Question 1

A force $$F is $$applied at an angle $$	heta to $$the horizontal, moving a box a distance $$d$$ along a flat surface as shown in the first image. What is the work done by the force $$F$$?

Accepted Answer

$$W = Fd \cos	heta$$

Question 2

A person holds a brick of mass $$m at a $$height $$h$$ above the ground, as shown in the second image. What is the gravitational potential energy of the brick relative to the ground?

Accepted Answer

$$PE_G = mgh$$

Question 3

A block of mass $$m$$ slides on a frictionless surface with velocity $$v ($$third image). What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$

Question 4

A box of mass $$m$$ starts from rest at height $$h on a $$frictionless incline (fourth image). What is its speed at the bottom of the incline?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 5

A block of mass $$m is $$compressed against a spring with spring constant $$k by $$distance $$d$$ and released on a surface with friction coefficient $$\mu ($$fifth image). What is the equation for the velocity $$v_f of $$the block as it leaves the spring?

Accepted Answer

Question 6

Two objects, $$m_1$$ and $$m_2$$, collide as shown in the sixth and seventh images. Which quantity is always conserved in any collision?

Accepted Answer

Total linear momentum

Question 7

Given three masses $$m_1 = 0.01$ kg at (1$$,1)$$, m_2$ = 0.02 kg at$$ $$(2,3)$$, and $$m_3 = 0.03$ kg at (4$$,2)$$ (eighth image), what is the x$-coordinate of the center of mass?

Accepted Answer

$$x_{cm} = 2.83 m$$

Question 8

A particle moves in a circle with velocity $$v$$ and radius $$R ($$ninth image). What is the magnitude of its centripetal acceleration?

Accepted Answer

$$a_c = \frac{v^2$}{R}$$

Question 9

A force $$F is $$applied at a distance $$r$$ from point $$O at an $$angle $$	heta ($$tenth image). What is the torque $$	au$$ about point $$O$$?

Accepted Answer

$$	au = Fr \sin	heta$$

Question 10

A mass $$m$$ moves with velocity $$v at a $$distance $$r$$ from a fixed point (eleventh image). What is the magnitude of its angular momentum $$L$$ about the point?

Accepted Answer

$$L = mvr \sin	heta$$

Question 11

Two masses, $$3 kg $$and $$2 kg$$, are separated by $$0.8 m ($$twelfth image). At what distance from the $$3 kg $$mass is their center of mass?

Accepted Answer

$$x = 0.48 m$

Question 12

A figure skater spins with arms outstretched (large $$I$$, small $$\omega) $$and then pulls her arms in (thirteenth image). What happens to her angular velocity $$\omega$$?

Accepted Answer

$$\omega$$ increases

Question 13

According to Newton's law of universal gravitation (fourteenth image), what is the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by distance $$r$$?

Accepted Answer

$$F = G \frac{m_1$ m_2$}{r^2$}$$

Question 14

A planet orbits the Sun in an elliptical path. According to Kepler's second law, what is true about the area swept out by the line joining the planet and the Sun?

Accepted Answer

It is constant for equal time intervals.

Question 15

A rolling object has both translational and rotational kinetic energy. Which equation correctly expresses its total kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}Mv_{CM}^2 + \frac{1}{2}I_{CM}\$$omega^2$$

Question 16

A satellite of mass $$m$$ orbits a planet of mass $$M at $$radius $$r. $$What is the total mechanical energy of the satellite in a circular orbit?

Accepted Answer

$$E = -\frac{1}{2}\frac{GmM}{r}$$

Work, Energy, Momentum, Rotational Dynamics, and Gravitation: Study Guide

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