Work and Energy - Skier, spring and friction force

Problem Statement:

A skier of mass m = 70 kg descends a frictionless track of height h = 15 m starting from a position A at rest (see figure). Before reaching a spring at the end of the track, the skier crosses a horizontal section of length d = 20 m where the coefficient of friction is μ. The spring (with a stiffness K = 800 N / m) is compressed by length x = 0.2 m to stop the skier, determine what is the coefficient of friction μ of the section with friction of the track.

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Solution:

A non-conservative force (the friction for the section of length d) acts on the skier during his motion. We will use the following equation to solve this problem:

The variation of mechanical energy will be evaluated between the initial (A) and final (B) points when the spring is already compressed.

In state B the mechanical energy is accumulated in the spring in the form of elastic potential energy. In state A we have the gravitational potential energy of the skier.

After doing the substitution in the previous equation we obtain:

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You can consult Problem 1 to see how the work of the friction force is calculated as well as its magnitude when an object moves on a horizontal plane:

After substituting the givens of the problem we obtain the value of the coefficient of friction:

In the problem we have used g = 10 m/s2

Do not forget to include the units in the results of the problems.

 

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