Question

Find the acceleration $\left(m/s^2\right)$ of the two blocks, The system is initially at rest and the friction coefficient are as shown in the figure?

• A. $a_A=5.0,a_B=5.1$
• B. $a_A=5.0,a_B=5.0$
• C. $a_A=5.1,a_B=5.1$
• D. $a_A=5.1,a_B=5.0$

Answer 1

The correct option is D $a_A=5.1,a_B=5.0$

Let assume both block are moving with same acceleration $a$,

$F=2ma$ , $\Rightarrow a=5.05m{s}^{-2}$

Now from FBD of block A,

$F-f=ma$ $\Rightarrow f=101-10\times 5.05=50.5$ N

For the limiting case value of frictional force $f=\mu N=.5\times 10\times 10=50$ N which is lower than calculated value of frictional force so our assumption is wrong , both blocks are moving with different acceleration.

Let

$a_1$ = 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,

$\Rightarrow a_1=5.1m{s}^{-2}$,

From FBD of Block B,

$f=m{a}_2$ $\Rightarrow a_2=\frac{f}{m}=5m{s}^{-2}$