Q.A body of mass 37 kg rests on a rough horizontal surface. The minimum horizontal force required to just start the motion is 68.5 N. In order to keep the body moving with constant velocity, a force of 43 N is needed. What is the value of a) coefficient of static friction? and b) coefficient of kinetic friction?

When an applied horizontal force $F$ acts on a body resting on a surface but the body does not move, the frictional force balancing $F$ is called the force of static friction, $F_s$. Static friction is a self-adjusting force — as $F$ increases from a small value, $F_s$ increases right along with it to keep balancing it exactly, up to a maximum value called the limiting force of friction, $F_L$, reached just before the body starts to slide. The laws of static friction state that $F_L$ is directly proportional to the normal reaction $N$ between the two surfaces, $F_L = \mu_s N$, where $\mu_s = F_L/N$ is the coefficient of static friction; that $F_L$ is independent of the apparent area of contact (for a fixed $N$); and that $F_L$ depends on the materials and surface nature of the two bodies in contact.

Once the body actually starts sliding, the opposing force typically drops and is then called the force of kinetic (or dynamic) friction, $F_k$. The laws of kinetic friction are directly analogous: $F_k = \mu_k N$, where $\mu_k = F_k/N$ is the coefficient of kinetic friction; $F_k$ is independent of the shape and apparent contact area of the surfaces; it depends on the nature and material of the surfaces in contact; and, provided the sliding speed is neither too large nor too small, its magnitude is independent of that speed. For the same pair of surfaces, the coefficient of static friction is always somewhat larger than the coefficient of kinetic friction, which is exactly why it takes a larger force to start a body sliding than to keep it sliding steadily afterward.