Practice Test 11 - 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 roller coaster car goes through a vertical loop-the-loop of radius $R$. At the bottom of the loop, the normal force on a passenger of mass $m$ is three times their weight. What is the speed of the car at the bottom of the loop?
2. A 2.0 kg block rests on a horizontal surface with coefficient of static friction $\mu_s = 0.40$ and coefficient of kinetic friction $\mu_k = 0.30$. A horizontal force $F$ is applied to the block, starting from zero and gradually increasing. When analyzing the free-body diagram at the moment just before the block begins to slide, which statement about the forces is correct?
3. A solid sphere is rolling without slipping on a horizontal surface. A horizontal force $F$ is applied to the center of the sphere, causing it to accelerate. Static friction $f$ acts on the sphere. The sphere has mass $M$, radius $R$, and rotational inertia $I=\frac{2}{5}MR^2$. Which equation correctly applies Newton's second law for rotation about the sphere's center of mass?
4. A satellite of mass $m$ orbits the Earth in a perfect circle of radius $R$. What is the work done by the gravitational force on the satellite as it completes half of an orbit?
5. For a geostationary satellite, what orbital radius $r$ satisfies $T=24\,\text{h}$ using $T=2\pi\sqrt{r^3/(GM)}$?
6. A massless rod of length 4 m is pivoted at its center. A downward force of 10 N is applied perpendicularly at the right end, and an upward force of 5 N is applied perpendicularly at a point 1 m to the right of the pivot. What is the net torque about the pivot?
7. Two cars move east on a highway: Car A at $30\ \text{m/s}$ and Car B at $25\ \text{m/s}$. A reference frame is the chosen observer and axes used to measure motion. Relative motion uses velocity differences to describe how one object appears from another. This applies to traffic merging and passing maneuvers. Based on the scenario described, what is the relative speed between the cars?
8. A particle with total mechanical energy $E_{tot}$ oscillates in a region described by a potential energy function $U(x)$. The kinetic energy of the particle is maximized when...
9. For two non-zero vectors $\vec{A}$ and $\vec{B}$, the condition $\vec{A} \times \vec{B} = \vec{0}$ is met. Which of the following statements must be true as a necessary consequence?
10. What is the magnitude of the upward force $N_1$ exerted by Support 1 for the plank to be in equilibrium?
11. A student sits at rest on a frictionless rotating stool, holding a bicycle wheel that is spinning with its axis vertical, creating an upward angular momentum $\vec{L}_w$. The student flips the wheel over so its axis is vertical but pointing downward. What is the final angular velocity of the student-stool system?
12. Consider raising a satellite from a circular orbit at $r_1$ to a larger circular orbit at $r_2$. Using $E=-\frac{\mu m}{2r}$ and $v=\sqrt{\mu/r}$ (from gravity providing centripetal force), Kepler's 3rd law predicts the higher orbit has a longer period. What energy transformations occur as a satellite moves from a low Earth orbit to a high Earth orbit?
13. Two skaters collide elastically: $m_1=50\,\text{kg}$ at $+4.0\,\text{m/s}$, $m_2=70\,\text{kg}$ at rest. What is the final velocity of $m_1$?
14. A system consists of two identical particles, each of mass m. One particle moves with velocity $+v\hat{i}$ and the other moves with velocity $-v\hat{i}$. What is the total translational kinetic energy of the system?
15. A net torque given by $\tau = \tau_0 \sin(\theta)$ is applied to a rotor, where $\tau_0$ is a positive constant. What is the work done by this torque as the rotor moves from an angular position of $\theta = 0$ to $\theta = \pi$ radians?
16. A particle starts from the origin with an initial velocity of $\vec{v}_0 = 5\hat{i}$ m/s. It experiences a time-varying acceleration given by $\vec{a}(t) = 6t\hat{i} - 4\hat{j}$ m/s$^2$. What is the velocity vector $\vec{v}(t)$ of the particle at $t = 3$ s?
17. A velocity-time graph of a moving object is a curve that is always in the first quadrant, and its slope is continuously decreasing, approaching zero as time increases. Which of the following is a correct statement about the object's motion?
18. A block undergoing simple harmonic motion on a frictionless surface has a total mechanical energy $E$. At which displacement from the equilibrium position is the kinetic energy of the block equal to its potential energy?
19. In the described system, calculate the potential energy stored in the spring when compressed $x=0.0800\,\text{m}$ ($k=500\,\text{N/m}$).
20. An ideal spring with spring constant $k$ is cut into two identical halves. One of the halves is designated Spring A. The two halves are then connected in parallel to form a new spring system, designated System B. What is the ratio of the spring constant of System B to the spring constant of Spring A?

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