Practice Test 3 - AP Physics C Mechanics

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

In a laboratory on Earth, a student measures the mass of a block to be $m_g$ using a spring scale and $m_i$ using an inertial balance. The experiment is then moved to a spaceship accelerating at $a=g$ in deep space. How will the new measurements, $m'_g$ and $m'_i$ , compare to the original measurements?
A physical pendulum has a certain period of oscillation. If the mass of the pendulum is doubled, but its shape, size, and pivot point remain exactly the same, what is the effect on its period?
A particle moves along the x-axis with a velocity given by $v_x(t) = 4t^3 - 2t$ . If the particle is at $x=1$ at time $t=1$ , what is its position at time $t=2$ ?
An ice skater rotates about a vertical axis with $I_i=3.0\ \text{kg}\cdot\text{m}^2$ and $\omega_i=2.0\ \text{rad/s}$ . The skater pulls in arms to $I_f=1.2\ \text{kg}\cdot\text{m}^2$ with negligible external torque, so $L=I\omega$ is conserved. Considering the described system, what is the final angular velocity of the system after the skater pulls in arms?
Based on the scenario, a $600\,\text{kg}$ boat has drag $F_d=kv^2$ with $k=100\,\text{N\,s}^2/\text{m}^2$ ; calculate terminal speed if engine thrust is constant $1600\,\text{N}$ .
A wind turbine rotor with $I=2.0\times10^4\ \text{kg}\cdot\text{m}^2$ spins at $\omega_i=0.80\ \text{rad/s}$ . The wind drops and net torque becomes $\tau=-2.0\times10^3\ \text{N}\cdot\text{m}$ for $t=4.0\ \text{s}$ , using $\Delta L=\tau t$ and $L=I\omega$ . Considering the described system, what is the final angular velocity of the system after 4.0 seconds?
In a circular orbit, what energy exchange occurs if a satellite is boosted from LEO to a higher circular orbit?
A $12.0\,\text{kg}$ box is pulled up a $30^\circ$ incline at constant speed by a rope parallel to the plane; $\mu_k=0.15$ . Consider the scenario described above, with kinetic friction opposing the motion and $g=9.8\,\text{m/s}^2$ . The normal force is perpendicular to the incline and weight is vertical. No air resistance acts. Calculate the frictional force given the conditions.
An object of mass m has a momentum of magnitude p. Which of the following expressions correctly represents its translational kinetic energy, K?
Two billiard balls collided head-on elastically: ball 1 ( $0.16\,\text{kg}$ ) moved right at $+2.0\,\text{m/s}$ and ball 2 ( $0.16\,\text{kg}$ ) moved left at $-1.0\,\text{m/s}$ , with negligible external impulse. Determine the velocity of the second object after the collision.
A 90 kg load is lifted 6.0 m using an ideal block-and-tackle with mechanical advantage 2, so the rope tension is $T=\tfrac{mg}{2}$ while the load rises at constant speed. Because two rope segments support the load, the free end of the rope must be pulled 12 m to raise the load 6.0 m. The pull takes 8.0 s, and friction is negligible. Use $g=9.8\,\text{m/s}^2$ . In the given system, what is the average power output of the system described?
A uniform solid sphere rolls down a curved track and then moves along a horizontal loop-the-loop of radius $R$ . If the sphere is released from rest at height $h$ above the bottom of the track, what is the minimum value of $h$ required for the sphere to maintain contact with the track at the top of the loop?
A satellite in an elliptical orbit follows Kepler's laws: (1) orbits are ellipses with Earth at a focus, (2) equal areas in equal times, and (3) $T^2\propto a^3$ . The equal-areas law is a consequence of constant angular momentum $L=mrv_\perp$ when gravity (a central force) exerts zero torque about Earth's center. How does conservation of angular momentum affect the orbit of a satellite?
Two spheres, A and B, have the same translational kinetic energy. The mass of sphere A is four times the mass of sphere B ( $m_A = 4m_B$ ). What is the ratio of the speed of sphere A to the speed of sphere B, $v_A/v_B$ ?
A gyroscope has spin angular momentum magnitude $L=0.40\ \text{kg}\cdot\text{m}^2/\text{s}$ . Gravity exerts a torque of magnitude $\tau=0.080\ \text{N}\cdot\text{m}$ about the pivot, producing steady precession; assume the spin magnitude stays constant. Key equation: $\Omega=\tau/L$ . Using the given conditions, determine the precession rate $\Omega$ .
A $1500\ \text{kg}$ car moving east at $12\ \text{m/s}$ is brought to rest by a collision in $0.30\ \text{s}$ . Using the given data, determine the change in momentum of the car.
Based on the described system, a vertical spring-mass oscillator has $m=0.50\,\text{kg}$ , $k=80\,\text{N/m}$ , and amplitude $0.03\,\text{m}$ about equilibrium; calculate the frequency of the given system in Hz.
A uniform disk of mass $M$ and radius $R$ is pivoted at a point on its rim. A horizontal force $F$ is applied at the opposite point on the rim. For the disk to remain in rotational equilibrium, what must be the relationship between $F$ and the other parameters?
A wheel of radius $R$ and moment of inertia $I$ about its center is initially at rest on a horizontal surface. A horizontal force $F$ is applied to the axle for time $t$ . If the coefficient of static friction between the wheel and surface is $\mu_s$ , and the wheel rolls without slipping throughout the motion, what is the angular acceleration of the wheel?
What is the total translational kinetic energy of the two-car system as measured by an observer stationary on the ground?

Practice tests