Question 1

A simple pendulum is made from a 0.205-kg metal ball attached to a massless string of length 75 cm. The pendulum is held horizontally and then released from rest. Find the speed of the metal ball (in m/s) when the pendulum passes through the lowest point.

Accepted Answer

$$3.8$$

Question 2

A steel spring stores 18 J of potential energy when it is stretched by 2.40 cm. Determine the spring constant of the spring in N/m.

Accepted Answer

$$62500$$

Question 3

A 2.3 kg object traveling at 4.1 m/s in the positive x direction catches up and collides with a 3.5 kg object moving in the same direction at 2.1 m/s. The two objects stick together in a totally inelastic collision. What is the final velocity in m/s of the combined object?

Accepted Answer

$$2.7$$

Question 4

A tennis ball of mass $$m = 0.25 kg$$, moving horizontally with speed $$15.0 m/s$$, makes a perfectly elastic collision with a wall and after the collision rebounds with velocity $$-11.0 m/s in $$the opposite direction. The ball is in contact with the wall for $$0.015 s. $$The magnitude of the average force exerted on the ball by the wall is closest to:

Accepted Answer

$$670 N$$

Question 5

In a bike repair shop a wheel is given an initial angular velocity of $$+526$$ rad/s. After that, the wheel makes $$234$$ full revolutions and stops. What is the magnitude of the angular acceleration of the wheel in rad/s$$^2$$?

Accepted Answer

$$118$$

Question 6

A 3.5 kg block is attached to a spring with a spring constant of $$150 N/m. $$The block is then displaced $$20 cm $$from equilibrium and is released from rest. Find the maximum speed (in m/s) achieved by the block.

Accepted Answer

$$1.4$$

Question 7

In order to find the speed of a $$7.8$$ gram bullet as it is fired into a $$5.8 kg $$wooden block resting on a horizontal frictionless surface, note that the block (with the bullet stuck in it) moves with speed of $$2.3 m/s. $$Find the initial speed of the bullet.

Accepted Answer

$$1710 m/s$$

Question 8

A hoop is given an initial linear speed of $$10.0 m/s $$and is sent rolling up a $$30-$$degree incline without slipping. Using the conservation of energy, how far along the incline (in meters) will the hoop roll before stopping? (Use $$g = 9.8 m/s$^2.)$$

Accepted Answer

$$11$$

Question 9

A wheel rotating about a fixed axis has an angular position given by $$	heta = 4.0 - 6.0t + 2.0t^2$, where $$	heta$$ is measured in radians and t$ in seconds. At t = 1$ s, the magnitude of angular acceleration in rad/s^2$ is:

Accepted Answer

$$2$$

Question 10

Two unequal blocks of mass $$4.0 kg $$and $$5.0 kg $$are suspended from either end of a light rope over a massless pulley as shown in the figure. The blocks are released from rest. After the heavier block descends $$0.56 m$$, what is the speed of the blocks in m/s? Select the closest answer.

Accepted Answer

$$2.1$$

Question 11

A ball (a spherical shell) with $$I = \frac{2}{3}MR^2$ of mass M = 0.13$ kg and radius R = 13.3$ cm rolls without slipping a distance of 1.8$ meters down an incline which makes an angle of 20$$^{\circ}$$ with horizontal. If the sphere starts from rest, what is its speed at the bottom of the incline?

Accepted Answer

$$2.3 m/s$$

Question 12

A bowling ball of mass $$M = 10 kg $$and radius $$R = 12 cm is $$rolling without slipping along a horizontal surface with speed of $$0.9 m/s. $$Find the total kinetic energy (in Joules) due to the rotational and the translational motion of the ball. The bowling ball can be treated as a solid sphere, with $$I = \frac{2}{5}MR^2$.

Accepted Answer

$$4.0$$

Question 13

A mass $$1.7 kg is $$attached to a vertical spring with a spring constant $$k = 121 N/m. $$Originally, the spring is unstretched and the mass is released from rest. How far down (relative to initial position) will the mass fall?

Accepted Answer

$$0.14 m$$

Question 14

A small metal sphere with mass $$1.3 kg $$and negligible radius is fixed at the end of a $$1.2$$ meter rod. If mass of the rod is $$1.4 kg$$, find the total moment of inertia of the system (i.e., stick+handle) if it spins at 10 rad/s about an axis which is perpendicular to the rod and passes through its center (use the moment of inertia for a thin rod about its center as $$I = \frac{1}{12}ML^2$).

Accepted Answer

$$5.8$$

Question 15

A firework rocket moving with velocity $$100 m/s in $$the positive x-direction and with mass $$1.0 kg $$explodes into two parts of equal mass. One half of the mass is observed moving in the positive x-direction with velocity $$250 m/s. $$Find the velocity (in m/s) of the second half.

Accepted Answer

$$-150$$

Question 16

The mass of Sun is $$2.0 	imes 10$$^{30}$$ kg and the mass of Earth is 6.0$$ 	imes $$10^{24} kg. If $$the distance between Sun and Earth is $$1.5 	imes 10$$^{11}$$ m, what is the speed of the Sun as it orbits the center of mass of the Sun-Earth system? (Assume the Sun and Earth move in circular orbits about their common center of mass.)

Accepted Answer

$$0.45 m/s$$

Physics Practice Exam: Mechanics, Energy, and Rotational Motion

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