Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 9 - Work and Kinetic Energy - Exercises and Problems: 22

Answer

The particle's velocity at x = 2 m is 5.1 m/s The particle's velocity at x = 4 m is 4.0 m/s

Work Step by Step

The work done on the particle is equal to the area under the force versus position graph. We can find the work done during the interval 0 - 2 m: $W = \frac{1}{2}(10~N)(2~m)$ $W = 10~J$ We can use the work-energy theorem to find the particle's velocity at x = 2 m. $KE_2 = KE_1+W$ $\frac{1}{2}mv_2^2 = \frac{1}{2}mv_1^2+W$ $v_2^2 = \frac{mv_1^2+2W}{m}$ $v_2 = \sqrt{\frac{mv_1^2+2W}{m}}$ $v_2 = \sqrt{\frac{(2.0~kg)(4.0~m/s)^2+(2)(10~J)}{2.0~kg}}$ $v_2 = 5.1~m/s$ The particle's velocity at x = 2 m is 5.1 m/s We can find the work done during the interval 2 - 4 m: $W = \frac{1}{2}(-10~N)(2~m)$ $W = -10~J$ The total work done on the particle during the interval 0 - 4 m is zero. Therefore the kinetic energy at x = 4 m is the same as the kinetic energy at x = 0. Therefore, the particle's velocity at x = 4 m is 4.0 m/s
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.