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AP Physics C: Mech

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Unit 4

4.5 MC Answers and Review

9 min read•december 30, 2021

AP Physics C: Mechanics ⚙️

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Answers and Review for Multiple Choice Practice on Systems of Particles and Linear Momentum

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⛔STOP⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 4. Click here for the AP Physics C: Mechanics Multiple Choice Questions. Facts about the test: The AP Physics C: Mechanics exam has 35 multiple choice questions and you will be given 45 minutes to complete the section. That means it should take you around 15 minutes to complete 12 questions.

The following questions were not written by College Board and, although they cover information outlined in the AP Physics C: Mechanics Course and Exam Description, the formatting on the exam may be different.

1. A ball of mass m strikes a vertical wall with a velocity vi and rebounds with a speed of vf. What is an expression for the magnitude of the impulse exerted on the ball by the floor?

A. mvf

B. m(vf-vi)

C. m(vi-vf)

D. m(vf + vi)

Answer: Use Impulse-Momentum Theorem to answer this question. The impuse is equal to the change in momentum, or pf - pi. pf = mvf and pi = mvi. Simplify. Remember that when asked specifically about magnitude, you can disregard the sign of the final answer.

📄 Study AP Physics C: Mechanics, Unit 4.2: Impulse and Momentum

2. A billiards ball (m = 0.16kg) moves with an initial velocity of +2 m/s and collides with an identical billiards ball initially at rest. After the elastic collision, one ball travels with a speed of +0.5 m/s. What is the speed of the other ball?

A. The speed of the other ball is -3 m/s.

B. The speed of the other ball is -1.5 m/s.

C. The speed of the other ball is +1.5 m/s.

D. The speed of the other ball is +3 m/s.

Answer: Use conservation of momentum to solve this problem. First, calculate the initial momentum of the system to be 0.32 kg m/s. This is also the final momentum of the system. Use p = mv to find the speed of the second ball.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

3. A 60kg person and a 75kg person sit on opposite sides of a 4 meter long seesaw. Where is their center of mass?

A. 1.6 meters

B. 2 meters

C. 2.2 meters

D. 3.8 meters

Answer: Use the center of mass formula to calculate. If you calculated an answer of 1.8m, that is also correct -- you just put the 75kg person at zero. To find one of the options, subtract 4 - 1.8 to get 2.2 meters.

📄 Study AP Physics C: Mechanics, Unit 4.1: Center of Mass

4. The blue line on the graph shows the applied force on a 15.0kg shopping cart as a shopper moves down an aisle in the grocery store. Assuming the cart starts at rest, determine the speed of the cart after 3 seconds.

A. 5 m/s

B. 10 m/s

C. 50 m/s

D. 75 m/s

Answer: Find the area under the Force-time graph using geometry in order to find the impulse. The formula for area of a right triangle is 1/2 x base x height, which gives you 75 Ns. Then, use impulse-momentum theorem by setting 75 = change in momentum. Solve for final velocity.

📄 Study AP Physics C: Mechanics, Unit 4.2: Impulse and Momentum

5. A convertible moving with constant velocity on the open highway gets stuck in a snowstorm. Which of the following statements are true?

A. As the snow accumulates in the car, the speed of the car will increase because of conservation of energy.

B. As the snow accumulates in the car, the speed of the car will increase because of conservation of momentum.

C. As the snow accumulates in the car, the speed of the car will decrease because of conservation of energy.

D. As the snow accumulates in the car, the speed of the car will decrease because of conservation of momentum

Answer: As snow accumulates, the mass of the car increases. In order for momentum to be conserved, the car's speed must decrease.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

6. How does an airbag work to protect a passenger in a car crash?

A. It increases the momentum change of the passenger.

B. It decreases the momentum change of the passenger.

C. It lengthens the stopping time of the passenger, which reduces the force applied during the crash.

D. It shortens the stopping time of the passenger, which reduces the force applied during the crash.

Answer: The passenger's momentum change must remain the same, because of conservation of momentum. Airbags increase the time over which the passenger's momentum is changing. Change in momentum = Impulse, and Impulse = Ft. By increasing the stopping time, the force decreases.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

7. Two hockey mascots (named Gritty and Tommy Hawk) are standing at rest in the center of an ice rink. They push apart in opposite directions. The velocity of Gritty is 3 m/s, and the velocity of Tommy Hawk is - 6m/s. Which statement about the masses of the respective mascots is true?

