Question

A block of 8 kg is moving on a frictionless surface with velocity $4m/s$. After compressing a spring, this block comes to rest. What is the compression in spring if spring constant is $2\times {10}^{-4}N/m$ ?

Answer 1

Kinetic energy of block can be calculated as follows:

$\frac{1}{2}m{v}^2=\frac{1}{2}\times 8\times 4^2=64j$

The KE will be equal to work done on compressing the spring.Hence, compression can be calculated as

$W=\frac{1}{2}k{x}^2$

Or, $64=\frac{1}{2}\times 2\times {10}^4\times x^2$

Or, $x^2=\frac{64}{{10}^4}$

Or, $x=\frac{8}{{10}^2}=0.08m$