You are tilting a bookcase to the side to clean under it, as schematically shown

Question

You are tilting a bookcase to the side to clean under it, as schematically shown on the Figure 1. Assume that the bookcase is evenly loaded with books (not shown here). Using protractor, you measure the maximum angle to which you can tilt the bookshelf as beta=18degree, i.e. if you tilt it further, it tips over. How tall is the bookcase, i.e. what is the length of the AC line segment on the Figure 1, if the distance AB (base length of the bookcase, see Figure 1) is AB = 85 cm? Report your answer in both meters, and centimeters.

Explanation / Answer

balancing torque

mg sin 18 (AC) = mg cos 18 ( AB)

AB = AC tan 18

AC = 261.6 cm

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