, increasing buoyant force
The hull spreads its weight over a shape that displaces more water, increasing buoyant force. By taking up a larger volume, the hull pushes aside enough water for the upward buoyant force to equal its weight, while the compact block displaces too little water to float.
- Water is held in a closed pipe with no openings. If a piston squeezes one end of the pipe, what happens to the volume of the water inside?
- It expands greatly to absorb the force
- It compresses to roughly half its size
- It changes very little because liquids are nearly incompressible
- It turns into a gas under the added pressure
Correct answer: It changes very little because liquids are nearly incompressible
The volume changes very little because liquids are nearly incompressible. This near-incompressibility is exactly why hydraulic systems work: the fluid transmits the applied pressure rather than simply squashing down.
- Two storage tanks are filled with water to the very same depth, but one tank is much wider than the other. How does the water pressure at the bottom of each tank compare?
- The pressure is higher in the wider tank
- The pressure is higher in the narrower tank
- The pressure at the bottom is the same in both tanks
- The pressure cannot be compared without knowing the tank shapes
Correct answer: The pressure at the bottom is the same in both tanks
The pressure at the bottom is the same in both tanks. Fluid pressure depends on depth, not on the width or total amount of water, so equal depths produce equal pressure regardless of how wide each tank is.
- A hydraulic system uses a 1-square-inch input piston and a 6-square-inch output piston. A worker wants to lift a 600-pound load on the output piston. About how much force must be applied to the input piston, ignoring friction?
- 600 pounds
- 300 pounds
- 100 pounds
- 60 pounds
Correct answer: 100 pounds
About 100 pounds of input force is needed. The load requires a pressure of 600 pounds over 6 square inches, or 100 pounds per square inch, and that same pressure acting on the 1-square-inch input piston requires only 100 pounds of force.
- A balloon weighted to hang motionless underwater neither rises nor sinks. What is true about the forces acting on it?
- The buoyant force is greater than its weight
- The buoyant force is less than its weight
- The buoyant force exactly equals its weight
- There is no buoyant force at that depth
Correct answer: The buoyant force exactly equals its weight
The buoyant force exactly equals its weight. When the upward buoyant force and the downward weight are balanced, the net force is zero, so the object stays suspended at its depth without rising or sinking.
- A ball is whirled in a circle on the end of a string. If the string suddenly breaks, in which direction does the ball travel?
- Straight outward, directly away from the center
- Continuing in a curved path for a moment, then straightening
- Straight inward, toward where the center had been
- In a straight line along the path it was moving at the instant of release
Correct answer: In a straight line along the path it was moving at the instant of release
The ball flies off in a straight line along the path it was moving at the instant of release. Once the inward pull of the string vanishes, no force bends its path, so by inertia it continues straight along the tangent rather than flying directly outward.
- What does Newton's First Law state about an object that is at rest?
- It will gradually begin moving on its own
- It will resist only pushing forces, not pulling forces
- It will stay at rest unless an unbalanced force acts on it
- It loses its mass until a force is applied
Correct answer: It will stay at rest unless an unbalanced force acts on it
An object at rest stays at rest unless an unbalanced force acts on it. This is Newton's First Law, the law of inertia, which says objects keep their current state of motion until a net outside force changes it.
- A force pulls on a crate at an angle above the floor. Into which two component directions is this single angled force commonly resolved?
- A horizontal component and a vertical component
- Two equal forces pointing straight up
- A clockwise force and a counterclockwise force
- A single force that doubles in size
Correct answer: A horizontal component and a vertical component
An angled force is resolved into a horizontal component and a vertical component. Breaking the diagonal pull into these two perpendicular parts shows how much of the force slides the crate along the floor and how much lifts it.
- As a car drives faster around the same curve, what happens to the centripetal force needed to keep it on its circular path?
- It decreases as speed rises
- It stays exactly the same
- It increases as speed rises
- It drops to zero at high speed
Correct answer: It increases as speed rises
The required centripetal force increases as speed rises. A faster car needs a stronger inward force to bend its path around the same radius, which is why tight curves taken at high speed are so demanding on tires and road grip.
- Passengers in a bus that stops suddenly are thrown forward in their seats. What explains this motion?
- The bus pushes the passengers forward as it stops
- A centrifugal force pulls them toward the front
- The passengers' inertia keeps them moving forward while the bus slows
- Gravity increases when the bus brakes
Correct answer: The passengers' inertia keeps them moving forward while the bus slows
The passengers' inertia keeps them moving forward while the bus slows. Their bodies tend to continue at the original speed until a force, such as a seatbelt, stops them, so they appear to lurch forward relative to the braking bus.
- Two ropes pull on a ring, one straight north and one straight east, each with 30 pounds of force. Compared with a single 30-pound pull, the combined effect on the ring is:
- A smaller net pull than 30 pounds
- Exactly 60 pounds straight north
- A larger net pull aimed toward the northeast
- Zero, because the pulls cancel out
Correct answer: A larger net pull aimed toward the northeast
The two pulls combine into a larger net pull aimed toward the northeast. When forces act at right angles they add as vectors, producing a resultant that points between them and exceeds either single 30-pound force.
- Clothes in a spinning washing-machine drum press hard against the outer wall during the spin cycle. Why do they move toward the wall?
- The drum wall pulls the clothes outward with a real outward force
- Their inertia carries them straight while the drum wall curves them inward, so they pile against the wall
- Gravity reverses direction during fast spinning
- The water makes the clothes lighter and they float outward
Correct answer: Their inertia carries them straight while the drum wall curves them inward, so they pile against the wall
The clothes' inertia carries them straight while the drum wall curves them inward, so they pile against the wall. The wall supplies the inward force that bends each item's path; the apparent outward shove is just the clothes resisting that change in direction.
- A heavy boulder and a small pebble both sit motionless on flat ground. Which requires more force to start moving, and why?
- The pebble, because small objects resist motion more
- They require equal force, because both start at rest
- Neither requires force, since resting objects move freely
- The boulder, because its greater mass gives it more inertia
Correct answer: The boulder, because its greater mass gives it more inertia
The boulder requires more force because its greater mass gives it more inertia. Inertia is an object's resistance to changes in motion, and a larger mass resists being set in motion more strongly than a small one.
- A crate is dragged by a rope angled at 30 degrees above horizontal. How does the horizontal pulling component compare with the full force in the rope?
- It is larger than the full rope force
- It is smaller than the full rope force
- It exactly equals the full rope force
- It points straight down into the floor
Correct answer: It is smaller than the full rope force
The horizontal component is smaller than the full rope force. Only part of an angled pull acts along the floor; the rest is directed upward, so the sideways component that actually drags the crate is always less than the total force in the rope.
- A spinning grinding wheel suddenly shatters and a fragment breaks loose. What path does the fragment follow as it leaves the wheel?
- A straight tangent line away from the wheel's edge
- A spiral that widens outward
- Straight back toward the center of the wheel
- A circle the same size as the wheel
Correct answer: A straight tangent line away from the wheel's edge
The fragment follows a straight tangent line away from the wheel's edge. With nothing left to hold it in its circular path, inertia sends it straight along the direction it was traveling at the moment it broke free.
