Question

A person pushes on a 57-kg refrigerator with a horizontal force of 267 N; the - sign indicates that the force points in the +x direction. The coefficient of static friction is 0.65. (a) If the refrigerator does not move, what are the magnitude and direction of the static frictional force that the floor exerts on the refrigerator? (b) What is the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move?

Answer 1

(a) -267 N

Explanation: if the refrigerator is not moving, it means that the net force acting on it is zero.

We are only interested in the motion along the horizontal direction; there are two forces acting in this direction:

- The pushing force, forward, F=+267 N

- The static frictional force, backward, $F_f$

Since the net force must be zero, we have

$F+F_f =0F_f = -F = -267 N$

(b) 363.1 N

The largest pushing force that can be applied to the refrigeratore before it begins to move is equal to the magnitude of the maximum static frictional force, which is given by:

$F_f = \mu mg$

where

$\mu=0.65$ is the coefficient of static friction

m = 57 kg is the mass of the refrigerator

g = 9.8 m/s^2 is the gravitational acceleration

Substituting,

$F_f = (0.65)(57 kg)(9.8 m/s^2)=363.1 N$