Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 4 - Forces and Newton's Laws of Motion - Problems - Page 118: 90


The required time is $8.2s$

Work Step by Step

1) Find the acceleration $a$ of the girl - The weight of the girl and the sled is manifest in the form $Mg\sin30=65\times9.8\sin30=318.5N$, which pushes them downward. - The wind also pushes them downward with $F=105N$ - Kinetic friction opposes the motion: $f_k=\mu_kF_N=\mu_kMg\cos30=0.15(65\times9.8\cos30)=82.75N$ (Normal force $F_N$ here is equal with the vertical component of the weight of the girl and the sled, which is $Mg\cos30$) Newton's 2nd Law: $$Mg\sin30+F-f_k=Ma$$ $$a=\frac{Mg\sin30+F-f_k}{M}=5.24m/s^2$$ 2) Find $t$ We have $a=5.24m/s^2$, $v_0=0$ and slope length $x=175m$ $$x=v_0t+1/2at^2=1/2at^2$$ $$t=8.2s$$
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