Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 5 - Section 5.1 - Using Newton’s Second Law - Example - Page 72: 5.1

Answer

a) $5.2 \ m/s^2$ b) $532 \ N$

Work Step by Step

We first break the forces into x and y components: $F_{nx} + F_{gx} = ma_x$ $F_{ny} + F_{gy} = ma_y$ We see that the x-component can be simplified as follows: $F_{nx} + F_{gx} = ma_x$ $ mgsin\theta= ma_x$ $ gsin\theta= a_x$ Thus: $a_x = (9.8)(sin32^{\circ}) = 5.2 \ m/s^2$ We use the y component to find the normal force: $F_{ny} + F_{gy} = ma_y$ $F_n = mgcos\theta $ $F_n = 65(9.81)(cos32^{\circ})=532 \ N $
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