Question

In figure assume that there is negligible friction between the blocks and table. Compute the tension in the cord connecting $m_2$ and the pulley and acceleration of $m_2$ if $m_1=300g,m_2=200g$ and $F=0.40N$.

Answer 1

Let , Tension in the string connecting pulley and block of mass $m_2$ be $T$, therefore tension on string connecting pulley and block of mass $m_1$ will be $T/2$.let acceleration of block of mass $m_2$ be $a_2$ and that of $m_1$ be $a_1$.

Now,

from F.B.D. of block of mass $m_2$,

we get,

$F-T=m_2\left(a_2\right)$ .....$\left(1\right)$

also, from F.B.D. of block of mass $m_1$,

we get,

$T/2=m_1\left(a_1\right)$ .....$\left(2\right)$

Using constraint equation,

we get,

$\left(a_2\right)(-T)+\left(a_1\right)\left(T/2\right)=0$

$a_1=2\left(a_2\right)$ .....$\left(3\right)$

On solving eqn1 , 2 , and 3;

we've

Ans:

$a_2$ = 0.37$\frac{m}{s^2}$

and $T$ = $0.296N$