Question

A block of mass m moving at a speed v compresses a spring through a distance x before its speed is speed is halved. Find the spring constant of the spring.

Answer 1

Let the velocity of the body at A be v.

So, the velocity of the body at B is $\frac{v}{2}.$

Energy at point A = Energy at point B

$So,\frac{1}{2}m{v}_A^2-\left(\frac{1}{2}\right)m{v}_B^2=\frac{1}{2}k{x}^2$

$\Rightarrow \frac{1}{2}k{x}^2=\frac{1}{2}m(V_A^2-V_B^2)$

$\Rightarrow k{x}^2=m(v^2-\frac{v^2}{4})$

$\Rightarrow k{x}^2=m\frac{(4v^2-v^2)}{4}$

$\Rightarrow k=\frac{3m{v}^2}{4x^2}$