Final answer:
The magnitude and direction of the static frictional force acting on the refrigerator can be found using the equation fs(max) = μsN, where fs(max) is the maximum static frictional force, μs is the coefficient of static friction, and N is the normal force. The maximum pushing force that can be applied before the refrigerator starts to move is equal to the maximum static frictional force.
Step-by-step explanation:
The magnitude and direction of the static frictional force that the floor exerts on the refrigerator can be found using the equation fs(max) = μsN, where fs(max) is the maximum static frictional force, μs is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the refrigerator, which is mg, where m is the mass of the refrigerator and g is the acceleration due to gravity. Therefore, the magnitude of the static frictional force is fs(max) = μs(mg). The direction of the static frictional force is opposite to the direction of the applied force, which in this case is in the -x direction. So, the static frictional force is -fs(max) in the +x direction.
To determine the maximum pushing force that can be applied to the refrigerator before it just begins to move, we need to compare the applied force to the maximum static frictional force. If the applied force is less than or equal to the maximum static frictional force, the refrigerator will not move. If the applied force is greater than the maximum static frictional force, the refrigerator will start to move. So, the magnitude of the largest pushing force that can be applied to the refrigerator before it just begins to move is equal to the magnitude of the maximum static frictional force, which is fs(max) = μs(mg).