Question

Block $A$ has a weight of $300N$ and block $B$ has a weight of $50N.$ The coefficient of kinetic friction between the incline and block $A$ is ${\mu }_k=0.2$. Determine the speed of block $A$ after it moves $1m$ down the plane, starting from rest. Neglect the mass of the cord and pulleys. (Take $g=10m/s^2$)

• A. $1.12m/s$
• B. $1.2m/s$
• C. $1.32m/s$
• D. $1.4m/s$

Answer 1

The correct option is A $1.12m/s$

If $A$ moves $1m$ down the plane and its speed is $v,$ then $B$ will move $2m$ upwards and its speed will be $2v$.
Using the equation,
$E_i-E_f=$ Work done against friction
$\therefore 0-\left[\frac{1}{2}\times 30\times v^2+\frac{1}{2}\times 5\times (2v{)}^2+5\times 10\times 2-30\times 10\times \frac{3}{5}\right]$

$=0.2\times 30\times 10\times \frac{4}{5}\times 1$

Solving this equation we get,

$v=1.12\frac{m}{s}$