Question

A 1.10E+2 kg crate is being pushed across a horizontal floor by a force P that makes an angle of 25.5° below the horizontal. The coefficient of kinetic friction is 0.210. What should be the magnitude of P, so that the net work done by it and the kinetic frictional force is zero?

Answer 1

here,

mass of crate , m = 1.1 * 10^2 kg = 110 kg

theta = 25.5 degree

coefficient of kinetic friction , uk = 0.21

the normal force on crate , N = m * g + P * sin(theta)

and

as the net work done by it and the kinetic frictional force is zero

the net force on the crate is zero

so,

P * cos(theta) - kinetic friction force = 0

P * cos(theta) - uk * N = 0

P * cos(theta) - uk * ( m * g + P * sin(theta)) = 0

P * cos(25.5) - 0.21 * (110 * 9.81 + P * sin(25.5)) = 0

solving for P

P = 279 N

the magnitude of P is 279 N