Question

A block of mass $4kg$ slides on a horizontal frictionless surface with a speed of $2m/s$. It is brought to rest in compressing a spring in its path. If the force constant of the spring is $400N/m$, by how much the spring will be compressed?

• A. $2\times {10}^{-2}m$
• B. $0.2m$
• C. $20m$
• D. $200m$

Answer 1

Answer: (B)

$0.2m$

The kinetic energy of the sliding block is $=1/2\times m\times v^2$ $=1/2\times 4\times 2^2=8J$

Now since there is no friction on the surface then it is a conservative system. So all the energy of the block will be transferred to the spring and will store as a potential energy. Suppose it will compress the spring by an amount of $x$ m. So the potential energy of the spring will be $=1/2\times k\times x^2$

Equating there two energies and solving for x, we will get, $1/2\times k\times x^2=8$

Or $0.5\left(400\right)x^2=8$

$⟹x=0.2$ m.