Question

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

• A. $\frac{m{v}^2}{2x^2}$
• B. $\frac{3m{v}^2}{4x^2}$
• C. $\frac{m{v}^2}{4x^2}$
• D. $\frac{5m{v}^2}{3x^2}$

Answer 1

The correct option is B $\frac{3m{v}^2}{4x^2}$

From conservation of energy,

Loss in kinetic energy of block=Gain in potential energy of spring

$⟹\frac{1}{2}m{v}^2-\frac{1}{2}m(\frac{v}{2}{)}^2=\frac{1}{2}k{x}^2$

$⟹\frac{3m{v}^2}{8}=\frac{1}{2}k{x}^2$

$⟹k=\frac{3m{v}^2}{4x^2}$