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Question:

A body of mass 5 kg moving with a speed of 1.5 m/s on a horizontal smooth surface collides with a nearly weightless spring of force constant k= 5 N/m. The maximum compression of the spring would be?

0.15 m

0.12 m

1.5 m

0.5 m

Solution:

At the maximum compression, the whole of the kinetic energy of the body would be transformed to the elastic potential energy of the spring.
⟹ 1/2mv² = 1/2kx²max
⟹ xmax = √(mv²/k) = √((5 kg)(1.5 m/s)²/(5 N/m)) = √(1.5² m²/s²) = 1.5 m