Practice Test 4 - 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 simple pendulum of length $L$ oscillates with small amplitude in a region where the gravitational acceleration is $g$. If the pendulum bob is replaced with one having twice the mass and the length is increased by a factor of 4, what is the ratio of the new period to the original period?
2. A ball is thrown from ground level at $v_0=18\,\text{m/s}$ and $\theta=50^\circ$ above the horizontal, with $g=9.8\,\text{m/s}^2$ downward and no air resistance. Take $t=0$ at launch and analyze motion during the first $2.0\,\text{s}$. The only force during flight is gravity, so acceleration is constant and vertical. Initial position is $\vec r_0=\langle 0,0\rangle\,\text{m}$, and $v_x$ remains constant. Use component kinematics to model the motion. Based on the scenario described, describe the motion of the object using kinematic equations.
3. A horizontal disk with rotational inertia $I_0$ is rotating freely with angular velocity $\omega_0$ about a vertical axis. A small piece of putty of mass $m$ is dropped vertically and sticks to the disk at a distance $r$ from the axis. What is the final angular velocity of the disk-putty system?
4. A uniform chain of mass $M$ and length $L$ hangs vertically from one end. A portion of length $x$ (measured from the bottom) is then lifted and placed horizontally on a frictionless table while the remaining portion of length $(L-x)$ continues to hang vertically. What is the position of the center of mass of the entire chain, measured vertically downward from the table surface?
5. The total angular momentum of a system of particles is conserved under which of the following conditions?
6. A block is pulled up a rough inclined plane at constant velocity by a force $\vec{F}$ applied parallel to the incline. The incline makes angle $\theta$ with the horizontal, and the coefficient of kinetic friction is $\mu_k$. In the free-body diagram analysis, which expression correctly represents the relationship between the applied force and other forces?
7. A projectile is launched from the surface of a planet of mass $M$ and radius $R$. What is the minimum total mechanical energy required for the projectile-planet system so that the projectile can escape the planet's gravitational pull? Assume the potential energy of the system is zero at infinite separation.
8. A $2.0\ \text{kg}$ cart moves right at $6.0\ \text{m/s}$ and experiences a constant leftward force of $10\ \text{N}$ for $0.50\ \text{s}$. Using the given data, determine the change in momentum of the cart.
9. A parachutist falling toward Earth opens their parachute and reaches a constant terminal velocity. At this point, what is the relationship between the magnitude of the gravitational force $F_g$ and the magnitude of the upward air drag force $F_d$?
10. An object's position is given by the function $x(t) = 2t^3 - 15t^2 + 36t - 8$. At which of the following times is the object momentarily at rest?
11. Two point masses, $m_1 = 2.0$ kg and $m_2 = 3.0$ kg, are located at $x_1 = -1.0$ m and $x_2 = 2.0$ m, respectively, on the x-axis. What is the rotational inertia of this system about the y-axis?
12. A $1500\,\text{kg}$ car descends a frictionless hill from rest and reaches $30\,\text{m/s}$; how much work is done on the car by gravity?
13. An object's momentum along a straight line is plotted as a function of time. The graph is a straight line passing through the points $(t=1 \text{ s}, p=5 \text{ kg⋅m/s})$ and $(t=4 \text{ s}, p=14 \text{ kg⋅m/s})$. What is the constant net force acting on the object?
14. Two vectors $\vec{P}$ and $\vec{Q}$ are added to form a resultant vector $\vec{R} = \vec{P} + \vec{Q}$. If the magnitudes satisfy the relation $|\vec{P}| + |\vec{Q}| = |\vec{R}|$, what must be true about the vectors $\vec{P}$ and $\vec{Q}$?
15. Based on the scenario, calculate $K_\text{rot}$ for a flywheel with $I=2.5\ \text{kg}\cdot\text{m}^2$ spinning at $\omega=20\ \text{rad/s}$.
16. A uniform rod of length $L$ and mass $M$ is pivoted at one end and released from a horizontal position. What is its rotational kinetic energy when it reaches the vertical position? The rotational inertia of a rod about its end is $I = \frac{1}{3}ML^2$. Use $g$ for the acceleration due to gravity.
17. A grinding wheel, initially at rest, accelerates with a uniform angular acceleration of $4.0 \, \text{rad/s}^2$ for $5.0 \, \text{s}$. What is its final angular velocity?
18. A particle of mass $m$ is located inside a uniform solid sphere of mass $M$ and radius $R$ at a distance $r$ from its center ($r < R$). The gravitational force on the particle is $F_g(r) = -G\frac{Mmr}{R^3}$. If the potential energy is defined to be zero at the center of the sphere ($U(0)=0$), what is the potential energy $U(r)$ of the particle-sphere system?
19. A thin hoop of mass $M$ and radius $R$ has two small beads, each of mass $m$, attached to its rim at opposite ends of a diameter. What is the total rotational inertia of the hoop-beads system about an axis perpendicular to the plane of the hoop and passing through its center?
20. A system consists of three point masses: $m_1 = 2.0\text{ kg}$ at position $x_1 = 0\text{ m}$, $m_2 = 3.0\text{ kg}$ at position $x_2 = 4.0\text{ m}$, and $m_3 = 1.0\text{ kg}$ at position $x_3 = 6.0\text{ m}$. What is the $x$-coordinate of the center of mass of this system?

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