Question

A crate of mass m1 = 15.3 kg is pulled by a massless rope up a 36.9° ramp. The rope passes over an ideal pulley and is attached to a hanging crate of mass m2 = 16.3 kg. The crates move 1.4 m, starting from rest.

Find the work done by gravity on the sliding crate.

A crate of mass m1 = 12.4 kg is pulled by a massless rope up a 36.9° ramp. The rope passes over an ideal pulley and is attached to a hanging crate of mass m2 = 16.3 kg. The crates move 1.70 m, starting from rest. If the frictional force on the sliding crate has magnitude 21.5 N and the tension in the rope is 121.5 N, find the total work done on the sliding crate.

The total work done on the sliding crate is

Answer 1

here,

1)

the mass of sliding crate , m1 = 15.3 kg

theta = 36.9 degree

s = 1.4 m

the work done by gravity on the sliding crate , Wg = - change in gravitational potential energy

Wg = - (m1 * g * s * sin(theta))

Wg = - 15.3 * 9.81 * 1.4 * sin(36.9)

Wg = - 126.1 J

2)

the mass of sliding crate , m1 = 12.4 kg

theta = 36.9 degree

s = 1.7 m

the tension in the rope , T = 121.5 N

frictional force , ff = 21.5 N

the total Work done on sliding crate , W = Wff + Wg + Wt

W = (- ff * s ) + ( - m1 * g * s * sin(theta) + (T * s))

W = 1.7 * ( - 21.5 - 12.4 * 9.81 * sin(36.9) + 121.5) J

W = 45.9 J