Practice Test 5 - 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. Two blocks, $M_1$ and $M_2$, are in contact on a frictionless horizontal surface. A horizontal force $F$ is applied to $M_1$, causing both blocks to accelerate. What forces should be shown on a free-body diagram for block $M_2$?
2. A 0.60 kg cart is attached to a spring with $k=240\ \text{N/m}$ and oscillates on a frictionless track about $x=0$. It is pulled to $x=+0.070\ \text{m}$ and released from rest at $t=0$, so $A=0.070\ \text{m}$ and $\phi=0$. The motion is $x(t)=A\cos(\omega t+\phi)$ with $\omega=\sqrt{k/m}$. The acceleration is $a(t)=-\omega^2 x(t)$ and $a_{\max}=\omega^2 A$. All quantities are in SI units and amplitude remains constant. Find the maximum acceleration magnitude $a_{\max}$.
3. A particle moves along a helical path described by the parametric equations $x(t) = a\cos(\omega t)$, $y(t) = a\sin(\omega t)$, and $z(t) = bt$, where $a$, $b$, and $\omega$ are positive constants. What is the magnitude of the particle's acceleration?
4. A person stands on a moving walkway that travels at $1.5 \text{ m/s}$. The person walks forward on the walkway at $2.0 \text{ m/s}$ relative to the walkway for $10 \text{ s}$, then turns around and walks backward at the same speed relative to the walkway for another $10 \text{ s}$. What is the person's displacement relative to the ground after the entire $20 \text{ s}$ journey?
5. A rocket in space ejects exhaust gases at a rate of 100 kg/s with a velocity of 3000 m/s relative to the rocket. At a particular instant, the rocket has a mass of 5000 kg and is accelerating at $60 \text{ m/s}^2$. What is the magnitude of the force that the exhaust gases exert on the rocket according to Newton's third law?
6. A hollow spherical shell of mass $M$ and inner radius $a$ and outer radius $b$ has uniform density. A point mass $m$ is located at the geometric center of the shell. What is the gravitational force on the point mass?
7. A mass $m$ is attached to two identical springs, each with spring constant $k$, arranged in parallel (both springs attached between the mass and a fixed wall). The mass is displaced from equilibrium by distance $x_0$ and released. At the moment when the displacement is $\frac{x_0}{2}$, what is the ratio of kinetic energy to elastic potential energy?
8. An object moves at a constant speed in a circular path. Which of the following statements about the work done on the object is correct?
9. Using the given parameters, a pendulum of length $L=2.0\,\text{m}$ swings at small angles; determine the time for one full oscillation.
10. A fan blade of radius $0.25$ m is rotating at $120$ rad/s. It is then turned off and decelerates uniformly, coming to rest in $8.0$ s. What is the magnitude of the total linear acceleration of a point on the tip of the blade at the instant it is turned off ($t=0$)?
11. Two identical balls collide head-on. Ball 1 initially moves at 6 m/s to the right, and ball 2 initially moves at 2 m/s to the left. After collision, ball 1 moves at 1 m/s to the left. Assuming the collision occurs along a straight line, what can be concluded about this collision?
12. A particle's velocity vector is $\vec{v} = (-3.0 \hat{i} + 4.0 \hat{j})$ m/s. What is the approximate angle of the velocity vector, measured counterclockwise from the positive x-axis?
13. A rigid body with rotational inertia $I$ experiences a net torque $\tau$, resulting in an angular acceleration $\alpha$. If the mass of the body is doubled, with its shape and dimensions remaining identical, what is the new angular acceleration for the same net torque $\tau$?
14. Two identical uniform rods, each of mass $M$ and length $L$, are initially at rest. Rod A lies along the x-axis with its center at the origin. Rod B lies along the y-axis with its center also at the origin, forming a cross. A brief torque is applied about the z-axis (perpendicular to both rods) to the entire system, giving it an angular impulse $J$. What is the final angular momentum of rod A about the origin?
15. A uniform solid sphere of mass $M$ and radius $R$ rolls without slipping down an incline that makes an angle $\theta$ with the horizontal. What is the magnitude of the linear acceleration of the sphere's center of mass? The rotational inertia of a solid sphere is $I = \frac{2}{5}MR^2$.
16. A wind turbine rotor with $I=1.0\times10^3\ \text{kg}\cdot\text{m}^2$ spins at $\omega_i=2.0\ \text{rad/s}$; the wind drops and the net torque becomes $\tau=-200\ \text{N}\cdot\text{m}$ for $t=5.0\ \text{s}$, so $\Delta L=\tau t$ and $L=I\omega$. Neglect other torques. Based on the scenario above, what is the final angular velocity of the system after 5.0 seconds?
17. An object moves along the x-axis with a velocity given by $v(t) = 3t^2 + 2t$, where $v$ is in m/s and $t$ is in seconds. What is its displacement during the interval from $t=1$ s to $t=3$ s?
18. How does conservation of angular momentum affect satellite speed if orbital radius decreases due to a brief inward impulse?
19. A block of mass $m$ slides from rest down a frictionless incline of height $h$. It then moves onto a rough horizontal surface with a coefficient of kinetic friction $\mu_k$. How far does the block slide on the horizontal surface before coming to rest?
20. A square plate of side length L is pivoted at its center. Four forces of equal magnitude F are applied. Which of the following applications produces the greatest magnitude of torque about the pivot?

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