Practice Test 12 - AP Physics C Mechanics

20 questions. Answer them in any order, then submit to see your score and every explanation.

An object is in uniform circular motion. Which of the following statements about the work done on the object during any time interval is correct?
An ideal spring is fixed at one end to a wall. When a block attached to the other end is at position $x > 0$ , the spring is stretched. When the block is at $x < 0$ , the spring is compressed. The equilibrium position is at $x=0$ . Which statement correctly describes the force $\vec{F}_s$ exerted by the spring on the block?
A stationary $8.0\ \text{kg}$ object explodes into $5.0\ \text{kg}$ and $3.0\ \text{kg}$ fragments; the $5.0\ \text{kg}$ fragment moves at $-4.0\ \text{m/s}$ . Determine the $3.0\ \text{kg}$ fragment velocity.
A particle moving in one dimension experiences a net force given by $F(t) = F_0 \cos(\omega t)$ . What is the change in the particle's momentum during the time interval from $t=0$ to $t=\pi/(2\omega)$ ?
Which of the following statements must be true?
A projectile is launched at angle $\theta$ above horizontal with initial speed $v_0$ . At the highest point of its trajectory, which kinematic quantities have their minimum values?
A particle's motion is described by the differential equation $\frac{d^2x}{dt^2} + 9x = 12\cos(3t)$ . To determine if any component of the motion exhibits simple harmonic motion, which analysis is most appropriate?
A $2.0\,\text{kg}$ cart at $+3.0\,\text{m/s}$ sticks to a $1.0\,\text{kg}$ cart at rest. What is the final velocity?
A physical system undergoes oscillatory motion described by $x(t) = A e^{-\gamma t} \cos(\omega t)$ . Is this simple harmonic motion?
Two blocks of masses $m_1 = 3.0$ kg and $m_2 = 5.0$ kg are connected by a light string over a massless pulley. Block 1 is on a horizontal frictionless surface, and block 2 hangs vertically. When drawing separate free-body diagrams for each block, the tension forces in the string appear as $T_1$ on block 1 and $T_2$ on block 2. Which statement about these tension forces is correct?
If the same force is applied to an object of mass $2m$ , also initially at rest, for the same time interval $T$ , what is the impulse of the force on the second object?
Two uniform disks, each of mass $M$ and radius $R$ , are mounted on a common axle. Initially, the upper disk rotates at $\omega_1 = 10 \text{ rad/s}$ and the lower disk rotates at $\omega_2 = -6 \text{ rad/s}$ (opposite direction). A clutch mechanism suddenly connects the disks so they rotate together. What is their common angular velocity after engagement?
A model rocket launches vertically from $y_0=0\ \text{m}$ with initial speed $v_0=18\ \text{m/s}$ upward. After launch, the engine cuts off immediately, so the only force is gravity with $a=-9.8\ \text{m/s}^2$ . Air resistance is neglected, and the motion is one-dimensional along the vertical axis. Analyze the motion from $t=0$ until the rocket reaches its peak. Based on the scenario described, determine the maximum height reached by the projectile.
A particle moves along a curved path in three-dimensional space. Its velocity vector is $\vec{v}$ and its acceleration vector is $\vec{a}$ . Which of the following scalar quantities is equivalent to the instantaneous rate of change of the particle's kinetic energy with respect to time?
A particle is subject to a conservative force described by $F(x) = -ax^3$ , where $a$ is a positive constant. If the potential energy is taken to be zero at $x=0$ , what is the potential energy function $U(x)$ ?
An object of mass $m$ , starting from rest, is acted upon by a constant force $F$ for a time $t$ . Its change in momentum is $\Delta p$ and its change in kinetic energy is $\Delta K$ . If the time interval is doubled to $2t$ while the force remains the same, how do the new change in momentum $\Delta p'$ and change in kinetic energy $\Delta K'$ compare to the originals?
A hoop of radius $R$ and mass $M$ is pivoted at its rim and oscillates as a physical pendulum. The rotational inertia of a hoop about its center is $MR^2$ . What is the period of the hoop for small-amplitude oscillations?
A 1500 kg elevator starts from rest and reaches 4.0 m/s in 5.0 s while moving upward, rising 10 m during that interval. The cable tension does work that increases both gravitational potential energy $mgh$ and kinetic energy $\tfrac12 mv^2$ . Take $g=9.8\,\text{m/s}^2$ and neglect frictional losses. Treat the power as the average rate of total mechanical energy increase over the 5.0 s. In the given system, what is the average power output of the system described?
A projectile is fired from ground level with an initial velocity of 50 m/s at an angle of 37° above the horizontal. Assuming negligible air resistance and using $g \approx 10$ m/s $^2$ , what is the maximum vertical height reached by the projectile? (sin 37° ≈ 0.6, cos 37° ≈ 0.8)
A thin uniform rod of mass $M$ and length $L$ has a linear mass density that varies as $\lambda(x) = \lambda_0\left(1 + \frac{x}{L}\right)$ , where $x$ is measured from one end. What is the $x$ -coordinate of the center of mass?

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