# The work done on skiers taking different trails

Three sisters -- Alice, Betty and Colleen -- go skiing. Each has a mass of m = 50 kg. When they get to the top of the hill, they see three different routes to the bottom.

• Route A: a constant slope of 3.81 degrees for 12,027 meters
• Route B: a gentle slope of 1.83 degrees for 25,013 meters
• Route C: a steep slope of 18.43 degrees for 2527 meters

Alice takes route A, Betty takes route B, Colleen takes route C. Each one starts from rest at the top of the hill and lets gravity do the work.

1. How much work does gravity do on each sister during the descent?
2. How fast is each sister going when she reaches the bottom?

Joe the ski-lift operator is at the top of the hill. He walks to a sheer cliff and drops a ball, which falls straight down to the bottom of the hill.

3. How far does the ball fall?
4. How fast is the ball moving when it reaches the bottom?

The sisters meet at the bottom. "That was fun!" they cry, "let's do it again!". They go back up to the top of the hill and ski down the same routes as before. Now, however, the snow has melted a bit and become sticky. The coefficient of kinetic friction is mu = 0.02.

5. How much work does friction do on each sister during the descent?
6. Now how fast is each sister going when she reaches the bottom?

7. How large would the coefficient of static friction have to be to prevent each sister from sliding at all?
8. If the mass of the sisters was NOT 50 kg, which of the above anwers would you have to change?