10.8 Friction between horizontal surfaces

Friction plays different roles in motion. Consider the case of a block on a plane slab (plank), which, in turn, is placed on a horizontal surface. Typically, friction moderates the motion of a body. In other words, friction retards motion. On the other hand, friction also acts as the “cause” of the motion under certain circumstance. In the role of a “moderator”, friction negates external force. In the role of the “cause” of motion, it is either the sole external force or the greater external force on the body responsible for its motion.

In the "block - plank" set up, we can apply force either on the block or on the plank or on both of them simultaneously. The resulting motion depends on varieties of factors such as friction, external force and location of application of external force etc.

In order to analyze situation as mentioned above, we need to have clear understanding of the way friction works on each of bodies. In this module, we seek to organize ourselves so that we have well thought out plan and method to deal with this kind of motion.

First thing that we need to know is about friction – its magnitude and direction. Secondly, we need to know the nature of friction – whether friction is static, limiting or kinematic. Once, we have complete picture of various friction forces at different interfaces, we are in position to draw the free body diagram and analyze the motion.

Friction between interfaces

We shall consider three cases. In order to keep the matter simple, we make one simplifying assumption that the friction between plank and the horizontal surface is negligible. In other words, the underlying horizontal surface is smooth.

• An external force is applied on the block.
• An external force is applied on the plank.
• One external force each is applied on block and plank.

To keep the description uniform, we refer block as “A”, having mass, “m”, and plank as “B”, having mass, “M”. We shall find that a consistency in denoting block and plank is very helpful in analyzing motion. The analysis of motion for first two cases is similar. It differs only to the extent that point of application of external force changes. Nevertheless, it is interesting to analyze two cases separately to score the differences in two cases.

An external force is applied on the block

The external force is applied on the block as shown in the figure below. There are two possibilities : (i) there is no friction between "A" and "B" or (ii) there is friction between "A" and "B".

There is no friction between block and plank

We first analyze the motion for a case when all interfaces are “friction – less”. In this situation, the external force on block, “A”, accelerates only the block. As there is no friction between the interface of block and plank, there is no external force on the plank in horizontal direction. As such, plank, “B”, is not accelerated. The free body diagrams of “A” and “B” are as shown in the figure.