Den Hartog’s Mechanics

A web-based solutions manual for statics and dynamics

Problem 36

The free-body diagram of the hoist is given below. The three reaction forces are constrained in the horizontal and vertical directions as described in the problem statement.

The vertical equilibrium equation is

\sum F_y = R_C - P = 0

and its solution is R_C = P. The horizontal equilibrium equation is

\sum F_x = R_B - R_A = 0

and its solution is R_A = R_B. Notice that these two solutions give us two pure couples. Therefore, the moment about any point will be the algebraic sum of the two couples:

\sum M = P a - R_A c = 0

and the solution is

R_A = R_B = P \frac{a}{c}

which, except for the sign convention for the reactions at A and B, matches the answer at the back of the book.

Problem 37Problem 35

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