Practice Test 2 - AP Physics C Mechanics

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. A mass attached to a vertical spring oscillates with amplitude $A$. Taking the equilibrium position as the reference for gravitational potential energy, at what displacement from equilibrium is the total mechanical energy (including gravitational potential energy) equal to twice the elastic potential energy?
2. The potential energy of a particle moving along the x-axis is given by the function $U(x) = -4x^3 + 6x^2$ J, where x is in meters. What is the force on the particle at $x = -1$ m?
3. Consider two oscillating systems: System X has restoring force $F_X = -kx$ and System Y has restoring force $F_Y = -kx^3$ where $k > 0$ in both cases. A physics student argues that both systems exhibit simple harmonic motion because both have restoring forces that oppose displacement. Which analysis correctly evaluates this argument?
4. A mass $m$ is attached to a spring with spring constant $k$ and undergoes simple harmonic motion. At the moment when the displacement is $x = \frac{A}{2}$ (where $A$ is the amplitude), the speed is $v = \frac{A\sqrt{3}}{2}\omega$, where $\omega$ is the angular frequency. What is the period of this motion?
5. A car travels around a banked curve with banking angle $\theta = 25°$. The coefficient of static friction between the tires and road is $\mu_s = 0.40$. For a curve of radius 200 m, what is the maximum speed the car can travel without slipping?
6. Two objects, a rubber ball and a clay ball of identical mass, are thrown with the same speed toward a brick wall. The rubber ball bounces back with nearly the same speed, while the clay ball sticks to the wall. Which statement correctly compares the impulse delivered by the wall to each ball?
7. The potential energy of a particle undergoing one-dimensional simple harmonic motion is given by the function $U(x) = (2.0 \text{ J/m}^2)x^2$. If the total mechanical energy of the particle is 8.0 J, what is the amplitude of the oscillation?
8. A roller coaster car of mass $m$ travels along a frictionless track with several hills and valleys. Which of the following statements about the work done by the normal force, $W_N$, exerted by the track on the car is correct?
9. A satellite in elliptical orbit obeys Kepler's second law; what happens to its speed as it approaches perigee?
10. A 1500 kg car moves at 10 m/s and then speeds up to 25 m/s on level ground. Calculate the change in translational kinetic energy.
11. A uniform sphere of mass $M$ and radius $R$ is in rotational equilibrium when suspended by a string attached to a point on its surface. A small mass $m$ is then attached to the opposite point on the sphere's surface. What is the angle $\theta$ that the string makes with the vertical when the system reaches new equilibrium?
12. A block is attached to a horizontal spring with spring constant $k$. The block is pulled from its equilibrium position at $x=0$ to a position $x=A$. What is the work done by the spring on the block during this displacement?
13. Rotational inertia is the physical quantity that quantifies an object's...
14. A spacecraft with $I=80\ \text{kg}\cdot\text{m}^2$ must reach $\omega=0.60\ \text{rad/s}$ from rest; during a short burn, external torques are negligible except for the thrusters, so $J=\Delta L=I\Delta\omega$. Assume the torque direction matches the desired rotation. Considering the described system, calculate the angular impulse applied to the spacecraft during the interval.
15. A parachutist of mass 70 kg reaches terminal velocity when the drag force equals 686 N. If the drag coefficient and air density remain constant, what would be the terminal velocity of the same parachutist carrying an additional 30 kg of equipment?
16. A physical pendulum consists of a rigid object of mass $M$ that oscillates about a pivot point a distance $d$ from its center of mass. It is released from rest at a small maximum angular displacement $\theta_{max}$. Which of the following changes will increase the total mechanical energy of the pendulum-Earth system?
17. Two hockey pucks slide on frictionless ice. Puck A (mass 2kg) moves east at 8 m/s, and puck B (mass 3kg) moves north at 6 m/s. They collide and stick together. What is the magnitude of their velocity immediately after the collision?
18. A block slides down a frictionless inclined plane of height $h$ and angle $\theta$. At the bottom, it encounters a rough horizontal surface with coefficient of kinetic friction $\mu_k$ and slides a distance $d$ before coming to rest. What is the total work done by friction on the block during its entire motion?
19. Two cars move in opposite directions: Car A travels east at $20\ \text{m/s}$ and Car B travels west at $15\ \text{m/s}$. A reference frame is the viewpoint used to assign signs and directions to velocities. Relative motion compares one object's velocity as measured from another object's frame. This helps estimate closing speeds in traffic and collision analysis. Based on the scenario described, what is the relative speed between the two cars?
20. A balloon is released with internal pressure $1.3\times10^{5}\,\text{Pa}$ while ambient pressure is $1.0\times10^{5}\,\text{Pa}$; escaping air jets backward and a force sensor estimates the balloon exerts $F_{\text{balloon}\to\text{air}}=5.0\times10^{-1}\,\text{N}$ backward on the air as it accelerates out. What is the relationship between the force the balloon exerts on the air and the force the air exerts on the balloon?

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