Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 5 - Force and Motion - Exercises and Problems: 14

Answer

The mass is 0.25 kg

Work Step by Step

The graph shows us the acceleration versus the force. We can find the slope of the graph. On the graph, we can see that the acceleration is $a = 4~m/s^2$ when the force is $F = 1.0~N$. We can use the data pairs $(0,0)$ and $(4~m/s^2,1.0~N)$ to find the slope. $slope = \frac{\Delta a}{\Delta F}$ $slope = \frac{4~m/s^2 - 0~m/s^2}{1.0~N-0~N}$ $slope = 4~kg^{-1}$ We know that $F = Ma$. Then $\frac{1}{M} = \frac{a}{F}$ We can see that the inverse of the mass $M$ is equal to the slope of the acceleration versus force graph. $\frac{1}{M} = slope$ $M = \frac{1}{slope}$ $M = \frac{1}{4~kg^{-1}}$ $M = 0.25~kg$ The mass is 0.25 kg.
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