A skier of mass m=70kg starts from rest and skis down a hill that is 100m high,

Question

A skier of mass m=70kg starts from rest and skis down a hill that is 100m high, and has a constant slope. a) (10pts) If there was no friction on the slope, what would the final speed of the skier be? b) (5 pts) If the final speed of the skier is actually 30m/s, what is total work done by Friction on the skier? Name (last name only) _______________ Section Number____________ Problem 3 Cont. c) (10pts). If the coefficient of friction for skis on snow is ?k=0.25, what is the slope of the hill (?)? Hint: first calculate the frictional Force on the skier and the length of the hill as a function of ?

Explanation / Answer

The motor must overcome the force of gravity. The effective mass of the skier as far as gravity is concerned is 70 kg*sin(30)= 35 kg. [This is because the slope supports some of the weight of the skier.] The force of gravity is 9.8 Newtons per kilogram, so the force of gravity on the skier is 35*9.8= 343 Newtons. The work done by the motor is equal to the force done multiplied by the distance in the direction of the force. In this case that is 343*60m = 20580 Joules. The problem suggests only 1 or 2 significant figures, so 21000 Joules or 20000 joules is correct. Power is equal to work per time. Each second the cable must drag the skier 2 meters, so the work done each second is 343*2 = 686 Watts. Thus either 690 or 700 [taking into account signficant figures] is the most precise answer possible.

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