Question

A 20 - kg block attached to a spring of spring constant 5 N $m^{-1}$ is released from rest at A. The spring at this instant is having an elongation of 1 m. The block is allowed to move in smooth horizontal slot with the help of a constant force 50 N in the rope as shown. The velocity of the block as it reaches B is (assume the rope to be light)

• A. $4m{s}^{-1}$
• B. $2m{s}^{-1}$
• C. $1m{s}^{-1}$
• D. $3m{s}^{-1}$

Answer 1

The correct option is B

$2m{s}^{-1}$

Consider the rope and the blocks as a system.From work-energy theorem, $△k=W_{net}$

Here only two forces do non-zero work on the system: one is the spring force and the other is the constant force of 50 N acting on the cable.Let v be the speed of the block when it reaches B, then

$\frac{m{v}^2}{2}-0=-[\frac{5\times 5^2}{2}-\frac{5\times 1^2}{2}]+50\times 2$

= $\frac{20\times v^2}{2}=40$

$\Rightarrow v=2m{s}^{-1}$