Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 4 - Dynamics: Newton's Laws of Motion - Problems - Page 101: 15

Answer

The acceleration is $2800 ~m/s^2$ which is around 280 g's. The force felt by the 68-kg occupant is $1.9\times 10^5 ~N$.

Work Step by Step

$v = (35 ~\frac{km}{h})(\frac{1000 ~m}{1 ~km})(\frac{1 ~h}{3600 ~s})$ $v = 9.722 ~m/s$ $a = \frac{v^2-v_0^2}{2x}$ $a = \frac{-(9.72 ~m/s)^2}{(2)(0.017 ~m)}$ $a = -2779 ~m/s^2$ $a \approx -2800 ~m/s^2$ The magnitude of acceleration is $2800 ~m/s^2$. Next, finding the number of g's: $\frac{2779 ~m/s^2}{9.8 ~m/s^2} \approx 280\times g$ Now finding the force felt by the occupants of the car: $F=ma$ $F = (68 ~kg)(2800 ~m/s^2)$ $F = 1.9\times 10^5 ~N$
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