A body, of mass m, moving along a horizontal plane with a speed v, due to the presence

A body, of mass m, moving along a horizontal plane with a speed v, due to the presence of a friction force, stops after passing the path S. Determine the friction force, the work of this force and the separated body.

Given:

m (kilogram) is the mass of a certain body;

v (meter per second) is the speed at which the body is moving;

S (meter) – the path that the body took to stop.

It is required to determine F friction (Newton) – friction force, A (Joule) – friction force work and Q (Joule) – released heat.

Let’s find the acceleration with which the body braked:

S = a * t ^ 2/2, taking into account the fact that in this case t = v / a, we get:

S = a * (v / a) ^ 2/2 = v ^ 2 / (2 * a), from here we find that:

a = v ^ 2 / (2 * S).

Then the friction force will be equal to:

F friction = m * a = m * v ^ 2 / (2 * S).

The work of the friction force will be equal to:

A = F friction * S = m * v ^ 2 / (2 * S) * S = m * v ^ 2/2.

This work will be spent on the release of heat, that is:

Q = A = m * v ^ 2/2.

Answer: the friction force is equal to m * v ^ 2 / (2 * S), the work of the friction force and the released heat will be equal to m * v ^ 2/2.