- A tablecloth is yanked quickly from under a set of dishes and the dishes barely move. Which principle best explains why the dishes stay in place?
- The dishes are heavier than the tablecloth
- Inertia keeps the resting dishes in place during the brief, fast pull
- Centrifugal force pins the dishes down
- Friction speeds the dishes up to match the cloth
Correct answer: Inertia keeps the resting dishes in place during the brief, fast pull
Inertia keeps the resting dishes in place during the brief, fast pull. Because the cloth moves so quickly, there is too little time for friction to drag the dishes along, and their tendency to stay at rest keeps them on the table.
- A sign hangs from two cables that each rise at an angle to the ceiling. Together the upward vertical components of the two cable tensions must:
- Equal the weight of the sign
- Be twice the weight of the sign
- Point sideways to keep the sign from swinging
- Be zero so the sign stays still
Correct answer: Equal the weight of the sign
The upward vertical components of the two cable tensions must equal the weight of the sign. For the hanging sign to stay balanced, the resolved upward parts of both cable forces have to support its full downward weight.
- A car rounds a sharp curve to the left and the driver feels pushed toward the right door. What is actually happening to the driver?
- A real outward force shoves the driver into the door
- Gravity tilts toward the outside of the curve
- The seat pushes the driver outward to start the turn
- The driver's body tends to continue straight while the car turns left beneath them
Correct answer: The driver's body tends to continue straight while the car turns left beneath them
The driver's body tends to continue straight while the car turns left beneath them. The sensation of being pushed outward is the driver's inertia resisting the turn; the door then provides the real inward force that bends the driver along with the car.
- A loaded freight train and an empty bicycle travel at the same speed. Which is harder to bring to a stop, and what property accounts for the difference?
- The train, because its much greater mass gives it more inertia
- The bicycle, because it has more inertia
- Both stop equally easily at the same speed
- Neither, because moving objects stop on their own
Correct answer: The train, because its much greater mass gives it more inertia
The train is harder to stop because its much greater mass gives it more inertia. Inertia grows with mass, so the massive train resists the change from motion to rest far more than the light bicycle moving at the same speed.
- When three light bulbs are wired in series and one bulb burns out, the other two bulbs:
- Go out, because the circuit is broken
- Get brighter
- Stay exactly the same
- Begin to flash
Correct answer: Go out, because the circuit is broken
The other two go out because the circuit is broken. In a series circuit there is only one path, so a single break stops current everywhere along the line.
- In a parallel circuit, if one of several bulbs burns out, the remaining bulbs:
- All go out
- Keep working because each has its own path
- Become dimmer than before
- Switch off one by one
Correct answer: Keep working because each has its own path
The remaining bulbs keep working because each has its own path. A parallel circuit gives current multiple routes, so one broken branch does not stop the others.
- A fuse protects a circuit by:
- Increasing the current to clear a jam
- Storing extra electricity
- Melting and breaking the circuit when current gets too high
- Speeding up the flow of current
Correct answer: Melting and breaking the circuit when current gets too high
A fuse melts and breaks the circuit when current gets too high. The thin metal element is designed to fail safely, cutting power before wiring overheats.
- Copper wire is widely used for electrical wiring because copper is a good:
- Insulator of electricity
- Magnet
- Heat shield
- Conductor of electricity
Correct answer: Conductor of electricity
Copper is a good conductor of electricity. Its electrons move freely, allowing current to flow with little resistance, which makes it ideal for wiring.
- Rubber or plastic coating on a wire serves as an insulator, meaning it:
- Resists the flow of electricity and prevents shocks
- Carries the current better than the metal
- Stores the electricity for later
- Increases the current
Correct answer: Resists the flow of electricity and prevents shocks
An insulator resists the flow of electricity and prevents shocks. The rubber or plastic keeps current confined to the metal conductor and protects anyone who touches the wire.
- An electromagnet can be made stronger by:
- Using a shorter wire only
- Increasing the current or adding more coils of wire
- Removing the iron core
- Lowering the current
Correct answer: Increasing the current or adding more coils of wire
An electromagnet is made stronger by increasing the current or adding more coils. More current and more turns of wire each boost the magnetic field around the iron core.
- A metal spoon left in a hot bowl of soup soon feels hot at the handle because metal:
- Conducts heat well from the hot end to the cool end
- Blocks heat completely
- Generates its own heat
- Cools the soup faster than it warms
Correct answer: Conducts heat well from the hot end to the cool end
Metal conducts heat well from the hot end to the cool end. Heat energy passes quickly through the metal, warming the handle even though it sits outside the soup.
- Hot air rises above a heater because warm air is:
- Heavier than cool air
- Less dense than the cooler air around it
- The same density as cool air
- Pulled down by gravity more strongly
Correct answer: Less dense than the cooler air around it
Warm air is less dense than the cooler air around it. Being lighter for its volume, it floats upward while denser cool air sinks to take its place, creating convection.
- A gap is left between sections of a long steel railroad rail to allow for:
- Water drainage only
- Easier painting
- Expansion of the metal when it gets hot
- The rail to slide sideways
Correct answer: Expansion of the metal when it gets hot
The gap allows for expansion of the metal when it gets hot. Steel lengthens as it warms, and the space prevents the rails from buckling against each other.
- A foam cup keeps coffee hot longer than a thin metal cup because foam is a good:
- Conductor that speeds heat loss
- Source of extra heat
- Reflector of cold
- Insulator that slows heat loss
Correct answer: Insulator that slows heat loss
Foam is a good insulator that slows heat loss. The trapped air pockets in foam resist the flow of heat, so the coffee stays warm longer than in conductive metal.
- You can feel the warmth of a campfire from several feet away even with no wind because heat travels by:
- Radiation through the air directly to you
- Conduction through the ground only
- Convection pulling you toward the fire
- Sound waves from the flames
Correct answer: Radiation through the air directly to you
Heat travels by radiation through the air directly to you. The fire emits infrared energy that warms your skin without needing to heat all the air in between.
- Water at the bottom of a pot on a stove heats the whole pot mostly through:
- Radiation from the water surface
- Convection currents that circulate the warmed water
- The water staying perfectly still
- Sound vibrations in the pot
Correct answer: Convection currents that circulate the warmed water
Convection currents circulate the warmed water. Heated water at the bottom rises and cooler water sinks, setting up a loop that distributes heat throughout the pot.
- A solid cube measures 2 inches on each side. Its volume is:
- 8 cubic inches
- 6 cubic inches
- 4 cubic inches
- 12 cubic inches
Correct answer: 8 cubic inches
The volume is 8 cubic inches. The volume of a cube equals side times side times side, so 2 times 2 times 2 equals 8.
- Two boxes hold the same volume, but Box A is a tall thin rectangle and Box B is a wide flat rectangle. Compared with each other, they:
- Box A always holds more
- Hold the same amount despite different shapes
- Box B always holds more
- Cannot hold equal amounts
Correct answer: Hold the same amount despite different shapes
They hold the same amount despite different shapes. Volume depends on the total space enclosed, not the shape, so equal volumes hold equal contents.
