## By Pavel Panchekha & Jeffrey Prouty

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Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

# Delve AP Physics C Quiz 2

The exact copies of the test used in class are available for reference: Multiple Choice and Free Response. But note that the below copy has a few errors fixed and also looks nicer.

## Multiple Choice

1. Between $$0.5kg$$ brick at the top of a $$10m$$ tall house, and a $$2kg$$ cinderblock $$2m$$ off the ground, which has higher potential energy relative to the ground? Relative to the center of the earth?
1. The brick has more relative to the ground but not the center of the earth
2. The cinderblock has more relative to the ground but not the center of the earth
3. The brick has more relative to both the ground and the center of the earth
4. The cinderblock has more relative to both the ground and the center of the earth
5. In both cases, both have the potential energy
2. A $$2kg$$ block falls from a height of $$10m$$; approximately what kinetic energy does it have?
1. $$100 J$$
2. $$200 J$$
3. $$300 J$$
4. $$400 J$$
5. $$500 J$$
3. Box A is on an inclined plane of angle $$θ$$, along with another box twice as tall (Box B) and a box twice as wide (Box C), and all are standing upright. Slowly, the angle is increased. Assuming the friction is sufficient so that the boxes do not slide, in what order do the boxes fall over?
1. A, then B, then C
2. A, then C, then B
3. B, then A, then C
4. B, then C, then A
5. C, then A, then B
4. A force parallel to an inclined plane pulls on a block on this plane. Assume the block is moving. The change in kinetic energy is equal to…
1. The change in potential energy
2. The negative of the change in potential energy
3. The work done by the force
4. The work done by gravity
5. The work done by gravity plus the work done by the force.
5. A block of width $$1m$$ and height $$Xm$$ is on an inclined plane at angle of $$30$$ degrees to horizontal. How tall can the block be before it falls over?
1. $$\frac1{\sqrt{2}} m$$
2. $$1m$$
3. $$\sqrt{2} m$$
4. $$\sqrt{3} m$$
5. $$2m$$
6. Two blocks, each of mass $$1kg$$ and traveling at $$10 \frac{m}{s}$$, collide completely inelastically. How much energy is liberated as heat?
1. $$25 J$$
2. $$50 J$$
3. $$100 J$$
4. $$200 J$$
5. $$250 J$$
7. Perry the Platypus falls from outer space toward the earth, and air friction slows him down. What form is Perry’s kinetic and potential energy mostly being transformed into?
1. Kinetic
2. Potential
3. Heat
4. Light
5. Sound
8. The wind blows anti-parallel to the motion of a sailboat, and the sailboat slows down. What happens to the total energy of the wind? To its kinetic energy of motion?
1. Both energies are unchanged
2. Its kinetic energy of motion increases and total energy decreases
3. Its kinetic energy of motion increases and so does its total energy
4. Its kinetic energy of motion decreases and total energy increases
5. Its kinetic energy of motion decreases, as does it total energy
9. Two springs, one of spring constant $$2 \frac{N}{m}$$ and one of spring constant $$5 \frac{N}{m}$$, are each attached to a wall and $$1kg$$ block. The first is extended (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) (from equilibrium position) $$5m$$, the second $$3m$$; and then both blocks are released. Which block will move faster when the spring reaches its equilibrium length? Which block will oscillate with a larger period?
1. The two blocks will oscillate with the same period, but the first will move faster at the equilibrium position
2. The first block will move faster and oscillate with the larger period
3. The first block will move slower but oscillate with larger period
4. The first block will move faster but oscillate with lesser period
5. The two block will move with the same speed but the first block will oscillate with a larger period
10. What are the units of energy?
1. $$kg / s^2$$
2. $$kg m / s^2$$
3. $$kg m^2 / s^2$$
4. $$kg m / s$$
5. $$kg / s$$
11. Approximately how much energy does a $$1 ft^3$$ box of weight $$3 lbs$$, situated $$312 in$$ above the ground, have?
1. $$55 J$$
2. $$70 J$$
3. $$85 J$$
4. $$100 J$$
5. $$115 J$$
12. Would you have preferred that problem be in metric units?
1. Yes
13. You have a meterstick, a spring of known spring constant, a block of known mass, a pencil, and perfect reaction time. You also have a nyan cat. Which of the following could you not measure?
1. The mass of the nyan cat
2. The volume of the meterstick
3. The period of oscillation of the block, were it attached to the spring
4. The equilibrium length of the spring
5. The speed of sound
14. A pendulum swings with period $$10s$$, and achieves a maximum angle from vertical of $$10$$ degrees. What is the approximate speed of the pendulum bob at the bottom of its path?
1. $$0.1 m/s$$
2. $$0.3 m/s$$
3. $$1 m/s$$
4. $$3 m/s$$
5. $$10 m/s$$
15. Power is defined as work done over the time to do it. A freight elevator raises boxes at speed $$1 \frac{m}{s}$$ and has maximum capacity $$1 Mg$$. What is the maximum power it produces? (The Watt, labeled W, is a Joule per second)
1. $$100 W$$
2. $$1000 W$$
3. $$10,000 W$$
4. $$100,000 W$$
5. $$1,000,000 W$$
16. A block moves up an incline at a constant speed, and friction does $$+5J$$ of work to the block. If the block were instead moving down the slope (with the same constant speed), how much work does friction do to the block?
1. $$+ 5 J$$
2. $$0 J$$
3. $$-5 J$$
4. It depends on the angle of incline
5. It depends on the absolute speed of the block
17. A block of mass $$2kg$$ spins in a circle around a central axis, attached to it by a spring of spring constant $$3 \frac{N}{m}$$ and equilibrium length $$2m$$. How much work does the spring do to the block?
1. $$+12 J$$
2. $$+6 J$$
3. $$0 J$$
4. $$-6 J$$
5. $$-12 J$$
18. A bullet hits a block suspended from the ceiling by a spring and embeds itself into it. The block and string system thus becomes a pendulum. How does this process change the kinetic energy of the system and of the block?
1. The kinetic energy of the system does not change; that of the block increases
2. The kinetic energy of the system increases, that of the block increases
3. The kinetic energy of the system decreases, that of the block does not change
4. The kinetic energy of the system does not change, and neither does that of the block
5. None of the above
19. You have a standard, symmetric, four-legged table, standing on an inclined plane, oriented as the figure on the below. Let’s say the front of the table is the edge facing downhill. Removing which set of legs would cause the table to fall over, no matter the angle (greater than zero) of the inclined plane? Assume the legs are infinitely thin.

