### Brain Teasers

# Skier and Forces

Patrick, a student who was humiliating himself on the ski slopes, decided to take a break in the lodge. Patrick was so discouraged that he turned to his physics teacher for help in skiing. Dr. Moore, the professor, was very keen on seeing daily lives as physics problems. So, the professor wanted Patrick to prove that skiing dealt with conservative forces. The professor said, "My mass is exactly 80kg. If I started from rest at the top of the slope and skied down the slope (total elevation = 110m) and you clocked my speed at 20m/s at the bottom of the slope, would this system be conservative?"

What's the answer to the professor's question?

What's the answer to the professor's question?

### Hint

If this example is conservative, then total initial mechanical energy will equal total final mechanical energy.### Answer

The system is not conservative.To solve:

1) First write down the givens:

mass = 80kg

velocity initial = 0

velocity final = 20m/s

height = 110m

2) First calculate the initial potential energy at the top of the slope. Assume that the bottom of the slope is the true point of zero height.

Energy initial = mgh

(80kg)(9.8m/s^2)(110m)=

8.6*10^4J

3) After you found that figure, you must find the mechanical energy at the bottom of the slope.

Energy=1/2mv^2

1/2(80kg)(20m/s)^2=1.6*10^4J

4) Since the final energy is much less than the initial energy, the system is not conservative. Energy was lost on the way down the slope, most likely due to friction and wind resistance.

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