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 116: 63

Answer

The tension in each wire is $191.6N$.

Work Step by Step

To find the tension in each wire, we need to translate these tension forces into their vertical components. So first, the angle $\theta$ relative to the vertical needs to be found. In the image below, on the left, $\theta$ is shown to be inside a right triangle with 2 known sides. We see that $$\cos\theta=\frac{1.5}{2}=0.75$$ The vertical component of each tension force would be $T\cos\theta=0.75T$ The tension forces help to keep the chandelier from falling due to its weight. Therefore, the sum of 3 tension forces from 3 wires and the weight balance each other as the chandelier is static in the air. $$3\times 0.75T=mg$$ $$2.25T=44\times9.8=431.2$$ $$T=191.6N$$
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