How high above floor can force P act so crate moves without tipping?

Question

crate is 2 ft wide, has a weight of 200 lb. coefficient of static friction is 0.35

Answer 1

Tip is a rotation caused by a net torque. Assume the pushing force is from left to right. At what height on the box must the push happen to tip it instead just slide it. The push needed to slide it is just greater than the static friction, so we find that first. Fsf = µFN and normal force = weight because the surface is flat.

Fsf = (0.35)(200 lb) = 70 lb.

A clockwise torque would be given by 70 lb acting at the unknown height (h). The counterclockwise torque is given by the normal force acting at the right lower corner which is 1 foot from the center of mass line (box is 2 feet wide). So that torque is (200 lb)(1 ft) = 200 lbft.

Set the torques equal and solve for h:

200 lbft = h(70 lb)

h = 200/70 = 2.7 ft.