Practice Test 1 - 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 force $\vec{F} = (4\hat{i} + 6\hat{j})$ N acts on an object that undergoes a displacement $\vec{d} = (3\hat{i})$ m. A second force $\vec{G}$ also acts on the object. The work done by force $\vec{G}$ on the object is zero, and the net force $\vec{F}_{net}$ on the object is parallel to the displacement $\vec{d}$. What is the vector $\vec{G}$?
2. A particle is in translational equilibrium. Which of the following statements must be true about the particle?
3. An object with mass $m$ is projected horizontally with initial velocity $v_0$ on a surface where the only horizontal force is a resistive force given by $F = -kv$. The velocity of the object as a function of time is $v(t) = v_0 e^{-kt/m}$. What is the total distance the object travels as it slows to a stop?
4. A wheel with moment of inertia $I=1.2\ \text{kg}\cdot\text{m}^2$ must speed up from $\omega_0=5.0\ \text{rad/s}$ to $\omega_f=17\ \text{rad/s}$ in $t=4.0\ \text{s}$ under a constant net torque (friction included). Key equations: $\alpha=(\omega_f-\omega_0)/t$ and $\tau=I\alpha$. Using the given conditions, what is the torque required to achieve this change?
5. A $1200\,\text{kg}$ car descends a frictionless hill and reaches $25\,\text{m/s}$ at the bottom; what is its translational kinetic energy there?
6. Which expression represents the magnitude of the torque produced by the wall's normal force ($N_w$) about the point where the ladder contacts the floor?
7. Two springs with spring constants $k_1 = 300 \text{ N/m}$ and $k_2 = 500 \text{ N/m}$ are placed end-to-end (in series) and compressed by a total of $0.20 \text{ m}$ from their combined natural length. What is the magnitude of the force exerted by the $k_2$ spring?
8. Which of the following lists contains only vector quantities?
9. Two projectiles are launched simultaneously from the same point. Projectile A is launched at angle $30°$ with initial speed $v_A$, and projectile B is launched at angle $60°$ with initial speed $v_B$. If both projectiles have the same range, what is the ratio $\frac{v_A}{v_B}$?
10. An electric motor operates at constant mechanical power output of 1.5 kW while lifting a load vertically. Initially, the load has a mass of 100 kg and is lifted at constant velocity. After 10 seconds, an additional 50 kg mass is suddenly attached to the load. Assuming the motor maintains the same power output, what is the new constant velocity of the combined load after the transient effects have died down?
11. The position of a particle is given by the function $x(t)$. Which of the following mathematical expressions represents the particle's instantaneous acceleration at time $t$?
12. An object is moving to the right with a constant velocity. If a single, constant force is then applied to the object, which of the following is NOT a possible resulting motion?
13. A position vector $\vec{r}$ makes an angle of $\theta$ with the positive x-axis and has magnitude $r$. The vector is then rotated clockwise by angle $\phi$ to create a new vector $\vec{r}'$. Which expression correctly represents the x-component of $\vec{r}'$?
14. A solid disk and a spoked wheel have the same mass $M$ and the same outer radius $R$. Both are accelerated from rest to the same final angular velocity $\omega$. Which object has more rotational kinetic energy, and why?
15. A 0.50 kg block on a frictionless track is attached to a spring with $k=200\ \text{N/m}$ and equilibrium at $x=0$. It is pulled to $x=+0.080\ \text{m}$ and released from rest at $t=0$, so $A=0.080\ \text{m}$ and $\phi=0$. The angular frequency is $\omega=\sqrt{k/m}$ and the motion is $x(t)=A\cos(\omega t+\phi)$ with $x$ in meters and $t$ in seconds. The velocity is $v(t)=-A\omega\sin(\omega t+\phi)$ and the acceleration is $a(t)=-\omega^2 x(t)$. The restoring force is $F_s=-kx$. Assume SHM holds for all times. What is the period $T$ of the oscillation?
16. A block slides at a constant velocity across a horizontal, frictionless surface. A constant vertical force of magnitude F is then applied to the block. How much work is done by this new vertical force as the block continues to travel a horizontal distance $d$?
17. Where must the pivot be placed for the bar to be in static equilibrium?
18. A boat of mass $m$ starts from rest at $t=0$. A constant force $F_{app}$ is applied, and it experiences a resistive force $F_r = -kv$. The boat's speed $v$ as a function of time $t$ is given by which expression?
19. A diver performs a somersault after jumping from a diving board. They initially leave the board with their body extended, then tuck into a compact shape, and finally extend their body again before entering the water. Neglecting air resistance, which of the following correctly describes the changes in their rotational inertia $I$ and angular momentum $L$ about their center of mass during this process?
20. A particle moves in a one-dimensional potential given by $U(x) = x^4 - 8x^2 + 12$. If the particle has a total mechanical energy of $E = 4$ J, which of the following is a turning point of its motion?

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