Question

Two blocks of masses $10Kg$ each are placed over each other as shown in the figure. A force of $50N$ is exerted on the top block. The coefficient of friction $\mu$ between the blocks is 0.5. Find the acceleration of the two blocks.

Answer 1

Let assume both blocks are moving with different acceleration,

$a_1$ = acceleration of block A

$a_2$= acceleration block B,

From FBD of Block A,

$F-f=m{a}_1$, ......1

$f=\mu N$, $N=mg$, $\Rightarrow f=\mu mg$= $.5\times 10\times 10$= 50,

Using value of $f$ in equation 1,

$\Rightarrow a_1=0$ , So our assumption is wrong.

We take both block as system, let acceleration is $a$,

$F=2ma$ $\Rightarrow 2\times 10\times a=50$ $\Rightarrow a=2.5m{s}^{-2}$