Practice Test 9 - 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 point mass $m$ is moving in a circle of radius $R$ with a constant speed $v$. Its rotational kinetic energy about the center of the circle is $K_{rot}$. Which expression correctly relates $K_{rot}$ to its translational kinetic energy, $K_{trans} = \frac{1}{2}mv^2$?
2. What is the magnitude of the change in the particle's momentum?
3. What is the ratio of the total mechanical energy of System 2 to that of System 1, $E_2/E_1$?
4. A beam of negligible mass is pivoted at its left end and lies initially horizontal. A weight $W_1=30\,\text{N}$ hangs at $r_1=0.40\,\text{m}$ from the pivot, and a second weight $W_2=20\,\text{N}$ hangs at $r_2=0.70\,\text{m}$ from the pivot, both on the same side. The weights act vertically downward, and the beam rotates in a vertical plane. At the instant shown, the beam remains horizontal so each weight produces a moment arm equal to its distance from the pivot. Ignore friction at the pivot and any other forces. The net torque about the pivot is the sum of the individual torques from the two weights. Using the given information, compute the net torque magnitude about the pivot at this instant.
5. A flywheel consists of a uniform solid cylinder of mass $M$ and radius $R$ with four identical point masses, each of mass $m$, attached at the rim. The flywheel rotates about its central axis. What fraction of the total rotational kinetic energy is stored in the point masses when the system rotates at angular velocity $\omega$?
6. A compound system consists of a uniform rod of mass $2m$ and length $L$ with two point masses, each of mass $m$, attached at the ends. The system rotates about an axis perpendicular to the rod and passing through its center. If a constant torque $\tau$ is applied for time $t$, starting from rest, what is the final angular velocity?
7. On a disc, torque satisfies $\tau=rF\sin\theta$ and $\tau=I\alpha$. If $F$ stays constant and tangential, what happens to $\tau$ when $r$ doubles?
8. Three particles, each of mass $m$, are placed at the vertices of an equilateral triangle with side length $L$. What is the total gravitational potential energy of this system of particles?
9. An object of mass $m$ is in simple harmonic motion with total energy $E$. If the total energy is increased to $4E$ while the mass remains constant, by what factor does the maximum speed of the object change?
10. A box sits on the bed of a pickup truck that is accelerating forward. The box does not slide relative to the truck bed. In the free-body diagram for the box, which force provides the acceleration, and what can be concluded about its magnitude?
11. Based on the described system, a $0.80\,\text{kg}$ mass on a $k=50\,\text{N/m}$ spring oscillates; calculate the frequency in Hz.
12. A student wants to determine the coefficient of static friction $\mu_s$ between a block and a wooden board. The student places the block on the board and slowly raises one end of the board, increasing the angle of inclination $\theta$ until the block just begins to slide. Which of the following expressions represents $\mu_s$ in terms of the angle $\theta_{max}$ at which the block starts to slide?
13. A car travels around a circular track at constant speed. The driver claims the car obeys Newton's first law because "it maintains constant velocity." A physics student argues this violates Newton's first law. Who is correct and why?
14. An object of mass m has translational kinetic energy K. A net force is applied to the object, causing the magnitude of its momentum to double. Assuming the mass remains constant, what is the object's new translational kinetic energy?
15. A particle moves along a straight line with position given by $x(t) = A\cos(\omega t + \phi)$. The particle's acceleration as a function of position can be written as $a = -kx$ where $k$ is a positive constant. Which statement correctly identifies the relationship between $k$ and the other parameters, and explains why this motion constitutes simple harmonic motion?
16. A force is applied to a wrench handle to tighten a bolt. To produce the greatest possible torque on the bolt with a given force magnitude, the force should be applied:
17. A bicycle wheel with $I=0.40\ \text{kg}\cdot\text{m}^2$ starts from rest; a constant tangential force $F=10\ \text{N}$ is applied at radius $r=0.30\ \text{m}$ for $t=5.0\ \text{s}$, so $\tau=rF$ and $\Delta L=\tau t$. Ignore friction and keep the force perpendicular to the radius. Based on the scenario above, determine the change in angular momentum of the wheel.
18. A wind turbine generates electrical power according to $P = 0.4v^3$ kW, where v is the wind speed in m/s. During a particular day, the wind speed varies as $v(t) = 8 + 2\sin(\pi t/12)$ m/s, where t is time in hours. What is the average power generated during the first 12 hours?
19. A $3.0\ \text{kg}$ object starts from rest and experiences a constant net force of $18\ \text{N}$ to the right for $0.50\ \text{s}$. Using the given data, what is the final velocity of the object after the collision?
20. Based on the described system, a small-angle pendulum with $L=1.6\,\text{m}$ oscillates; calculate the frequency in Hz using $f=1/T$.

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