OAR mechanical comprehension: three choices per item

When a car brakes suddenly, a passenger without a seat belt slides forward toward the dashboard. What best explains this?

1. The body keeps moving as the car slows
   By inertia the unbelted body keeps moving at its old speed as the brakes slow the car around it.
2. The braking force pushes the body forward
   Braking acts backward on the car through the tires; nothing pushes the passenger forward.
3. The seat pushes the body toward the dashboard
   The seat can only push back on the body or slow it through friction; it does not push it forward.

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A sailor in a small rowboat at rest on calm water throws a heavy sandbag off the back of the boat. What does the boat do?

1. It stays still, since the sailor is inside it
   Being inside the boat does not matter; the sailor pushes against the bag and the boat recoils.
2. It moves backward with the bag
   The push on the bag is matched by an opposite push on the boat, so the boat goes the other way, not backward with the bag.
3. It moves forward, away from the bag
   The bag gets backward momentum, so the boat and sailor get equal forward momentum and move away from the bag.

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Cart A rolls from rest down a frictionless track that drops 20 feet. Cart B rolls down a similar track that drops 5 feet. How does A's speed at the bottom compare with B's?

1. Exactly the same
   Exactly the same speed would mean drop height does not matter, but more height gives more speed.
2. Twice as great
   Energy gives v = √(2gh); four times the height gives √4 = 2 times the speed.
3. Four times as great
   Four times is the height ratio; speed grows with the square root of height.

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A sealed, rigid tank of air at 27°C (300 K) is heated to 327°C (600 K). What happens to the pressure inside?

1. It rises about 12 times
   12 times divides the Celsius values (327 ÷ 27); gas laws need kelvins.
2. It becomes twice as high
   At constant volume pressure is proportional to absolute temperature: 600 K ÷ 300 K = 2, so it becomes twice as high.
3. It stays the same
   A fixed volume is exactly why the pressure must rise as the gas heats; it cannot stay the same.

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A merry-go-round turns at a steady rate. Compared with a rider near the center, what does a rider at the outer edge have?

1. The same rotation rate but more speed
   Every rider goes around once per turn, but the outer rider travels a larger circle, so moves faster.
2. A higher rotation rate and more speed
   The whole merry-go-round turns as one body, so the rotation rate is the same everywhere.
3. The same speed but a lower rotation rate
   This mixes up the two: the rate is shared and the speed differs.

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An egg dropped onto a pillow survives, but the same egg dropped from the same height onto concrete breaks. What best explains the difference?

1. The pillow makes the momentum change smaller
   The egg stops either way, so the change in momentum is the same.
2. The egg falls more slowly onto the pillow
   The fall is the same height, so the speed on arrival is the same.
3. The pillow stretches out the stopping time
   The momentum change is the same, but spreading it over a longer time makes the force on the egg smaller.

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At the same instant and from the same height, one bullet is fired horizontally from a rifle and another is simply dropped. Ignoring air resistance, which reaches the level ground first?

1. The dropped bullet
   The fired bullet goes farther but falls at the same rate.
2. The fired bullet
   Its speed is horizontal and does nothing to speed up its fall, so the fired bullet does not land first.
3. Both land at the same time
   Vertical motion is independent of horizontal speed, so both fall the same height in the same time.

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A solid block of wood floats with part of it above the water. It is sawed into two equal halves. How does each half float?

1. Lower, since each half has less volume
   Less volume comes with less weight in the same proportion.
2. The same, since the density is unchanged
   The submerged fraction equals the wood's density relative to water, and sawing does not change the density.
3. Higher, since each half is lighter
   Each half is lighter but also displaces half as much water, so the fraction is unchanged.

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A rolling railroad car couples to an identical car at rest, and the two roll on together. Ignoring friction, how does their speed compare with the first car's original speed?

1. Half as fast
   Momentum is conserved: m·v = 2m·v′, so v′ = v/2.
2. About 0.7 times as fast
   0.7 (1/√2) comes from conserving kinetic energy, which is not conserved when the cars couple.
3. Just as fast as before
   Just as fast is impossible: the same momentum now moves twice the mass, so the speed must drop.

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With a long bar, a worker lifts a 300-pound stone by pushing down with only 100 pounds. Ignoring friction, what must be true?

1. The stone rises 3 times as far as the hands move
   This gets the trade backward; a force gain always costs distance.
2. The hands move 3 times as far as the stone
   Work in equals work out: 100 lb × 3d = 300 lb × d, so the hands travel three times as far.
3. The worker does one-third of the work
   Ignoring friction, the worker does all the work; the lever only changes force and distance.

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A heavy shelf sticks out from a wall and is held up by a diagonal brace underneath, running from the wall up to the shelf's outer edge. What kind of force does the brace carry?

1. Tension (it is pulled)
   A tension member would hang from above, like a cable from the wall to the shelf edge.
2. No force; the wall carries it all
   Without the brace the shelf would bend down; the brace takes much of the load.
3. Compression (it is pushed)
   The load pushes the shelf's outer edge down, which pushes the brace end-on toward the wall.

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A bicycle chain connects the front sprocket to a smaller rear sprocket. When the pedals turn the front sprocket clockwise, which way does the rear sprocket turn?

1. Clockwise, the same way as the front
   A chain loop makes both sprockets turn the same way as each other, clockwise here, whatever their sizes.
2. It depends on sprocket size
   Sprocket size changes speed, not direction.
3. Counterclockwise, opposite to the front
   Reversal happens when gears mesh directly; a chain links the sprockets on the same side, so the rear does not turn opposite to the front.

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An ice cube floats in a glass of water filled exactly to the brim. What happens when the ice melts completely?

1. The level stays the same
   Floating ice displaces exactly its own weight of water, which is what it becomes when it melts.
2. Some water spills over the rim
   The ice already displaced the water its meltwater fills, so nothing spills.
3. The level drops slightly below the rim
   The meltwater fills exactly the space the ice displaced, so the level does not fall.

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When cutting thick cardboard with scissors, where along the blades should the cardboard be placed to cut it most easily?

1. Near the tips of the blades
   At the tips the load arm is longest, so the cutting force is smallest.
2. It makes no difference
   The force on the cardboard depends on its distance from the pivot.
3. As close to the pivot as possible
   Scissors are levers; the closer the cardboard is to the pivot, the shorter the load arm and the greater the cutting force.

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Why is it easier to move a heavy crate on rollers than to drag it across the floor?

1. Rollers reduce the weight of the crate
   The crate weighs the same; only the type of friction changes.
2. Rollers swap sliding for rolling friction
   Rollers replace sliding contact with rolling contact, and rolling friction is far smaller.
3. Rollers spread the load over a larger area
   Rollers touch the floor along thin lines, and friction hardly depends on contact area anyway.

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