A. Gritty is twice as massive at Tommy Hawk.

B. Tommy Hawk is twice as massive as Gritty.

C. Gritty is three times as massive as Tommy Hawk.

D. The mass of the two mascots is the same.

Answer: Use conservation of momentum to solve this problem. The initial momentum of the system is zero since both mascots are at rest. Set zero equal to the total momentum after the "explosion," and rearrange your values to get a ratio for the mass of Gritty to the mass of Tommy Hawk.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

8. Two objects of masses M and 4M are traveling at the same speed v towards each other, with the 4M mass traveling in the negative direction. They collide and stick together. How much kinetic energy is lost in the collision?

A. 0.6mv^2

B. 0.9mv^2

C. 1.6mv^2

D. 2.5mv^2

Answer: First, use conservation of momentum to find an expression for the final velocity of the objects. Then, use the kinetic energy equation (K = 1/2mv^2) to find the initial and final kinetic energies of the blocks. Subtract to find how much energy was lost.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

9. Three 5kg masses are on a 100 cm board. The board is suspended by a rope attached at the 50cm mark. If mass 1 is at 0cm and mass 2 is at 80cm, where must mass 3 be placed in order to keep the board level?

A. At the 20cm mark

B. At the 50cm mark

C. At the 70cm mark

D. At the 100cm mark

Answer: If the board is suspended at the 50cm mark, that's the location of the center of mass. Use the center of mass equation to find the location of mass 3.

📄 Study AP Physics C: Mechanics, Unit 4.1: Center of Mass

10. Two carts move towards each other and collide elastically. Cart 1 has a mass of 8kg and moves to the right with a speed of v = 5 m/s. Cart 2 has a mass of 25kg and moves to the left with a speed of v = 1 m/s. After the collision, Cart 1 moves to the left with a speed of 2 m/s. What direction does Cart 2 move after the collision?

A. Cart 2 moves right after the collision

B. Cart 2 moves left after the collision

C. Cart 2 is not moving after the collision

D. There isn't enough information to tell.

Answer: Use conservation of momentum. First, calculate the initial momentum of the system to be 15 kg m/s by adding the initial momentum of Carts 1 & 2. Then, set 15 equal to the total final momentum, and solve for the velocity of cart 2. Remember that left means negative!

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

11. A firework explodes into three equally massive pieces, each with their momentum represented by the expression mv. The momentum vectors of two out of the three firework pieces are drawn in the image. What direction does the momentum vector of the third piece point?

A. The third vector must point towards zero degrees.

B. The third vector must point towards 90 degrees.

C. The third vector must point towards 180 degrees

D. The third vector must point towards 270 degrees.

Answer: The initial momentum of the system is zero, and the momentum of the center of mass must remain zero. The y components of the momentum of the first two pieces cancel. In order to cancel the x components, the third momentum vector must point right, which is zero degrees.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

12. Two bocce balls make a partial collision during a game. In this case, which of the following is true about the momentum and kinetic energy?

A. Both momentum and kinetic energy are always conserved.

B. Kinetic energy is always conserved, and momentum may be conserved.

C. Momentum is always conserved, and kinetic energy is never conserved.

D. Momentum is always conserved, and kinetic energy may be conserved.

Answer: Momentum is always conserved, assuming no non-conservative forces. Kinetic energy may be conserved, but energy may be lost to other forms of energy. There's not enough information to tell.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

13. A rod with uniform density has a length of L and a mass of M. Which of the following is an expression for the rod's center of mass?

A. L/2

B. L/3

C. L/4

D. Not enough information to tell

Answer: The short way to do this is to see that if the rod has uniform density, then you can find the center of mass by inspection. It's just going to be in the center of the rod, or L/2. Alternatively, you can integrate to find an expression for center of mass.

📄 Study AP Physics C: Mechanics, Unit 4.1: Center of Mass

14. A 0.15kg baseball is thrown by a catcher and leaves the catcher's hand with a speed of 35 m/s. What is the magnitude of the impulse on the ball?

A. 5.25 Ns

B. 92 Ns

C. 233 Ns

D. 525 Ns

Answer: Impulse = change in momentum. The ball starts at rest, so its initial momentum is zero. The change in momentum is equal the final momentum (p=mv). Since the change in momentum is equal to the impulse, this is your final answer. Don't overthink this one! :-)

📄 Study AP Physics C: Mechanics, Unit 4.2: Impulse and Momentum

15. A force acting on an object is represented by the expression F(t) = 4t^2. If the object starts at rest, what is the momentum of the object after 5 seconds?

A. 1.1 kg m/s

B. 100 kg m/s

C. 167 kg m/s

D. 224 kg m/s

Answer: Get the change in momentum by integrating the force function with respect to time. Integrate to get (4/3)t^3, and then plug in 5 seconds to get the change in momentum. Since the object started at rest, the initial momentum was zero, so the change in momentum is equivalent to the total momentum of the object at 5 seconds.

📄 Study AP Physics C: Mechanics, Unit 4.3: Conservation of Linear Momentum and Collisions

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