Question

question
what is the relationship between kinetic and potential energy?
what evidence do you have to support your answer to the question above?
check the \speed\ box in the upper right corner. what is the relationship between speed and ke?
what happens to the total (mechanical) energy of the skater as time passes?
switch to the \friction\ tab at the top of the page. what does friction do to the skater?
re - read the law of conservation of energy in the 1st slide. what do you think happens to the skaters energy when friction is involved?
answer

Explanation:

1. Kinetic energy ($KE$) and potential energy ($PE$) are inter - convertible. As an object's height decreases (losing $PE$), its speed increases (gaining $KE$) and vice - versa, assuming no non - conservative forces.
2. Evidence can be seen in a pendulum's motion. At the highest points, it has maximum $PE$ and minimum $KE$ (speed is zero), and at the lowest point, it has maximum $KE$ and minimum $PE$.
3. Kinetic energy is given by the formula $KE=\frac{1}{2}mv^{2}$, so $KE$ is proportional to the square of the speed ($v$). As speed increases, $KE$ increases quadratically.
4. In the absence of non - conservative forces like friction, the total mechanical energy ($E = KE+PE$) of the skater remains constant over time.
5. Friction acts as a non - conservative force. It opposes the skater's motion, converting the skater's mechanical energy into heat energy, thus slowing the skater down.
6. When friction is involved, the skater's mechanical energy is not conserved. Some of the skater's kinetic and potential energy is dissipated as heat due to the frictional force, reducing the skater's overall energy and eventually stopping the skater.

Answer:

1. Kinetic and potential energy are inter - convertible.
2. Example of a pendulum's motion.
3. $KE$ is proportional to the square of speed.
4. Remains constant without friction.
5. Opposes motion and converts mechanical energy to heat.
6. Mechanical energy is dissipated as heat and the skater loses energy.