Question

An old metal bathtub with mass equal to 100.0 kg is found on a flat road. The coefficient of static friction between the bathtub and the road is equal to 0.500. The coefficient of kinetic friction between the bathtub and the road is equal to 0.300. A horizontal pushing force is applied to the bathtub, which is initially at rest, in attempt to move the bathtub. Identify the magnitude of the frictional force in each of the following situations.
(a) If the pushing force is equal to 100 N.

(b) If the pushing force is equal to 294 N.

(c) If the pushing force is equal to 490 N.

(d) If the pushing force is equal to 500 N

Answer 1

Until the pushing force exceeds the maximum static frictional force, the bath tub will not move.
Till this point, the static frictional reaction force will be equal to the pushing force,

Max Static Force,

Therefore, whenever the pushing force is less than the above value, frictional force will be equal to push force,

Whenever the push force exceeds the above value, it will be equal to dynamic frictional force,

Answers,
a)

b)

c)

As the push force exceeds the static force limit, it will be set into motion, and dynamics friction will start to act
d)