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 102: 28

Answer

(a) F = 19.0 N and $a = 1.03~m/s^2$ (b) F = 14.0 N and $a = 0.757~m/s^2$

Work Step by Step

(a) $F = \sqrt{F_1^2 + F_2^2}$ $F = \sqrt{(10.2 ~N)^2+(16.0 ~N)^2} = 19.0 ~N$ $ma = F$ $a = \frac{F}{m} = \frac{19.0 ~N}{18.5 ~kg} = 1.03~m/s^2$ (b) $F_x = F_{1x} = 10.2 ~cos(30^{\circ}) ~N = 8.83 ~N$ $F_y = F_{1y} + F_2 = -10.2 ~sin(30) ~N + 16.0 ~N = 10.9 ~N$ $F = \sqrt{F_x^2 + F_y^2}$ $F = \sqrt{(8.83 ~N)^2+(10.9 ~N)^2} = 14.0 ~N$ $ma = F$ $a = \frac{F}{m} = \frac{14.0 ~N}{18.5 ~kg} = 0.757~m/s^2$
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