Question

Derive an expression for the magnitude of the acceleration of the system using Newton’s laws given the presence of kinetic friction

Answer 1

"Newton's 2^nd law of motion" says that the acceleration of an object is directly proportional to the force which applied on it and inversely proportional to the object's mass.

Then, we have

a = F / m

The total force on an object subject to friction is equal to the sum of an applied force and the frictional force.

But the frictional force opposes motion & it's negative relative to the forward force.

Then, we have

F = F_applied - F_frictional

We know that, the friction force is the product of friction coefficient and the normal force which in the absence of extra downward forces.

F = F_applied - _k N

where, N = normal force = m g

then, we get

F = F_applied - _k m g

Therefore, an expression for the magnitude of the acceleration of a system which will be given by -

a = F / m

a = (F_applied - _k m g) / m