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}}=0.15\,m $