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 10 - Interactions and Potential Energy - Exercises and Problems: 19

Answer

The cart was moving with a speed of 3.0 m/s just before it hit the spring.

Work Step by Step

The cart's kinetic energy just before it hit the spring is equal to the energy $U_s$ stored in the spring after the spring is compressed by 60 cm. We can find the speed of the cart just before it hit the spring. Therefore; $KE = U_s$ $\frac{1}{2}mv^2=\frac{1}{2}kx^2$ $v^2=\frac{kx^2}{m}$ $v=\sqrt{\frac{kx^2}{m}}$ $v=\sqrt{\frac{(250~N/m)(0.60~m)^2}{10~kg}}$ $v = 3.0~m/s$ The cart was moving with a speed of 3.0 m/s just before it hit the spring.
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