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Question

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A mass m = 10.0 kg rests on a frictionless table and accelerated by a spring with spring constant k = 4188.0 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is ?k = 0.43. The mass leaves the spring at a speed v = 3.2 m/s.
How much work is done by the spring as it accelerates the mass?
How far was the spring stretched from its unstreched length
The mass is measured to leave the rough spot with a final speed vf = 1.5 m/s.

How much work is done by friction as the mass crosses the rough spot?

Explanation / Answer

work done by the spring as it accelerates the mass = 0.5 * 10* 3.2*3.2 = 51.2 J spring stretched from its unstreched length from 0.5*k* (x^2) = 51.2 x = 0.156 m magnitude of work done by friction as the mass crosses the rough spot = 0.5*10*{ (3.2^2) - (1.5^2) } = 39.95 J

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