A 60.0-kg skier starts from rest at point A in the Figure. The curvy slope is ve

Question

A 60.0-kg skier starts from rest at point A in the Figure. The curvy slope is very icy and frictionless except for the section BC, of length 10.0 m that was previously groomed by a snow groomer. The skier skies down the slope and hits a rubber bumper that can be modeled as a spring with force constant k = 1.63 x 104 N/m. The skier compresses the bumper 0.300 m from its equilibrium position before coming to rest momentarily 60.0 kg 5.00 m hooo 10.0 m a) List all conservative and non-conservative forces acting on the skier in this problem. b) Calculate the work done by kinetic friction. c) Calculate the stored potential energy in the bumper when it is compressed 0.300 m from its equilibrium position. d) Determine the coefficient of kinetic friction between the groomed surface BC and the skier.

Explanation / Answer

a)The forces acting the the skier are:

i)gravity acting down (conservative)

ii)frictioanl force acting on the rough patch (non conservative)

iii)Hooks force (conservative)

b)The work done by frictional force from conservation of energy is:

Wf = Wg - Uspring

Wf = m g h - 1/2 k x^2

Wf = 60 x 9.8 x 5 - 0.5 x 1.63 x 10^4 x 0.3^2 = 2206.5 J

Hence, Wf = 2206.5 J

c)U = 1/2 k x^2

U = 0.5 x 1.63 x 10^4 x 0.3^2 = 733.5 J

Hence, U = 733.5 J

d)We know that,

Wf = uk m g d

uk = Wf/m g d = 2206.5/60 x 9.8 x 10 = 0.375

Hence, uk = 0.375

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