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A block of mass 2 kg moves along a rough horizontal surface with a speed of 4 m/s. It then hits a compressed spring and comes to rest after compressing it. If the kinetic friction force is 15 N and the spring constant is 10,000 N/m, what is the compression of the spring?

1. 8.5 cm
2. 5.5 cm
3. 2.5 cm
4. 11.0 cm

Correct answer: 5.5 cm

Solution

Initial KE = friction work + spring PE: 0.5*2*4^2 = 15*x + 0.5*10000*x^2. So 5000 x^2 + 15 x - 16 = 0, giving x = 0.0551 m ≈ 5.5 cm.

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