- If you double the length of every side of a cube, its volume becomes:
- Twice as large
- Four times as large
- Eight times as large
- Unchanged
Correct answer: Eight times as large
The volume becomes eight times as large. Volume scales with the cube of the side, so doubling each side multiplies volume by 2 times 2 times 2, which is 8.
- A cylinder and a cone have the same base radius and the same height. The cone holds:
- More than the cylinder
- Exactly the same
- Twice as much
- Less than the cylinder
Correct answer: Less than the cylinder
The cone holds less than the cylinder. A cone of equal base and height has only one-third the volume of the cylinder, because it tapers to a point.
- A sheet of metal is folded into an open box. Which shape encloses the most volume for a given amount of material when forming a closed container?
- A sphere
- A tall thin cylinder
- A flat wide pan
- A long narrow tube
Correct answer: A sphere
A sphere encloses the most volume for a given amount of material. Its rounded surface holds the maximum space with the least surface area of any shape.
- A container is 10 inches long, 4 inches wide, and 3 inches deep. Its volume is:
- 17 cubic inches
- 120 cubic inches
- 40 cubic inches
- 30 cubic inches
Correct answer: 120 cubic inches
The volume is 120 cubic inches. The volume of a rectangular box equals length times width times height, so 10 times 4 times 3 equals 120.
- A loading ramp is 20 feet long and rises to a dock 4 feet high. Ignoring friction, what is the ideal mechanical advantage of this ramp?
Correct answer: 5
The ideal mechanical advantage is 5. For an inclined plane, mechanical advantage equals the ramp length divided by the vertical height, so 20 feet divided by 4 feet equals 5.
- Two flat roofs shed rainwater. Roof A is steeply pitched and Roof B is nearly flat. Which roof drains water faster?
- Roof B, because flat roofs spread water thinner
- Roof A, because the steeper slope speeds runoff
- Both drain at exactly the same rate
- Neither roof will drain without a pump
Correct answer: Roof A, because the steeper slope speeds runoff
Roof A drains faster. A steeper slope gives water a larger downhill component of gravity, so it runs off more quickly than on a nearly flat surface where water pools.
- A triangular roof truss is stronger than a square frame of the same material mainly because the triangle:
- Uses less material than any other shape
- Is easier to paint and maintain
- Cannot change shape without changing a side length, so it resists distortion
- Always weighs more, adding strength
Correct answer: Cannot change shape without changing a side length, so it resists distortion
The triangle resists distortion because it cannot change shape unless a side length changes. A square can collapse into a parallelogram under load, but a triangle's fixed angles make it rigid, which is why trusses use triangles.
- A worker must roll a heavy drum up to a platform. To make the job require the least pushing force, the ramp should be:
- As short and steep as possible
- Exactly as long as the platform is high
- Curved upward at the top
- As long and gradual as possible
Correct answer: As long and gradual as possible
A long, gradual ramp requires the least force. Lengthening the incline for the same height increases mechanical advantage, trading a longer push distance for a smaller required force.
- An arch bridge carries loads from above primarily by:
- Converting downward load into compression along the curve to the supports
- Stretching the stone in tension across the span
- Storing the weight as heat in the keystone
- Floating the deck on the air beneath it
Correct answer: Converting downward load into compression along the curve to the supports
An arch carries load by converting it into compression directed along the curve to the supports. Stone is strong in compression, so the arch shape channels weight outward and down to the abutments.
- A guy wire is run from the top of a tall antenna to a stake in the ground. Compared with attaching the wire halfway up the antenna, attaching it at the very top:
- Has no effect on stability
- Provides greater leverage to resist the antenna tipping over
- Makes the antenna easier to tip
- Reduces the tension to zero
Correct answer: Provides greater leverage to resist the antenna tipping over
Attaching at the top provides greater leverage against tipping. A higher attachment point gives the support wire a longer moment arm to counter sideways forces, stabilizing the tower more effectively.
- A board leans against a wall, forming a ramp. If the bottom of the board is slid farther from the wall, the ramp becomes:
- Steeper, so an object needs more force
- Vertical
- Less steep, so an object on it needs less force to be pushed up
- Unchanged in steepness
Correct answer: Less steep, so an object on it needs less force to be pushed up
The ramp becomes less steep, requiring less pushing force. Moving the base outward lowers the angle of the incline, increasing its mechanical advantage.
- A wide foundation footing is placed under a heavy column instead of resting the column directly on the soil because the wider footing:
- Makes the column taller
- Increases the total weight on the soil
- Channels load into a single point
- Spreads the load over more area, lowering the pressure on the soil
Correct answer: Spreads the load over more area, lowering the pressure on the soil
The wide footing spreads the load over more area, lowering soil pressure. Pressure equals force divided by area, so enlarging the contact area reduces the chance the soil will give way.
- Switchback roads zigzag up a mountainside instead of going straight up because the longer, gentler path:
- Reduces the slope so vehicles need less force to climb
- Saves fuel by being shorter
- Is steeper and therefore faster
- Removes the need for brakes going down
Correct answer: Reduces the slope so vehicles need less force to climb
The switchback reduces the effective slope, so vehicles need less force to climb. It trades a longer travel distance for a gentler grade, the same principle as a long inclined plane.
- A cantilever balcony juts out from a building with no support under its free end. The wall connection must resist mainly:
- Pure compression only
- A bending and twisting force trying to rotate the balcony down
- Buoyant force from the air
- A pulling force toward the building
Correct answer: A bending and twisting force trying to rotate the balcony down
The wall connection must resist a bending force trying to rotate the balcony downward. With no support at the free end, the entire load creates a turning moment that the anchored end alone must counter.
- A plank rests across two sawhorses. A heavy box is placed much closer to the left sawhorse. Which sawhorse bears more of the box's weight?
- The right sawhorse
- Both bear exactly equal weight
- The left sawhorse, because the load is nearer to it
- Neither, the plank carries it all
Correct answer: The left sawhorse, because the load is nearer to it
The left sawhorse bears more weight because the load is nearer to it. A support closer to the load carries a larger share, following the seesaw balance principle.
- Tent poles and a kickstand both work because a tripod or angled brace:
- Adds weight to hold things down
- Eliminates the force of gravity
- Works only on perfectly level ground
- Forms a stable base that resists tipping in multiple directions
Correct answer: Forms a stable base that resists tipping in multiple directions
An angled brace or tripod forms a stable base that resists tipping in multiple directions. Spreading supports outward widens the base of support and braces against sideways collapse.
- A bimetallic strip in a thermostat bends when heated because the two bonded metals:
- Expand by different amounts, forcing the strip to curve
- Melt at the same temperature
- Carry equal electric current
- Have identical thermal expansion rates
Correct answer: Expand by different amounts, forcing the strip to curve
The strip curves because the two metals expand by different amounts. When heated, the metal that expands more is forced to the outside of the curve, bending the strip to open or close a circuit.
