Answer
84.2 N
Work Step by Step
The crate weighs 165N and we are told the frictional coefficients are fs = 0.510 and fk = 0.32. To find the frictional force we need to find the normal force. Since the only forces in the y direction are the normal force and the weight of the crate, we know that the normal force, N = 165N. Then to find the maximum force of static friction we take Ff,max = N*fs = 84.2 N. In order to have the crate be on the verge of sliding you need to push with a force equal to the maximum Frictional Force, Ff, max
