6.3 MC Answers and Review

⛔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 6. 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.

A. Not enough information to know.

B. The period of the pendulum would decrease.

D. The period of the pendulum would increase.

Answer: The period of a pendulum depends on g and the length of the pendulum's string. The mass of the bob does not affect the period.

📄Study AP Physics C: Mechanics, Unit 6.1: Simple Harmonic Motion, Springs, and Pendulums

A. The velocity of the mass is greatest when it is furthest away from the equilibrium point.

B. The elastic potential energy in the system is greatest when the mass passes through the equilibrium point.

C. The energy in the system is all elastic potential energy.

Answer: There are no non-conservative forces, so the total energy in the system remains constant. The two types of energy present are elastic potential energy and kinetic energy. Elastic potential energy is the greatest when the object is furthest from its equilibrium point. Velocity is greatest at the equilibrium point, because that is where the total energy is all kinetic energy.

📄Study AP Physics C: Mechanics, Unit 6.1: Simple Harmonic Motion, Springs, and Pendulums

B. At max amplitude, the block's velocity is also at a maximum.

C. At max amplitude, the block's displacement is zero.

D. At max amplitude, the block's acceleration is zero.

Answer: At max amplitude, the block's displacement from its equilibrium position is at a maximum. According to Hooke's law, the restoring force is also at a maximum. Since force and acceleration are directly proportional, max force means max acceleration.

📄Study AP Physics C: Mechanics, Unit 6.1: Simple Harmonic Motion, Springs, and Pendulums

A. 5 Joules

B. 10 Joules

D. 20 Joules

Answer: This is a conservation of energy question. At max displacement, all of the pendulum's energy is potential, so the total energy of the system is 20 Joules. If the pendulum's kinetic energy is 5 Joules, its potential energy must be 15 Joules to get a total energy of 20 Joules.

5. A particle moves in a circle in such as way that the x- and y-coordinates of its motion, given in meters as functions of time t in seconds, are: x = 2 cos(4t) y = 2 sin(4t) What is the radius of the circle?

A. 0.5 meters

B. 1 meter

D. 4 meters

Answer: Remember that the equation for simple harmonic motion of any kind is A cos(omega*t). For uniform circular motion, the amplitude is the radius. So, the amplitude in these equations is 2, which makes the radius of the circle equal to 2.

A. T/10

B. T/2

D. 2T

Answer: Two things affect the period of a mass-spring oscillator: the mass of the object and the spring constant. Neither one of those things were changed by moving to Mars, so the period remains the same.

A. 0.2 meters

C. 0.5 meters

D. 0.8 meters

Answer: First, recognize that at 0.5 meters, all of the energy is elastic potential energy, since it is the max amplitude. The total energy of the system is 12 J, so plug that into the elastic potential energy equation to solve for k. Then, recognize that if the kinetic energy of the block is 4J, the elastic potential energy at that point must be 8 J (12-4). Finally, use the elastic potential energy equation again and solve for x.

A. At max amplitude, the bob's displacement from its equilibrium position is at a maximum. The component of the tension counteracting the bob's weight is at a minimum, so there is max net force at max amplitude. Therefore, there must also be max acceleration.

C. At max amplitude, the bob's displacement is zero.

D. At max amplitude, the bob's acceleration is zero.

Answer: At max amplitude, the bob's displacement from its equilibrium position is at a maximum. The component of the tension counteracting the bob's weight is at a minimum, so there is max net force at max amplitude. Therefore, there must also be max acceleration.

A. g/4

B. g/2

C. 2g

Answer: Use the equation for the period of a pendulum to solve this problem. Solve the period equation for g using both 4 seconds and 2 seconds, and then see how they relate to each other.

📄Study AP Physics C: Mechanics, Unit 6.1: Simple Harmonic Motion, Springs, and Pendulums

A. 0.7 Hz

C. 2.6 Hz

D. 3.2 Hz

Answer: Remember that period and frequency are inverses of each other, so the period of the initial motion is 0.5 seconds. Use the period of a mass-spring oscillator formula to find k. Then, replug in k with the 2kg mass. Solve for period, and then take the inverse to find frequency.

11. A particle moves in the xy-plane with coordinates given by x = 2cos(0.5t) and y = 2sin(0.5t) What is the magnitude of the particle’s acceleration?

B. 1 m/s^2

C. 1.5 m/s^2

D. 2 m/s^2

Answer: First, find the velocity of the particle moving in uniform circular motion by multiplying the angular velocity (0.5) by the radius (2). Then, use the formula for centripetal acceleration to solve for the answer.

B. pi

C. 2*pi

D. 4*pi

Answer: The function given in the general form for simple harmonic motion, so find the angular frequency of the motion by remembering that "16x" is (omega)^2*x. Omega (aka the angular frequency) is 4, and then use the formula that relates angular frequency to period to solve.

A. The period of the pendulum will remain constant, and the period of the mass-spring system will also remain constant.

B. The period of the pendulum will remain constant, and the period of the mass-spring system will increase.

C. The period of the pendulum will increase, and the period of the mass-spring system will also increase.

Answer: The acceleration due to gravity only affects the period of a pendulum, as seen in each of the period equations for pendulums and mass-spring oscillators. If g gets smaller, the period of the pendulum will increase.

A. kx = ma

C. mg = ma

D. -mg = ma

Answer: The restoring force in a mass-spring oscillator is represented by F = -kx, and that is the only force acting on a horizontal mass-spring oscillator.

A. 3 Joules

B. 20 Joules

C. 39 Joules

Answer: First, use the mass in the period formula to find k. Then, use the max amplitude and the potential energy of a spring formula to solve for the potential energy at max amplitude. Since the block is not moving at max amplitude, the potential energy at this point is equal to the total energy.

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