Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 7 - Kinetic Energy and Work - Problems - Page 171: 13c


$Work$ $Done = -5.8\times10^{4}$ $J$

Work Step by Step

We know that: $W= F.d$ To find W, we need the values of distance and the force. Since they are travelling with an initial velocity of $37m/s$ and with a retardation of $2m/s^{2}$, we get the distance $d$ by using $v^{2}= v_{o}^{2}+2ad$ Plugging respective values in it, we get: $0^{2}=37^{2}+2(−2)d$ $\frac{−37^{2}}{−4}=d$ $d ≈3.4×10^{2}$ $m$ Now, we need to find the force. We know; $F= ma$ So plugging in the values of mass and acceleration, we get: $F=85\times(-2)= -170$ $N$ Now putting the values of force and distance in the expression $W=F.d$ and solving we get: $W= (-170)\times 3.4\times 10^{2}= -57800J$ $W= -5.78\times 10^{4}J\approx -5.8\times 10^{4}$ $J$
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