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A mass of 0.5 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 = 50 N/m. The maximum compression of the spring would be:

1. 0.15 m
2. 0.20 m
3. 0.25 m
4. 0.30 m

Correct answer: 0.20 m

Solution

The kinetic energy of the mass is converted into the potential energy of the spring at maximum compression. Using the energy conservation principle: (1/2)mv² = (1/2)kx². Substituting m = 0.5 kg, v = 1.5 m/s, and k = 50 N/m, we get x = √((mv²)/k) = √((0.5 × 1.5²)/50) = 0.15 m.

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