Question

A 215−kg crate is being pushed across a horizontal floor by a force P that makes an angle of 30.5

below the horizontal. The coefficient of kinetic friction is 0.265 . What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

Answer 1

To find the magnitude of the force P, we need to calculate the net work done by it and the kinetic frictional force. If the net work is zero, the force P will be balanced by the kinetic frictional force.

Step-by-step explanation:

To find the magnitude of the force P, we need to calculate the net work done by it and the kinetic frictional force. If the net work is zero, the force P will be balanced by the kinetic frictional force.

The net work done is given by the formula: W_net = W_P - W_fr, where W_P is the work done by force P and W_fr is the work done by kinetic friction.

Since the crate is being pushed horizontally, the work done by P can be calculated as W_P = P * d * cos(theta), where d is the displacement of the crate. The work done by kinetic friction can be calculated as W_fr = mu_k * N * d, where mu_k is the coefficient of kinetic friction and N is the normal force.

Setting the net work to zero, we can solve for P: 0 = P * d * cos(theta) - mu_k * N * d. Now, substitute the values and solve for P.