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A block of mass 2 kg moves along a level surface with speed 4 m/s and then comes into contact with an initially uncompressed spring. The block continues until it momentarily stops. If the kinetic friction force is 15 N and the spring constant is 10,000 N/m, what is the maximum 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

Energy: (1/2)(2)(4^2) = (1/2)(10000)x^2 + 15x, i.e. 5000x^2 + 15x - 16 = 0. Solving gives x ~= 0.055 m = 5.5 cm.

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