Question

Is it true that limiting equilibrium means $ma = 0$ in $F - f = ma$ ?

Answer 1

Limiting friction is a term that corresponds to the maximum value of the friction that can exist between two surfaces in a particular situation. When a body is under limiting equilibrium, the forces will always sum up to 0. This concept will be used in the question to get the answer.

Complete step by step answer:
Limiting friction is that value of friction which is the maximum and would not be increased further even if more force is applied. This is also called the saturation condition. When the value of limiting friction is approached, the system is under limiting equilibrium. The body will either move with a uniform velocity or will be on the verge to move.If it is on the verge to move, there is no motion. Hence, we may consider that the acceleration is zero in such a case.

If the body is moving with a uniform velocity, there will be no change in the velocity. Hence, no acceleration will act on the system. So, in all cases, if the body is under limiting equilibrium, the acceleration is zero.In the given expression $F - f = ma$ , $F$ represents the force applied externally, $f$ is the frictional force and a is the acceleration.If acceleration is zero, $ma = 0$.

Hence, it is true that limiting equilibrium means $ma = 0$ in $F - f = ma$.

Note: In limiting equilibrium, it is fundamental to note that the frictional force does not exceed no matter how much external force is applied because it is dependent on the normal reaction of the object and the coefficient of friction between the surfaces. In a particular situation, these two factors do not change normally and hence the frictional force also does not change.