Peter, a student was humiliating himself on the ski slopes. So, he decided to take a break in the lodge. Peter was so discouraged that he turned to his physics teacher for help in skiing.
Dr. Miller, the professor, was very keen on seeing daily lives as physics problems. So, the professor wanted Peter to prove that skiing dealt with conservative forces.
Dr. Miller 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 is the answer to the professor's question? Explain your answer with valid reasoning.
Looking up the definition of a conservative system, I find that this involves forces that depend only on position, such as when a charged particle moves through an electric field where the field has a value which is a function solely of position.
But while static friction of a ski on snow typically depends only on mass, g, and slope; dynamic friction most likely depends on velocity.
So a key force, friction, depends not just on position but also on velocity. It is easy to imagine a skier getting to a particular point, say, half way down the run via 2 different pathways but arriving at that point with different velocities.
So from this, it seems the system is not conservative.
Now if the professor claimed the skier arrived at the bottom of the slope at a particular speed and after a particular amount of time, then there would be more math to do to answer the question with this added boundary condition.
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Posted by Larry
on 2023-02-23 11:07:56 |
my thought