i) The two back legs

ii) One front leg;

iii) One front and one back leg, diagonally opposite each other.

1. (i) only
2. (i) and (iii)
3. (iii) only
4. (ii) and (iii)
5. (i), (ii), and (iii)
20. Consider a wheel, of mass $$10kg$$, $$10$$ seconds into rolling down an inclined plane. Would its speed be lesser or greater if we added more spokes? If we made the rim thicker (inwards; the radius of the wheel does not increase)? Assume that in either case, the wheel is made correspondingly less dense to keep its mass exactly $$10kg$$.
1. The speed would increase if we did either
2. The speed would decrease if we did either
3. The speed would increase if we added spokes, but decrease if we thickened the rim
4. The speed would decrease if we added spokes, but increase if we thickened the rim
5. The speed would be unchanged in either case
21. Dr. Doofenshmirtz, located in Ohio, has coated the eastern seaboard with tin foil and is planning to use a giant magnet to pull the eastern seaboard towards him, thus reversing the rotation of the earth. Why won’t his plan work?
1. Conservation of momentum
2. Conservation of angular momentum
3. Conservation of energy
4. First law of thermodynamics
5. Newton’s law of Universal Gravitation
22. A box is sliding back and forth within a bowl spherical.  Every time it moves from one side of the bowl to the other, it loses $$2J$$ of energy due to friction. If the radius of the bowl is $$10m$$ and the mass of the box is $$2kg$$, how many times oscillations will the box do before coming to rest?
1. 10
2. 25
3. 50
4. 100
5. 200
23. Which of the following is a correct equation for the kinetic energy due to angular acceleration of an object?
1. $$I ω^2$$
2. $$\frac{L^2}{2 I}$$
3. $$ω \frac{L}{2I^2}$$
4. $$(\frac{d}{dt}) L ω^2$$
5. $$2 π / ω$$
24. As an object falls, what happens to its potential and kinetic energy?
1. The potential energy decreases linearly with time, the kinetic energy decreases quadratically with time
2. The potential energy increases quadratically, the kinetic energy decreases linearly
3. The potential energy and kinetic energy do not change
4. Potential energy decreases linearly with time, the kinetic energy increases linearly
5. The potential energy decreases quadratically with time, the kinetic energy increases quadratically with time
25. Two cannon balls of different mass but same shape, and made of the same material (one is hollow inside) are dropped from the top of the Leaning Tower of Pisa. When they hit the ground, which has more kinetic energy per unit of mass?
1. The heavier one is has less kinetic energy per unit of mass
2. The lighter one is has less kinetic energy per unit of mass
3. It depends on the masses of the two objects
4. Their relative energy per unit of mass depends on the absolute mass of the two objects
5. The two objects have the same energy per unit of mass
26. In Roller Coaster: The Musical, Phineas and Ferb construct a roller coaster that’s “like a leisurely ride around downtown, but it starts with a three-mile drop straight down”. Three miles is approximately $$5km$$. How much energy does their one-half-ton roller coaster cart have at the bottom of this drop?
1. $$2.5 kJ$$
2. $$25 kJ$$
3. $$250 kJ$$
4. $$2.5 MJ$$
5. $$25 MJ$$
27. A ball is rolls down from the top of an inclined plane. What is the angular velocity of rotation of the ball, halfway down the inclined plane, in terms of its angular velocity ω at the bottom of the inclined plane?
1. $$\frac14 ω$$
2. $$\frac1{2\sqrt2} ω$$
3. $$\frac12 ω$$
4. $$\frac1{\sqrt2} ω$$
5. $$ω$$