- A ratchet wrench lets you tighten a bolt without removing the wrench because the ratchet mechanism:
- Locks in both directions equally
- Allows turning in one direction while slipping freely in the other
- Spins continuously like a motor
- Reverses the bolt threads
Correct answer: Allows turning in one direction while slipping freely in the other
The ratchet allows turning in one direction while slipping freely in the other. A spring-loaded pawl catches the gear teeth one way and rides over them the other way, so you can re-cock the handle without resetting.
- A spirit (bubble) level shows a surface is level when the bubble:
- Moves to the high end
- Disappears completely
- Sits centered between the marked lines
- Splits into two bubbles
Correct answer: Sits centered between the marked lines
The surface is level when the bubble sits centered between the marks. The air bubble always rises to the highest point of the curved liquid-filled vial, so a centered bubble means neither end is higher.
- A flywheel is added to an engine mainly to:
- Increase the engine's fuel use
- Cool the engine with airflow
- Reduce the engine's total mass
- Smooth out speed fluctuations by storing rotational energy
Correct answer: Smooth out speed fluctuations by storing rotational energy
A flywheel smooths speed fluctuations by storing rotational energy. Its rotational inertia carries the shaft through moments between power strokes, evening out the engine's rotation.
- A check valve in a pipe is designed to:
- Let fluid flow in only one direction and block backflow
- Mix two fluids together
- Measure the fluid temperature
- Speed up flow in both directions
Correct answer: Let fluid flow in only one direction and block backflow
A check valve lets fluid flow only one direction and blocks backflow. Internal pressure opens it in the forward direction and reverse pressure seats it shut, preventing return flow.
- A spring scale measures weight by relying on the principle that within its limit, a spring:
- Stretches a fixed amount regardless of force
- Stretches an amount proportional to the force applied
- Becomes stronger the more it is stretched
- Compresses only when heated
Correct answer: Stretches an amount proportional to the force applied
A spring stretches an amount proportional to the applied force. This linear relationship lets the marked scale convert the stretch distance directly into a weight reading.
- A governor on an engine controls its speed by sensing rotation and then:
- Adding fuel as speed rises
- Shutting the engine off immediately at any speed
- Reducing fuel or throttle as speed rises to prevent overspeed
- Increasing the load randomly
Correct answer: Reducing fuel or throttle as speed rises to prevent overspeed
A governor reduces fuel or throttle as speed rises. Spinning weights fly outward with speed and act through linkage to close the throttle, holding the engine near a set speed.
- A worker uses a pipe slipped over a wrench handle to loosen a stuck bolt. The pipe helps because it:
- Makes the bolt threads weaker
- Reduces friction on the bolt
- Adds weight to the bolt head
- Lengthens the handle, increasing the turning force for the same effort
Correct answer: Lengthens the handle, increasing the turning force for the same effort
The pipe lengthens the handle, increasing the turning force (torque) for the same effort. A longer lever arm multiplies the twisting moment applied to the bolt.
- A funnel works best for filling a narrow bottle because it:
- Guides a wide stream of liquid into a small opening
- Heats the liquid as it pours
- Increases the liquid's volume
- Slows evaporation
Correct answer: Guides a wide stream of liquid into a small opening
A funnel guides a wide stream of liquid into a small opening. Its tapered shape collects liquid over a large mouth and channels it down to the bottle's narrow neck without spilling.
- A turnbuckle is used to tighten a cable or rod by:
- Cutting the cable to length
- Drawing two threaded ends together as the center sleeve is turned
- Adding electrical insulation
- Heating the cable to shrink it
Correct answer: Drawing two threaded ends together as the center sleeve is turned
A turnbuckle draws two threaded ends together as the center sleeve is turned. Opposite-handed threads on each end pull both inward simultaneously, tensioning the cable.
- A worker should choose a coarse file over a fine file when the goal is to:
- Produce the smoothest possible surface
- Polish a finished part
- Remove material quickly, accepting a rougher finish
- Measure a part's thickness
Correct answer: Remove material quickly, accepting a rougher finish
A coarse file removes material quickly while leaving a rougher finish. Its larger, more widely spaced teeth cut deeper, so it is used for fast stock removal before fine finishing.
- A snap-action toggle switch clicks firmly between on and off because a spring:
- Slows the contact motion to a crawl
- Heats the contacts before they touch
- Locks the switch permanently on
- Stores energy and releases it suddenly to move the contacts quickly
Correct answer: Stores energy and releases it suddenly to move the contacts quickly
A spring stores energy and releases it suddenly to move the contacts quickly. The snap action minimizes arcing by opening or closing the contacts fast, regardless of how slowly the lever is pushed.
- A small gear with 10 teeth drives a large gear with 30 teeth. For every full turn of the large gear, the small gear turns:
- 3 times
- One-third of a turn
- 30 times
- 10 times
Correct answer: 3 times
The small gear turns 3 times. The turn ratio is inverse to the tooth ratio, so the 10-tooth gear must make 30 divided by 10, or 3, rotations for each single rotation of the 30-tooth gear.
- Two gears mesh directly together. Compared with the driving gear, the driven gear turns:
- In the same direction
- In the opposite direction
- Always faster
- Always slower
Correct answer: In the opposite direction
The driven gear turns in the opposite direction. When two external gears mesh, their teeth push against each other, so one spinning clockwise forces the other counterclockwise.
- A bicycle is shifted to a larger rear sprocket while the front gear stays the same. Pedaling now feels:
- Harder, with more distance per stroke
- Exactly the same
- Easier, but the bike moves less distance per pedal stroke
- Impossible to pedal
Correct answer: Easier, but the bike moves less distance per pedal stroke
Pedaling feels easier but covers less distance per stroke. A larger rear sprocket increases mechanical advantage, trading speed for easier turning, which helps when climbing hills.
- A belt connects two pulleys without crossing. The driven pulley turns:
- In the opposite direction
- Twice as fast always
- Backward then forward
- In the same direction as the drive pulley
Correct answer: In the same direction as the drive pulley
An open (uncrossed) belt makes the driven pulley turn in the same direction as the drive pulley. The belt links the two rims moving the same way around the loop.
- A drive pulley 2 inches across turns a driven pulley 6 inches across by belt. The driven pulley turns:
- Slower than the drive pulley
- Faster than the drive pulley
- At the same speed
- Not at all
Correct answer: Slower than the drive pulley
The driven pulley turns slower. A larger pulley travels less far per rotation for the same belt speed, so the 6-inch pulley rotates more slowly than the 2-inch drive pulley.
- In a gear train, an idler gear placed between the driver and the final gear mainly:
- Doubles the output speed
- Reverses the direction of the final gear without changing its speed ratio
- Eliminates all friction
- Stops the gear train
Correct answer: Reverses the direction of the final gear without changing its speed ratio
An idler gear reverses the final gear's direction without changing the overall speed ratio. The idler's own tooth count cancels out, affecting only rotation direction.
- A crossed (figure-eight) belt between two pulleys causes the driven pulley to:
- Turn in the same direction
- Stop turning
- Turn in the opposite direction from the drive pulley
- Spin twice as fast
Correct answer: Turn in the opposite direction from the drive pulley
A crossed belt makes the driven pulley turn opposite to the drive pulley. The figure-eight crossing reverses which side of each rim the belt contacts.
