Question

A smaller block of mass 'm' is placed on another block of mass M. When a horizontal force F is applied on the block of mass M as shown in the figure, the smaller block does not slide. If the magnitude of friction between the bigger block and ground is 'f' , determine the magnitude and direction of friction between the two blocks.

• A. $\frac{F}{M+m}$
• B. $\frac{F-f}{M+m}$
• C. $\frac{F+f}{M+m}$
• D. $\frac{F-f}{m}$

Answer 1

The correct option is B $\frac{F-f}{M+m}$

Let a be the combined acceleration of both blocks.

$F-f_r=(m+M)a$

$a=\frac{F-f_r}{(m+M)}$

Now, consider FBD from fig. (2);

$f_b-$ frictional force between the two blocks.

$f_b=ma$

$f_b=\frac{m(F-f_r)}{(m+M)}$

the direction of friction is shown in fig.