Practice Test 6 - 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 thin hoop of mass $M$ and radius $R$ rolls without slipping on a horizontal surface. Its rotational inertia is $I = MR^2$. What fraction of its total kinetic energy is rotational kinetic energy?
2. A horizontal beam of length $4.0\,\text{m}$ is held in static equilibrium by two vertical support cables at its ends. A $300\,\text{N}$ load hangs $1.0\,\text{m}$ from the left end, and the beam's own weight is negligible. The upward tensions $T_L$ and $T_R$ act at the left and right ends, respectively, and the load's weight acts downward at its attachment point. Taking torques about the left end, the lever arm for $T_R$ is $4.0\,\text{m}$ and for the load is $1.0\,\text{m}$. The beam does not rotate, so Newton's First Law in rotational form implies $\sum \tau_{\text{left}}=0$. Considering the forces acting on the object, calculate the force needed at a specific point to maintain equilibrium.
3. A mass-spring system oscillates with simple harmonic motion. When the displacement is $\frac{1}{3}$ of the amplitude, the ratio of kinetic energy to potential energy is:
4. An object of mass $m$ is released from rest at the top of a frictionless ramp of height $h$ and angle $\theta$. What is the work done by the normal force on the object as it slides down the entire length of the ramp?
5. A rope of negligible mass passes over an ideal pulley. A 4.0 kg mass hangs from one end, and a 6.0 kg mass hangs from the other end. When the system is released, what is the magnitude of the force that the 4.0 kg mass exerts on the rope?
6. A projectile is fired from the edge of a cliff at angle $\theta$ above the horizontal with initial speed $v_0$. The projectile lands at a horizontal distance $d$ from the launch point and at a vertical distance $h$ below the launch point. If the projectile were instead fired horizontally with the same initial speed from the same point, at what horizontal distance from the launch point would it land?
7. Two masses $m_1=2.0\,\text{kg}$ and $m_2=2.5\,\text{kg}$ are connected by a light rope over a frictionless pulley. Consider the scenario described above, with $m_2$ moving downward and the system accelerating. Take $g=9.8\,\text{m/s}^2$ and assume the rope is massless. Tension is the same on both sides. Determine the tension in the rope.
8. A ceiling fan blade rotating at $10 \, \text{rad/s}$ is switched off and slows down with a constant angular acceleration of magnitude $2.0 \, \text{rad/s}^2$. Through what angle does the blade rotate before coming to rest?
9. A ball is attached to a string and moves in a vertical circle. When the ball is at the side of the circle (horizontal position), the string makes an angle of 15° with the vertical. If the radius of the circular path is 0.6 m, what is the ball's speed at this position?
10. A mass on a spring oscillates vertically. When the mass is at position $y = +0.10$ m above equilibrium, its acceleration is $a = -4.0$ m/s² (downward). When the mass is at position $y = -0.05$ m below equilibrium, its acceleration is $a = +2.0$ m/s² (upward). What can be concluded about this motion?
11. A student is analyzing the forces on a block on an inclined plane. According to the course framework, which convention should be followed when drawing the forces on the free-body diagram?
12. A particle moves in the xy-plane such that its x-coordinate is given by $x(t) = R\cos(\omega t)$ and its y-coordinate is given by $y(t) = R\sin(\omega t)$, where $R$ and $\omega$ are positive constants. Which statement correctly describes the magnitude of the particle's acceleration vector?
13. An object of mass $m$ is released from rest in a fluid that exerts a resistive force $F_r = kv$, where $v$ is the object's speed. What is the initial acceleration of the object immediately after it is released?
14. A compound pendulum consists of a uniform disk of radius $R$ and mass $M$ that can pivot about a horizontal axis passing through a point on its rim. If the disk oscillates with small amplitude, what is the length of the equivalent simple pendulum that would have the same period?
15. An object of mass $m$ is placed inside a uniform solid sphere of mass $M$ and radius $R$ at a distance $r$ from its center, where $r < R$. The magnitude of the gravitational force on the object is proportional to which of the following quantities?
16. An object of mass m is moving east at a constant speed v. The object then makes a sharp turn and moves north at the same constant speed v. What is the change in the object's translational kinetic energy?
17. A drag car has translational kinetic energy $2.0\times10^5\,\text{J}$ at speed $20\,\text{m/s}$; determine the car's mass from these values.
18. A geostationary satellite orbits Earth at radius $r_{geo}$. A spy satellite is placed in a circular orbit at radius $r = \frac{r_{geo}}{4}$. How many times does the spy satellite orbit Earth while the geostationary satellite completes one orbit?
19. A vector $\vec{F}$ can be written as $\vec{F} = F_x\hat{i} + F_y\hat{j}$ where $F_x = 12$ N and $F_y = -5$ N. If this vector is rotated counterclockwise by $90°$ about the origin, what are the components of the resulting vector $\vec{F}'$?
20. Vector $\vec{A}$ has a magnitude of 8 units, and vector $\vec{B}$ has a magnitude of 5 units. The vector $\vec{C}$ is defined as $\vec{C} = \vec{A} - \vec{B}$. Which of the following is a possible magnitude for vector $\vec{C}$?

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