Work By Springs Video Lessons

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Problem: An object of mass, m, is traveling on a horizontal surface. There is a coefficient of kinetic friction, μ, between the object and the surface. The object has speed, v, when it reaches x=0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When the object reaches x=0 on its return trip, it stops. Find k, the spring constant. Express k in terms of mu , m, g, and v.

FREE Expert Solution

In this problem, we're going to use the equation for the Kinetic energy:

K=12mv2

From the law of conservation of energy:

Initial K = Work done against friction + spring energy.

12mv2=μmgx+12kx2........................ (1)

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Problem Details

An object of mass, m, is traveling on a horizontal surface. There is a coefficient of kinetic friction, μ, between the object and the surface. The object has speed, v, when it reaches x=0 and encounters a spring. The object compresses the spring, stops, and then recoils and travels in the opposite direction. When the object reaches x=0 on its return trip, it stops. Find k, the spring constant. Express k in terms of mu , m, g, and v.

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