(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](https://tex.z-dn.net/?f=%5Csum%20F%20%3D%20ma%20%3D%200)
So we have
![F-F_f = 0](https://tex.z-dn.net/?f=F-F_f%20%3D%200)
which means that the frictional force is equal in magnitude to the pushing force:
![F_f = F = 252 N](https://tex.z-dn.net/?f=F_f%20%3D%20F%20%3D%20252%20N)
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](https://tex.z-dn.net/?f=F_%7Bmax%7D%20%3D%20%5Cmu%20mg)
where
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