- A worm gear drives a toothed wheel. A key feature of a worm-and-wheel drive is that it:
- Speeds up the output dramatically
- Has no mechanical advantage
- Turns the wheel in random directions
- Produces a large speed reduction and often resists being driven backward
Correct answer: Produces a large speed reduction and often resists being driven backward
A worm-and-wheel drive produces a large speed reduction and often resists back-driving. Each turn of the worm advances the wheel only one tooth, giving high reduction and a self-locking tendency.
- If a belt slips on its pulley, the most direct effect is that the driven machine:
- Runs slower or stops while the drive pulley keeps turning
- Speeds up uncontrollably
- Reverses direction
- Locks solid
Correct answer: Runs slower or stops while the drive pulley keeps turning
The driven machine runs slower or stops while the drive pulley keeps turning. Slipping breaks the firm grip needed to transmit motion, so power transfer drops off.
- A 12-tooth gear meshes with a 48-tooth gear. The mechanical advantage favoring torque at the large gear is about:
Correct answer: 4:1
The torque advantage is about 4:1 at the large gear. The ratio equals 48 divided by 12, so the larger gear turns slower but delivers four times the torque of the small driving gear.
- Two balls are dropped from the same height at the same instant, one heavy and one light. Ignoring air resistance, they hit the ground:
- At the same time
- The heavy ball first
- The light ball first
- Only the heavy ball falls
Correct answer: At the same time
They hit the ground at the same time. Gravity accelerates all objects equally regardless of mass, so without air resistance both reach the ground together.
- A rock is dropped from a cliff. As it falls, its speed:
- Stays constant the whole way down
- Increases steadily until it lands
- Decreases as it falls
- Increases then decreases
Correct answer: Increases steadily until it lands
Its speed increases steadily until it lands. Gravity continuously accelerates the rock, adding velocity each second of the fall.
- A ball thrown straight up slows, stops at the top, then falls back. At the highest point, its velocity is:
- Maximum
- Equal to the launch speed
- Zero, while gravity still acts on it
- Pointed upward
Correct answer: Zero, while gravity still acts on it
At the highest point the velocity is zero, even though gravity still acts. The upward motion is fully canceled before the ball reverses and accelerates downward.
- A bullet fired horizontally and a bullet dropped from the same height at the same moment will, ignoring air resistance:
- Have the fired bullet land much later
- Have the dropped bullet land first
- Never reach the ground
- Reach the ground at the same time
Correct answer: Reach the ground at the same time
They reach the ground at the same time. Horizontal motion does not affect vertical fall, so gravity pulls both downward at the same rate.
- A car traveling at constant speed around a level circular track has a velocity that is:
- Constantly changing direction even though the speed is steady
- Completely unchanging
- Increasing each lap
- Zero on average
Correct answer: Constantly changing direction even though the speed is steady
Its velocity constantly changes direction even with steady speed. Velocity includes direction, so turning means the car is accelerating toward the center despite a fixed speedometer reading.
- On the Moon, where gravity is weaker than on Earth, a dropped hammer:
- Falls faster than on Earth
- Falls more slowly than it would on Earth
- Floats and does not fall
- Falls at the same rate as on Earth
Correct answer: Falls more slowly than it would on Earth
The hammer falls more slowly than on Earth. Weaker gravitational pull means a smaller acceleration, so the hammer gains speed less quickly as it falls.
- A skydiver eventually stops speeding up and falls at a steady terminal velocity because:
- Gravity turns off at high speed
- The diver runs out of weight
- Air resistance grows until it balances the pull of gravity
- The air pushes the diver upward faster than gravity pulls
Correct answer: Air resistance grows until it balances the pull of gravity
Air resistance grows until it balances gravity. Once the upward drag equals the downward weight, the net force is zero and the diver falls at a constant terminal speed.
- A stone takes longer to reach the ground when dropped from a taller building because it:
- Weighs more at greater height
- Slows down as it falls farther
- Falls at a constant low speed
- Has more distance to fall and keeps accelerating the whole way
Correct answer: Has more distance to fall and keeps accelerating the whole way
It has more distance to fall and keeps accelerating the whole way. A greater drop height means more time under gravity's continuous acceleration before landing.
- During a thunderstorm you see lightning before you hear thunder because:
- Light travels much faster than sound
- Sound travels faster than light
- Thunder happens after the lightning ends
- Your eyes react faster than your ears
Correct answer: Light travels much faster than sound
Light travels much faster than sound. The flash reaches you almost instantly, while the thunder lags behind because sound moves comparatively slowly through air.
- A straight stick appears bent where it enters a glass of water because light:
- Stops at the water surface
- Changes direction as it passes between water and air
- Travels in a perfect straight line through both
- Is absorbed by the water
Correct answer: Changes direction as it passes between water and air
Light changes direction as it passes between water and air. This bending, called refraction, makes the submerged part of the stick appear shifted, so the stick looks bent.
- A flat mirror forms an image that is:
- Larger than the object
- Always upside down
- The same size as the object and reversed left to right
- Smaller than the object
Correct answer: The same size as the object and reversed left to right
A flat mirror forms an image the same size as the object and reversed left to right. The reflected rays preserve scale but swap the apparent left and right sides.
- Soft, heavy curtains and carpet reduce echo in a room because they:
- Amplify all sounds
- Speed up sound waves
- Block light but not sound
- Absorb sound instead of reflecting it
Correct answer: Absorb sound instead of reflecting it
They absorb sound instead of reflecting it. Soft, porous materials soak up sound energy, reducing the reflections that cause echoes off hard walls and floors.
- A magnifying glass makes small print look larger because the convex lens:
- Bends light rays to form an enlarged image
- Reflects light back to the eye
- Blocks part of the light
- Slows the print's movement
Correct answer: Bends light rays to form an enlarged image
The convex lens bends light rays to form an enlarged image. Its curved shape converges light so the object appears bigger when held within the focal distance.
- The pitch of a sound is determined by the sound wave's:
- Loudness
- Frequency, or how rapidly it vibrates
- Color
- Distance traveled
Correct answer: Frequency, or how rapidly it vibrates
Pitch is determined by frequency, how rapidly the wave vibrates. Faster vibrations produce a higher pitch, while slower vibrations produce a lower pitch.
- A tall, narrow box tips over more easily than a short, wide box because the tall box has a:
- Higher center of gravity over a narrow base
- Lower center of gravity
- Heavier total weight always
- Wider base of support
Correct answer: Higher center of gravity over a narrow base
The tall box has a higher center of gravity over a narrow base. A high, narrow shape lets the center of gravity pass beyond the base with only a small tilt, so it topples easily.
- A race car is built low to the ground mainly to:
- Make it lighter
- Lower its center of gravity so it resists tipping in turns
- Improve its paint job
- Raise its center of gravity
Correct answer: Lower its center of gravity so it resists tipping in turns
A low build lowers the center of gravity so the car resists tipping in turns. Keeping the mass close to the ground makes it harder for cornering forces to roll the car over.
