## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 8 - Problems - Page 313: 32

#### Answer

The sculpture can be tipped up to a maximum angle of $17.0^{\circ}$ before it falls over.

#### Work Step by Step

The sculpture can be tipped to a maximum angle when the center of gravity is directly above the balance point on the floor. If the sculpture is tipped more than this angle, the torque from gravity will cause the sculpture to tip over. We can draw a triangle with half of the sculpture's base, which has a length of 0.55 meters, and a line connecting the center of the base to the center of gravity, and this line has a length of 1.8 meters. The hypotenuse of the triangle is a line from the balance point to the center of gravity. Let $\theta$ be the angle when the center of gravity is directly above the balance point on the floor. $tan ~\theta = \frac{0.55~m}{1.80~m}$ $\theta = tan^{-1}(\frac{0.55~m}{1.80~m})$ $\theta = 17.0^{\circ}$ The sculpture can be tipped up to a maximum angle of $17.0^{\circ}$ before it falls over.

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