## By Pavel Panchekha & Jeffrey Prouty

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# Delve AP Physics C Quiz 3

The exact copy of the test used in class is available for reference; however, the original had multiple errors that resulted in questions 4, 5, 7, 11, and 26 having no valid listed answers. Below, these questions are corrected so that they have a valid answer.

## Multiple Choice

1. A car has a constant acceleration of $$+10 m/s^2$$. It has zero initial velocity with respect to the road. You are moving along with a constant velocity of $$-5 m/s$$ with respect to the road. How far does the car travel in 3 seconds in the reference frame of the road?
1. $$30 m$$
2. $$45 m$$
3. $$55 m$$
4. $$60 m$$
5. $$65 m$$
2. How far does the same car travel in 3 seconds in your reference frame?
1. $$30 m$$
2. $$45 m$$
3. $$55 m$$
4. $$60 m$$
5. $$65 m$$
3. Which of the following is not a vector quantity?
1. Force
2. Velocity
3. Acceleration
4. Energy
5. Momentum
4. A projectile is launched from the ground at an angle of 45 degrees from the horizontal with an initial velocity $$6 m/s$$. What is the maximum height in meters achieved by the projectile?
1. $$0.81 m$$
2. $$0.92 m$$
3. $$1.17 m$$
4. $$1.33 m$$
5. $$1.59 m$$
5. How far from the launch point of the projectile does it hit the ground, in meters?
1. $$2.95 m$$
2. $$3.67 m$$
3. $$4.37 m$$
4. $$4.87 m$$
5. $$5.32 m$$
6. A particle's position is given by the equation $$x(t)=t^3 + 3t^2 + 2t + 4$$. What is the particle's velocity at $$t = 5 s$$?
1. $$214 m/s$$
2. $42 m/s$
3. $$107 m/s$$
4. $92 m/s$
5. $36 m/s$
7. Suppose this particle (from #6) has a mass of 0.2 kg. Which of the following equations gives the net force on the particle as a function of time?
1. $$1.2t + 1.2$$
2. $$30t + 30$$
3. $$3t^2 + 6t + 2$$
4. $$15t^2 + 30t + 10$$
5. $$0.6t^2 + 1.2t + 0.4$$
8. Two blocks, one of mass $$m$$ and one of mass $$M$$, are attached together by a thin rope on a frictionless surface. The block of mass $$m$$ is pulled away from the other block by a force $$F$$. What is the tension in the rope attaching the blocks?
1. $$F \frac{m}{M + m}$$
2. $$F \frac{M + m}{M}$$
3. $$F \frac{M + m}{m}$$
4. $$F \frac{M}{M + m}$$
5. $$F$$
9. A particle moves in a circle with constant speed. Which of the following must be true?
1. The net force on the particle is zero
2. The only force acting on the particle is a centripetal force
3. The particle's momentum is constant
4. There is a net force on the particle radially inward
5. The particle's acceleration is zero
10. A ball of mass m is dropped from a tall tower on earth and experiences a velocity dependent friction force given by $$F = -bv$$, where b is a constant. What is the terminal speed of the ball?
1. $$mg/b$$
2. $$2mg/b$$
3. $$b/mg$$
4. $$2b/mg$$
5. 0
11. An object is constructed by rigidly fixing together two hoops, each of mass $$m$$ and radius $$R$$. The hoops are joined together at a point on their circumferences to make an "8" shape. What is the moment of inertia of this body about the center of one of the hoops? (Recall that the moment of inertia of a single hoop about its center is given by $$MR^2$$.)
1. $$2mR^2$$
2. $$3mR^2$$
3. $$4mR^2$$
4. $$5mR^2$$
5. $$6mR^2$$
12. At some instant in time, the net torque on an object is nonzero. Which of the following must be true?
1. The net force on the object is nonzero
2. The object's angular momentum is changing
3. The object's linear momentum is changing
4. The object is undergoing uniform circular motion
5. None of the above
13. A body is initially moving away from you at a speed of $$5 m/s$$. Suddenly, the body explodes into two pieces of equal mass. One of the pieces returns toward you at a speed of $$5 m/s$$. Which of the following describes the motion of the other body?
1. Toward you at $$5 m/s$$
2. At rest with respect to you
3. Away from you at $$5 m/s$$
4. Away from you at $$10 m/s$$
5. Away from you at $$15 m/s$$
14. In your reference frame, a cart containing sand is traveling forward with some initial speed. A container at rest with respect to you begins dumping more sand into the cart from above. How will the cart's speed as measured by you change with time?
1. The cart's speed will increase
2. The cart's speed will not change
3. The cart's speed will decrease
4. The cart's speed will initially decrease, then increase
5. The cart's speed will initially increase, then decrease
15. Now suppose the container dumping sand into the cart is moving at constant velocity in your reference frame but initially at rest with respect to the cart. How will the cart's speed as measured by you change with time?