- An object will balance when it is supported directly under its:
- Heaviest corner
- Tallest point
- Center of gravity
- Outer edge
Correct answer: Center of gravity
An object balances when supported directly under its center of gravity. At that point the object's weight is evenly distributed so it neither tips one way nor the other.
- A person carrying a heavy backpack leans forward slightly in order to:
- Make the load feel heavier
- Shift weight onto their heels
- Raise the load higher
- Keep the combined center of gravity over their feet
Correct answer: Keep the combined center of gravity over their feet
Leaning forward keeps the combined center of gravity over their feet. The backpack pushes the center of gravity backward, so leaning forward returns it above the base for balance.
- A wide wheelbase on a tractor improves stability on slopes because it:
- Widens the base of support, so the center of gravity stays inside it longer
- Raises the tractor higher
- Reduces the tractor's weight
- Moves the center of gravity upward
Correct answer: Widens the base of support, so the center of gravity stays inside it longer
A wide wheelbase widens the base of support, keeping the center of gravity inside it through steeper tilts. The wider the stance, the more the machine can lean before tipping.
- The center of gravity of a uniform, straight ruler is located:
- At one end
- At its midpoint
- Just outside the ruler
- At the heaviest marking
Correct answer: At its midpoint
The center of gravity of a uniform ruler is at its midpoint. Because the mass is evenly spread, the balance point falls exactly halfway along its length.
- A door handle is mounted far from the hinges rather than close to them. Why does this placement make the door easier to open?
- It shortens the effort arm so less distance is traveled
- It lengthens the effort arm so the same force produces more turning effect
- It moves the fulcrum to the edge of the door
- It reduces the weight of the door
Correct answer: It lengthens the effort arm so the same force produces more turning effect
Lengthening the effort arm is the reason. The hinges act as the fulcrum, and placing the handle far from them creates a long effort arm. A longer effort arm multiplies the turning effect (torque) of your push, so the same force opens the door more easily.
- A worker lifts a 90-pound load using a movable pulley supported by two rope strands and pulls the rope a total of 8 feet. Ignoring friction, how far does the load rise?
- 2 feet
- 4 feet
- 8 feet
- 16 feet
Correct answer: 4 feet
The load rises 4 feet. A movable pulley with two supporting strands has a mechanical advantage of two, so the rope must be pulled twice as far as the load moves. Pulling 8 feet of rope raises the load 8 divided by 2, which equals 4 feet.
- In a third-class lever, where is the effort applied relative to the fulcrum and the load?
- Between the fulcrum and the load
- At the fulcrum itself
- On the opposite side of the fulcrum from the load
- At the same point as the load
Correct answer: Between the fulcrum and the load
The effort is applied between the fulcrum and the load. In a third-class lever the fulcrum is at one end, the load is at the other end, and the effort is applied somewhere in the middle. A human forearm lifting a weight is a common example.
- A balance beam holds a 60-pound box 5 feet from the pivot on one side. On the other side, a 100-pound box is placed to balance it. How far from the pivot must the 100-pound box sit?
- 2 feet
- 3 feet
- 5 feet
- 8.3 feet
Correct answer: 3 feet
The 100-pound box must sit 3 feet from the pivot. Balance requires weight times distance to be equal on both sides. The left side is 60 times 5, which equals 300. Dividing 300 by 100 pounds gives 3 feet.
- A block-and-tackle system has a mechanical advantage of five but the rope must be pulled 25 feet to raise the load. Ignoring friction, how high does the load rise?
- 5 feet
- 10 feet
- 25 feet
- 125 feet
Correct answer: 5 feet
The load rises 5 feet. With a mechanical advantage of five, the worker trades distance for force and must pull five times as much rope as the load moves. Dividing the 25 feet of rope pulled by the mechanical advantage of 5 gives 5 feet of lift.
- A bottle opener that pries off a cap by lifting one edge while the opposite tip rests on the cap is an example of which class of lever?
- First-class lever
- Second-class lever
- Third-class lever
- It is not a lever at all
Correct answer: Second-class lever
A bottle opener is a second-class lever. The tip resting on the cap acts as the fulcrum, the cap edge being lifted is the load located in the middle, and the effort comes from your hand at the far end. The load sits between the fulcrum and the effort, which defines a second-class lever.
- Two single fixed pulleys are connected in a line so a rope passes over both before reaching the load. What mechanical advantage does this arrangement provide?
- A mechanical advantage of one
- A mechanical advantage of two
- A mechanical advantage of four
- A mechanical advantage of one-half
Correct answer: A mechanical advantage of one
The arrangement gives a mechanical advantage of one. Fixed pulleys only change the direction of the force, not its size, no matter how many are used. Because no strand of rope directly supports the movable load, the worker still must pull with force equal to the full load.
- A lever has a load arm of 6 inches and an effort arm of 24 inches. What is its mechanical advantage?
Correct answer: 4
The mechanical advantage is 4. For a lever, mechanical advantage equals the effort arm divided by the load arm. Dividing 24 inches by 6 inches gives 4, meaning the lever multiplies the input force four times.
- A worker needs to lift a heavy beam but can only pull downward. Which single simple machine lets the worker lift the beam by pulling down without giving any force multiplication?
- A movable pulley
- A single fixed pulley
- A block-and-tackle with four strands
- A second-class lever
Correct answer: A single fixed pulley
A single fixed pulley is the answer. It redirects the rope so a downward pull lifts the load upward, which is convenient, but it provides a mechanical advantage of only one. The worker still applies force equal to the load while gaining a more comfortable pulling direction.
- A 40-pound child sits 6 feet from the center of a seesaw. An adult weighing 120 pounds wants to balance the seesaw. How far from the center should the adult sit?
Correct answer: 2 feet
The adult should sit 2 feet from the center. Balance requires equal weight-times-distance on both sides. The child's side is 40 times 6, which equals 240. Dividing 240 by the adult's 120 pounds gives 2 feet.
- A compound pulley system has a mechanical advantage of three. To lift a 270-pound load, how much force must the worker apply, ignoring friction?
- 30 pounds
- 90 pounds
- 135 pounds
- 270 pounds
Correct answer: 90 pounds
The worker applies 90 pounds. The required force equals the load divided by the mechanical advantage. Dividing the 270-pound load by a mechanical advantage of 3 gives 90 pounds of pulling force.
- Scissors cut paper using two blades pivoted at a central screw. Which class of lever describes each blade of the scissors?
- First-class lever
- Second-class lever
- Third-class lever
- Not a lever, but a wedge only
Correct answer: First-class lever
Each scissor blade is a first-class lever. The central screw is the fulcrum, the hand squeezing the handle is the effort on one side, and the paper being cut is the load on the other side. A fulcrum positioned between the effort and the load defines a first-class lever.
- Why does increasing the number of rope strands that support the movable block in a block-and-tackle reduce the effort needed to lift a load?
- The strands make the rope heavier, helping pull the load down
- The load's weight is shared among more strands, so each carries less
- More strands shorten the distance the rope must be pulled
- Extra strands eliminate friction in the system
Correct answer: The load's weight is shared among more strands, so each carries less
Sharing the weight among more strands is the reason. Each rope strand supporting the movable block carries an equal portion of the load, so adding strands divides the load over more lines. The worker only needs to match the tension in one strand, which falls as strands increase.
