Use the work–energy theorem to solve each of these problems. You can use Newton’

Question

Use the work–energy theorem to solve each of these problems. You can use Newton’s laws to check your answers.

1)A skier moving at 5.55 m/s encounters a long, rough, horizontal patch of snow having a coefficient of kinetic friction of 0.220 with her skis. How far does she travel on this patch before stopping?

2)Suppose the rough patch in part A was only 2.97 m long. How fast would the skier be moving when she reached the end of the patch?

3)At the base of a frictionless icy hill that rises at 25.0 above the horizontal, a toboggan has a speed of 12.5 m/s toward the hill. How high vertically above the base will it go before stopping?

Explanation / Answer

1)
initial kinetic energy = energy lost against friction
0.5*m*v^2 = miu*m*g*d
0.5*v^2 = miu*g*d
0.5*(5.55)^2 = 0.220*9.8*d
d = 7.14 m

2)
initial kinetic energy = energy lost against friction + final kinetic energy
0.5*m*vi^2 = miu*m*g*d + 0.5*m*vf^2
0.5*vi^2 = miu*g*d + 0.5*vf^2
0.5*(5.55)^2 = 0.220*9.8*2.97 + 0.5vf^2
15.4 = 6.4 + 0.5*vf^2
vf = 4.24 m/s

3)
initial kinetic energy = final potential energy
0.5*m*v^2 = m*g*h
0.5*v^2 = g*h
0.5*(12.5)^2 = 9.8*h
h = 7.97 m

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