Question

You are helping your friend move a new refrigerator into his kitchen. You apply a horizontal force of 252 N in the negative x direction to try and move the 56 kg refrigerator. The coefficient of static friction is 0.61. (a) How much static frictional force does the floor exert on the refrigerator? Give both magnitude (in N) and direction. magnitude N direction (b) What maximum force (in N) do you need to apply before the refrigerator starts to move?

Answer 1

(a) 252 N, opposite to the applied force

There are two forces acting on the refrigerator in the horizontal direction:

- the pushing force of 252 N, F, forward

- the frictional force, Ff, pulling backward

In this case, the refrigerator is not moving: this means that its acceleration is zero. According to Newton's second law, this also means that the net force acting on the refrigerator is also zero:

$\sum F = ma = 0$

So we have

$F-F_f = 0$

which means that the frictional force is equal in magnitude to the pushing force:

$F_f = F = 252 N$

and the direction is opposite to the pushing force.

(b) 334.8 N

The force that must be applied to the refrigerator to make it moving is equal to the maximum force of friction, which is given by:

$F_{max} = \mu mg$

where

$\mu = 0.61$ is the coefficient of static friction

m = 56 kg is the mass of the refrigerator

g = 9.8 m/s^2 is the acceleration of gravity

Substituting:

F_max = (0.61)(56 kg)(9.8 m/s^2)=334.8 N