- A pry bar lifts a 500-pound stone using only 100 pounds of effort. Ignoring friction, how many times longer is the effort arm than the load arm?
- 2 times longer
- 5 times longer
- 10 times longer
- Half as long
Correct answer: 5 times longer
The effort arm is 5 times longer. Mechanical advantage equals the load divided by the effort, which is 500 divided by 100, giving 5. For a lever, that mechanical advantage equals the ratio of the effort arm to the load arm, so the effort arm is 5 times the load arm.
- A worker uses a block-and-tackle to lift a 320-pound motor with only 80 pounds of effort. Ignoring friction, how many rope strands support the movable block?
- 2 strands
- 3 strands
- 4 strands
- 8 strands
Correct answer: 4 strands
Four strands support the movable block. The mechanical advantage equals the load divided by the effort, which is 320 divided by 80, giving 4. In a block-and-tackle the mechanical advantage equals the number of supporting strands, so 4 strands are needed.
- A ramp rises 5 feet over a sloped length of 25 feet. Ignoring friction, what is the ideal mechanical advantage of the ramp?
Correct answer: 5
The answer is 5. The ideal mechanical advantage of an inclined plane equals the sloped length divided by the vertical rise, so 25 feet divided by 5 feet gives a mechanical advantage of 5.
- A pyramid-shaped pile of sand is far more stable than a tall narrow column of the same sand mainly because the pyramid:
- Has a wide base directly under most of its weight
- Weighs much less than the column
- Is made of lighter grains of sand
- Stores energy in its peak
Correct answer: Has a wide base directly under most of its weight
The answer is that the pyramid has a wide base directly under most of its weight. A broad base keeps the center of gravity low and well inside the footprint, so the structure resists tipping far better than a tall, narrow column.
- A retaining wall that holds back a hillside is built thicker at the bottom than at the top primarily because the bottom:
- Is colder than the top
- Needs to look heavier than the top
- Receives the most rainfall
- Must resist the greatest sideways soil pressure
Correct answer: Must resist the greatest sideways soil pressure
The answer is that the bottom must resist the greatest sideways soil pressure. Soil pressure increases with depth, so the base of a retaining wall is made thicker to withstand the larger horizontal push near the ground.
- A road is cut into a steep hillside as a series of long, gently angled stretches rather than one straight steep climb. The main mechanical benefit of the gentler slope is that vehicles:
- Travel a shorter total distance
- Need less force to climb at any moment
- Use no fuel going up
- Avoid changing elevation
Correct answer: Need less force to climb at any moment
The answer is that vehicles need less force to climb at any moment. A gentler slope is a longer inclined plane, which trades extra distance for a smaller required pushing force at each point along the climb.
- Two triangular braces are added to a rectangular wooden gate to keep it from sagging. The braces work because a triangle, unlike a rectangle, cannot:
- Support any weight
- Be made of wood
- Be fastened at the corners
- Change shape without bending or breaking its sides
Correct answer: Change shape without bending or breaking its sides
The answer is that a triangle cannot change shape without bending or breaking its sides. A triangle is rigid by geometry, so a diagonal brace turns a flexible rectangle into stiff triangles that resist racking and sagging.
- A heavy statue stands on a flat base. Which change would make it tip over most easily?
- Making the base wider
- Lowering the statue's center of gravity
- Raising most of the statue's weight high and narrow at the top
- Adding weight evenly across the bottom
Correct answer: Raising most of the statue's weight high and narrow at the top
The answer is raising most of the statue's weight high and narrow at the top. A high center of gravity over a narrow base tips past the edge of support with only a small lean, making the statue far easier to topple.
- A long shelf bracket has one screw near the wall and a diagonal support strut running down to the wall below it. The diagonal strut mainly helps the shelf by:
- Making the shelf lighter
- Letting the shelf store the load's energy
- Pushing back against the downward load at the shelf's outer edge
- Removing the need for any screws
Correct answer: Pushing back against the downward load at the shelf's outer edge
The answer is pushing back against the downward load at the shelf's outer edge. The diagonal strut forms a triangle with the wall and shelf, transferring the load down to the wall and resisting the bending that would otherwise tear out the top screw.
- A ramp gives an ideal mechanical advantage of 4. To raise a 400-pound load using this ramp, about how much force is needed to push it up, ignoring friction?
- 100 pounds
- 200 pounds
- 400 pounds
- 1,600 pounds
Correct answer: 100 pounds
The answer is 100 pounds. With an ideal mechanical advantage of 4, the input force equals the load divided by 4, so 400 pounds divided by 4 requires only about 100 pounds of pushing force.
- A flat-roofed building in a snowy region is more likely to collapse than a steeply pitched roof of the same materials mainly because the flat roof:
- Is closer to the ground
- Lets snow build up and add heavy weight instead of sliding off
- Is made of weaker wood
- Faces more wind
Correct answer: Lets snow build up and add heavy weight instead of sliding off
The answer is that the flat roof lets snow build up and add heavy weight instead of sliding off. A steep slope sheds snow before it accumulates, while a flat roof collects a growing load that can exceed the structure's strength.
- A scaffold tower is made more stable against tipping by attaching wide outrigger legs that stick out from the base. These outriggers help mainly by:
- Raising the tower's center of gravity
- Reducing the tower's total weight
- Making the tower taller
- Widening the area of support beneath the tower
Correct answer: Widening the area of support beneath the tower
The answer is widening the area of support beneath the tower. Outriggers spread the base outward so the center of gravity stays well inside the footprint, requiring a much larger lean before the tower can tip.
- A doorstop is a thin wedge slid under a door. As the door pushes against the gentle slope of the wedge, the wedge mainly converts the door's:
- Small downward force into a large sideways gripping force
- Weight into heat that melts the floor
- Motion into electricity
- Color into sound
Correct answer: Small downward force into a large sideways gripping force
The answer is small downward force into a large sideways gripping force. A wedge is a moving inclined plane; its shallow slope multiplies the modest force on it into a strong wedging action that jams the door in place.
- An A-frame ladder stands open on the floor with its two legs spread apart and a brace between them. Spreading the legs wider mainly:
- Makes the ladder heavier
- Raises the top of the ladder higher
- Increases stability by widening the base
- Removes the need for the brace
Correct answer: Increases stability by widening the base
The answer is increasing stability by widening the base. Spreading the legs enlarges the support area at the floor, lowering the effective center of gravity relative to the footprint so the ladder resists tipping sideways.
- A suspension footbridge hangs from cables draped between two tall towers. The main cables mainly carry the bridge's load by:
- Being squeezed (in compression)
- Twisting back and forth
- Being stretched (in tension)
- Floating on air
Correct answer: Being stretched (in tension)
The answer is being stretched, or in tension. A hanging cable supports load by pulling, so the deck's weight stretches the main cables, which transfer that tension to the towers and anchorages.
