Den Hartog’s Mechanics

A web-based solutions manual for statics and dynamics

Problem 41

The free-body diagram of the balance arm is

The equilibrium equation for moments about the pivot, O, is

\sum M_O = W_2 b \cos\alpha - W_1 b \cos\alpha + w a \sin\alpha = 0

Since Den Hartog asks only for a “relation” between \alpha and W_1 - W_2, this equation could be our answer. But it’s easy enough to rearrange it to

\tan\alpha = \frac{W_1 - W_2}{w} \cdot \frac{b}{a}

which is the answer given in the book for part a).

The answer to part b) comes from studying the answer to part a). To make \alpha large, \tan\alpha must be large. And to get a large \tan\alpha when W_1 - W_2 is small, b/a must be large.

Problem 42Problem 40

Last modified: January 22, 2009 at 8:32 PM.