1. The cart's speed will increase
2. The cart's speed will not change
3. The cart's speed will decrease
4. The cart's speed will initially decrease, then increase
5. The cart's speed will initially increase, then decrease
16. Kepler's second law states that the line from a star to the planet orbiting it sweeps out equal areas in equal time intervals. This is equivalent to which of the following principles?
1. Conservation of energy
2. Conservation of linear momentum
3. Conservation of angular momentum
4. Conservation of mass
5. None of the above
17. A particle of mass $$m$$ sits at $$x = 1$$, a particle of mass $$2m$$ sits at $$x = 2$$, and a particle of mass $$3m$$ sits at $$x = 3$$. At what value of $$x$$ does the center of mass of this 3-particle system lie?
1. $$2$$
2. $$7/3$$
3. $$8/3$$
4. $$3$$
5. $$2/3$$
18. A solid cylindrical spool of thread of mass m and radius R, initially at rest, is fixed in place by a rod along its center axis. You pull on the thread with a constant tension T. What is the angular speed of the thread at time t after you start pulling?
1. $$\frac{2T t}{m R}$$
2. $$\frac{T t}{m R}$$
3. $$\frac{T}{m R}$$
4. $$\frac{2 m R}{t T}$$
5. $$\frac{m R t}{2 T}$$
19. A set of cubes may be attached end to end to form a rigid rectangular prism. What is the maximum number of cubes that may be stacked vertically such that the stack will not fall over when placed on a 30 degree incline?
1. 0
2. 1
3. 2
4. 3
5. 4
20. How many of these cubes may be stacked vertically such that the stack will not fall over when placed on a 60 degree incline?
1. 0
2. 1
3. 2
4. 3
5. 4
21. The potential energy of an object as a function of its position $$x$$ is given by $$U(x) = 2x^2$$. What is the force on this object as a function of $$x$$?
1. $$-4x$$
2. $$-2x$$
3. $$0$$
4. $$2x$$
5. $$4x$$
22. Suppose this object has mass $$4 kg$$ is released from rest at $$x = 2$$. What will be the period of oscillation of the object about its equilibrium point?
1. $$6.28 s$$
2. $$4.40 s$$
3. $$3.14 s$$
4. $$2.20 s$$
5. $$1.17 s$$
23. Which of the following is not a conservative force?
1. Air friction
2. Gravity
3. Spring force
4. a, b, and c are all conservative
5. a, b, and c are all non-conservative
24. A block of mass m is attached to a spring with spring constant $$k$$. The spring is stretched to a distance $$A$$ from equilibrium and then released. What is the maximum speed achieved by the block?
1. $$A \sqrt{k /m}$$
2. $$A \sqrt{m / k}$$
3. $$0.5A^2 (k / m)$$
4. $$A^2 (k / m)$$
5. None of the above
25. A satellite of mass $$m$$ orbits a planet of mass $$M$$ in uniform circular motion at a radius $$R$$ from the center of the planet. What is the kinetic energy of the satellite?
1. $$−G M m / R$$
2. $G M m / R$
3. $$-G M m / 2 R$$
4. $G M m / 2 R$
5. $$−G M m / R^2$$
26. What is the orbital period of the satellite?
1. $$2\pi \sqrt{G M / R^3}$$
2. $$2\pi \sqrt{R^3 / G M}$$
3. $$\pi \sqrt{R^3 / G M}$$
4. $$2\pi \sqrt{R^3 / G (M + m)}$$
5. $$\pi \sqrt{R^3 / G (M + m)}$$
27. A car of mass $$2m$$ traveling with speed $$v$$ collides completely inelastically with another car of mass $$m$$. How much kinetic energy is lost in this collision?
1. $$\frac16 m v^2$$
2. $$\frac13 m v^2$$
3. $$\frac12 m v^2$$
4. $$\frac23 m v^2$$
5. $$\frac56 m v^2$$
28. Which of the following is not a true statement about perfectly elastic collisions?
1. Momentum is conserved
2. Kinetic energy is conserved
3. They are symmetric with respect to time in the center of mass frame
4. In every reference frame, at least one body in the collision reverses direction
5. All of the above are true statements
29. A wheel of moment of inertia $$I$$ and mass $$m$$ rolls without slipping down a 30 degree incline. If the wheel starts from rest, what is the speed of its center of mass after rolling a distance $$d$$ along the incline?
1. $$\sqrt{g d}$$
2. $$\sqrt{2 g d}$$
3. $$\sqrt{m g d R^2 / I}$$
4. $$\sqrt{m g d R^2 /2I}$$
5. $$\sqrt{m g d / (m + \frac{I}{R^2})}$$
30. A planet has mass $$M$$ and radius $$R$$. What is the minimum speed required for a body of mass $$m$$ on the planet's surface to permanently escape?
1. $$\sqrt{G M / R}$$
2. $$\sqrt{2 G M / R}$$
3. $$\sqrt{G M / 2 R}$$
4. $$\sqrt{G M m / R}$$
5. $$\sqrt{2 G M m / R}$$

## Solutions

###### Warning

If you didn't happen to take the test in class, it is suggested that you do the test yourself. Use the standard timings: 45 minutes for the multiple choice section and 45 minutes for the free response.