Conceptual question about blocks and friction

1. Jun 16, 2013

Hello everyone,

Two blocks M and m (M is more massive) are sliding freely with the same initial speed
across a floor with friction coefficient μk > 0, and they
come to a stop. Initially there is a distance x between
them. While they are sliding to a stop,

A) The distance between them becomes smaller
B) The distance between them becomes greater
C) The distance between them stays the same

So the equation that I tried with is (Coefficient of Friction) ( Normal Force ) = Friction.

According to this equation, M should have a larger normal force, therefore, a bigger frictional force. But the correct answer is C? Can someone explain this please?!?

2. Jun 16, 2013

QED Andrew

Your conclusion that the frictional force acting on the block of mass $M$ is larger in magnitude than the frictional force acting on the block of mass $m$ is correct. However, this conclusion does not contradict the fact that the distance between the two blocks stays the same. The block of mass $M$ is acted on by a larger force, but it also has a larger mass. These two factors will cancel out when we use $F = ma$ to calculate the acceleration of the block. The block of mass $M$ undergoes the same acceleration as the block of mass $m$ undergoes.

Consider a more rigorous analysis. The magnitude of the frictional force $F$ acting on the block of mass $m$ is given by

$$F = -\mu_k n$$

Therefore, the block of mass $m$ undergoes an acceleration $a$ given by

$$a = \dfrac{F}{m} = \dfrac{-\mu_k n}{m} = \dfrac{-\mu_k mg}{m} = -\mu_kg$$

Note the acceleration is independent of the mass of the block. A similar analysis applies to the block of mass $M$.

Last edited: Jun 16, 2013