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.
The potential energy
E = m*g*h
where g=9.807 m/s^2.
In the professor's case, this is
E = 80*9.807*110 kg*m^2/s^2
= 86302 kg*m^2/s^2
= 86302 joules
The kinetic energy at the bottom of the slope is
E = m*v^2 / 2
In the professor's case,
E = 80*20^2 / 2 kg*m^2/s^2
= 16000 joules
Most of the energy was drained heating the air and the skier via air resistance, and heating the snow and skis via friction.
While the force of gravitation is conservative, other forces have intervened to prevent this system from being a demonstration of this.
Edit: corrected arithmetic in kinetic energy.
Edited on February 24, 2023, 5:25 pm
|
|
Posted by Charlie
on 2023-02-23 09:06:18 |
solution (sort of)