- A heavy crate must be moved up to a dock 3 feet high. Compared with using a ramp 9 feet long, using a ramp 18 feet long to reach the same dock will require:
- More pushing force but a shorter distance
- The same force and the same distance
- No force at all
- Less pushing force but a longer distance to travel
Correct answer: Less pushing force but a longer distance to travel
The answer is less pushing force but a longer distance to travel. Doubling the ramp length to the same height doubles the mechanical advantage, halving the needed force while the crate must be pushed twice as far.
- A tall freestanding sign is anchored with concrete footings spread out at its base. Spreading the footings over a larger area mainly helps by:
- Spreading the load so the soil is less likely to sink
- Making the sign lighter
- Raising the sign higher
- Letting the sign sway more in wind
Correct answer: Spreading the load so the soil is less likely to sink
The answer is spreading the load so the soil is less likely to sink. A wider footing distributes the sign's weight over more ground, lowering the pressure on the soil and reducing settling or tipping.
- A pressure relief valve on a water heater is designed to:
- Keep the tank permanently sealed under all conditions
- Increase the water temperature when pressure rises
- Open and release fluid when internal pressure exceeds a safe limit
- Measure how much hot water remains in the tank
Correct answer: Open and release fluid when internal pressure exceeds a safe limit
The pressure relief valve opens to release fluid when pressure exceeds a safe limit. It is a safety device that prevents the tank from rupturing by venting excess pressure once a set threshold is reached.
- A nut is held tightly against a bolt by a second nut threaded behind it. This second nut is known as a:
- Wing nut
- Coupling nut
- Cap nut
- Lock nut (jam nut)
Correct answer: Lock nut (jam nut)
The second nut is a lock nut, also called a jam nut. It is tightened against the first nut so the two jam together, creating friction that resists the bolt vibrating loose.
- A funnel-shaped venturi narrows in the middle. As fluid flows through the narrow section, its speed:
- Decreases while its pressure increases
- Increases while its pressure decreases
- Stays the same as in the wide section
- Drops to zero at the throat
Correct answer: Increases while its pressure decreases
In a venturi the fluid speeds up while its pressure decreases. Because the same volume must pass through a smaller area, the fluid accelerates, and by Bernoulli's principle faster flow means lower pressure.
- A grease fitting (zerk fitting) on a machine bearing is used to:
- Drain old oil out of the engine
- Force lubricant into the bearing under pressure
- Vent built-up steam from the housing
- Bolt two shafts together
Correct answer: Force lubricant into the bearing under pressure
A grease fitting forces lubricant into the bearing under pressure. A grease gun presses against the fitting's check ball, pushing grease past it into the bearing while preventing it from leaking back out.
- Two wires of the same metal carry the same current. The wire with the smaller diameter will:
- Have less resistance and stay cooler
- Carry no current at all
- Have exactly the same resistance as the thick wire
- Have more resistance and get hotter
Correct answer: Have more resistance and get hotter
The thinner wire has more resistance and gets hotter. A smaller cross-sectional area restricts current flow, raising resistance, and the higher resistance converts more electrical energy into heat.
- A shock absorber on a vehicle works mainly by:
- Storing energy and bouncing the car higher
- Generating electricity from road bumps
- Locking the wheel rigidly to the frame
- Forcing fluid through small orifices to dampen motion
Correct answer: Forcing fluid through small orifices to dampen motion
A shock absorber forces fluid through small orifices to dampen motion. The restricted flow resists rapid movement, converting the energy of bumps into heat so the spring stops oscillating quickly.
- A counterweight is added to a crane or elevator system mainly to:
- Make the structure heavier so it tips over more easily
- Balance the load so less force is needed to lift it
- Increase friction in the cable so it slips
- Speed up the motor without using power
Correct answer: Balance the load so less force is needed to lift it
A counterweight balances the load so less force is needed to lift it. By offsetting much of the load's weight, the motor or operator only has to move the difference, reducing the required effort.
- When a metal lid is stuck on a glass jar, running it under hot water helps because the metal:
- Expands more than the glass, loosening the lid
- Contracts faster than the glass, tightening the seal
- Becomes magnetic and releases its grip
- Dissolves slightly in the hot water
Correct answer: Expands more than the glass, loosening the lid
The metal lid expands more than the glass, loosening it. Metal has a higher coefficient of thermal expansion, so heating makes the lid grow more than the jar and the grip releases.
- A drill bit is more likely to break when drilling metal if the operator:
- Uses cutting oil and steady downward force
- Runs the drill at the correct speed for the material
- Applies too much side pressure and lets the bit overheat
- Clamps the workpiece firmly before drilling
Correct answer: Applies too much side pressure and lets the bit overheat
Applying too much side pressure while letting the bit overheat is most likely to break it. Sideways loading bends the bit and excess heat without lubrication weakens it, leading to snapping.
- A heat sink is attached to an electronic component primarily to:
- Increase surface area so heat dissipates faster
- Trap heat inside the component
- Add electrical insulation to the circuit
- Reduce the weight of the device
Correct answer: Increase surface area so heat dissipates faster
A heat sink increases surface area so heat dissipates faster. Its many fins expose more metal to the air, speeding the transfer of heat away from the component to keep it cool.
- A one-way clutch (freewheel) on a bicycle hub allows the wheel to:
- Spin only when the brakes are applied
- Coast forward while the pedals stay still
- Move backward but never forward
- Lock completely in both directions
Correct answer: Coast forward while the pedals stay still
A freewheel lets the wheel coast forward while the pedals stay still. The clutch engages only when pedaling drives the wheel; when you stop, it disengages so the wheel keeps spinning freely.
- A safety factor in mechanical design means a part is built to:
- Carry exactly the maximum expected load and no more
- Fail at half the expected load
- Withstand more load than it is expected to carry
- Use the cheapest possible material
Correct answer: Withstand more load than it is expected to carry
A safety factor means the part is built to withstand more load than it is expected to carry. The extra margin accounts for unexpected stresses, material flaws, and wear so the part does not fail in normal use.
- A rubber gasket placed between two bolted metal flanges serves to:
- Seal the joint and prevent leaks
- Increase the temperature of the fluid
- Conduct electricity between the flanges
- Make the bolts easier to remove later
Correct answer: Seal the joint and prevent leaks
A gasket seals the joint and prevents leaks. The soft rubber compresses to fill tiny gaps between the flange faces, blocking fluid or gas from escaping the connection.
- An anti-siphon (vacuum breaker) device on a faucet prevents:
- Contaminated water from being drawn back into the supply
- Water from flowing forward through the tap
- The faucet from ever shutting off
- Air from entering an empty tank
Correct answer: Contaminated water from being drawn back into the supply
An anti-siphon device prevents contaminated water from being drawn back into the supply. If supply pressure drops, the vacuum breaker admits air to stop backflow, protecting the clean water line.
- A torque wrench is used instead of an ordinary wrench when a bolt must be:
- Removed as quickly as possible
- Cut to a shorter length
- Tightened to a specific, measured amount of force
- Heated before installation
Correct answer: Tightened to a specific, measured amount of force
A torque wrench is used to tighten a bolt to a specific, measured amount of force. It indicates or limits the applied torque so fasteners are neither too loose nor over-tightened to the point of damage.
