Question

A mass of 0.5 kg moving with a speed of $1.5\text{m}{\text{s}}^{-1}$ on a horizontal smooth surface, collides with a nearly weightless spring of force constant $\text{k}\text{=}\text{50}\text{N}{\text{m}}^{-1}.$ The maximum compression of the spring would be

• A. 0.15 m
• B. 0.23 m
• C. 1.6 m
• D. 0.4 m

Answer 1

Answer: (A)

By the law of conservation of energy. Kinetic energy of mass = energy stored in spring
$\frac{1}{2}m{v}^2=\frac{1}{2}k{x}^2$
$x^2=\frac{m{v}^2}{k}$
The maximum compression of the spring
$x=\sqrt{\frac{m{v}^2}{k}}$
$x=\sqrt{\frac{0.5\times 1.5\times 1.5}{50}}=0.15m$