Question

A 370 N force is pulling an 85.1-kg refrigerator across a horizontal surface. The force acts at an angle of 22.0 ° above the surface. The coefficient of kinetic friction is 0.237, and the refrigerator moves a distance of 9.44 m. Find (a) the work done by the pulling force, and (b) the work done by the kinetic frictional force.

Answer 1

A 370 N force is pulling an 85.1-kg refrigerator across a horizontal surface. The force acts at an angle of 22.0° above the surface. The coefficient of kinetic friction is 0.237, and the refrigerator moves a distance of 9.44 m. Find (a) the work done by the pulling force, and (b) the work done by the kinetic frictional force.

Solution

Here we have

$$\begin{array}{l} m = 85.1\,kg \\ F = 370\,N \\ \alpha = 22.0{}^{\circ} \\ \mu = 0.237 \\ S = 9.44\,m \\ \end{array}$$

We choose the x-axis parallel to horizontal surface, y-axis orthogonal to horizontal surface.

In y-axis we have second Newton's equation law $P + F \sin \alpha - mg = 0$, where $P$ is reaction of surface. From hence $P = mg - F \sin \alpha = 695.4\,N$,

We have friction force $F_f = \mu P$.

The pulling force done work $A = FS = FS \cos \alpha = 3239\,f$ (here $\alpha$ is angel between pulling force and translation).

The friction forces done work $A_F = F_f S = \mu P S = 1556\,f$ (because friction force is antiparallel to translation).

Answer:

a) The pulling force done work $A = 3239\,f$.

b) The friction forces done work $A_F = 1556\,f$