part 1 questions
1. describe what is happening to potential energy as the skater’s height decreases.

2. describe what is happening to speed and kinetic energy as the skater’s height decreases.

3. does the total energy change as the skater’s height decreases? if it does, send the skater down the track again and look at the total energy at different points. comment on any differences.

4. if a quantity remains constant, we say that it is conserved. which of the following energies is conserved? potential, kinetic or total?

5. how does this lab demonstrate the law of conservation of energy?

Question

part 1 questions
1. describe what is happening to potential energy as the skater’s height decreases.

2. describe what is happening to speed and kinetic energy as the skater’s height decreases.

3. does the total energy change as the skater’s height decreases? if it does, send the skater down the track again and look at the total energy at different points. comment on any differences.

4. if a quantity remains constant, we say that it is conserved. which of the following energies is conserved? potential, kinetic or total?

5. how does this lab demonstrate the law of conservation of energy?

Accepted Answer

### Question 1
# Brief Explanations:
Potential energy (specifically gravitational potential energy) is given by the formula $ PE = mgh $, where $ m $ is mass, $ g $ is acceleration due to gravity, and $ h $ is height. As the skater’s height ($ h $) decreases, and $ m $ and $ g $ are constant (assuming no mass change and constant gravity), the potential energy will decrease.
# Answer:
As the skater’s height decreases, the potential energy (gravitational potential energy) decreases. This is because gravitational potential energy is proportional to height ($ PE = mgh $), so a lower height means less potential energy (assuming mass and gravity are constant).

### Question 2
# Brief Explanations:
Kinetic energy is given by $ KE=\frac{1}{2}mv^{2} $, where $ v $ is speed. As the skater’s height decreases, potential energy decreases (from Question 1). By the conservation of mechanical energy (assuming negligible friction), the lost potential energy is converted into kinetic energy. So kinetic energy increases. Since $ KE=\frac{1}{2}mv^{2} $ and mass $ m $ is constant, an increase in $ KE $ means an increase in speed $ v $ (because $ v = \sqrt{\frac{2KE}{m}} $).
# Answer:
As the skater’s height decreases, the speed increases, and the kinetic energy increases. This is because the decreasing potential energy is converted into kinetic energy (by conservation of mechanical energy, ignoring friction), and since kinetic energy is proportional to the square of speed ($ KE=\frac{1}{2}mv^{2} $), an increase in kinetic energy corresponds to an increase in speed.

### Question 3
# Brief Explanations:
Total mechanical energy is the sum of potential energy ($ PE $) and kinetic energy ($ KE $), i.e., $ E_{total}=PE + KE $. In an ideal scenario with no friction (or other non - conservative forces), mechanical energy is conserved. So as the skater’s height decreases, $ PE $ decreases and $ KE $ increases, but their sum (total energy) remains constant. If there is friction, total energy would decrease slightly over time due to energy being converted into heat, but in a typical physics simulation (like the skater simulation), we assume negligible friction for the purpose of this question, so total energy does not change. If we run the skater down the track again, in the ideal case, the total energy at different points should be the same. If there is friction, the total energy might decrease a bit, but the differences would be small and due to energy dissipation.
# Answer:
In an ideal situation (negligible friction), the total energy does not change as the skater’s height decreases. This is because the decrease in potential energy is equal to the increase in kinetic energy, so their sum (total mechanical energy) remains constant. If we send the skater down the track again, in the ideal case, the total energy at different points will be the same. If there is some friction (energy dissipation), the total energy might decrease slightly, but the differences would be due to energy being lost to non - conservative forces like friction.

### Question 4
# Brief Explanations:
- Potential energy: As we saw, it decreases as height decreases, so it is not conserved.
- Kinetic energy: It increases as height decreases (since potential energy is converted into kinetic energy), so it is not conserved.
- Total energy: In the absence of non - conservative forces (like friction), the sum of potential and kinetic energy remains constant. Even with small amounts of friction, in the context of this skater simulation (which is often a simplified model), we consider total mechanical energy to be conserved (or nearly conserved for the purpose of the question). So total energy is the conserved quantity.
# Answer:
Total energy is conserved. Potential energy decreases and kinetic energy increases as height decreases, so they are not conserved individually. But the sum of potential and kinetic energy (total energy) remains constant (in an ideal, frictionless scenario, or nearly constant in the simulation context), so total energy is conserved.

### Question 5
# Brief Explanations:
The Law of Conservation of Energy states that the total energy of an isolated system remains constant; energy can neither be created nor destroyed, only transferred or transformed from one form to another. In this lab (skater simulation), as the skater moves, potential energy (due to height) is transformed into kinetic energy (due to motion) and vice versa. When the skater is at a high point, most of the energy is potential; as they move down, potential energy is transformed into kinetic energy. When they move up again, kinetic energy is transformed back into potential energy. The total amount of mechanical energy (potential + kinetic) remains constant (in the ideal case with no friction), which demonstrates that energy is conserved as it is transformed between potential and kinetic forms.
# Answer:
This lab demonstrates the Law of Conservation of Energy by showing that as the skater moves, energy is transformed between potential energy (due to height) and kinetic energy (due to speed), but the total amount of mechanical energy (the sum of potential and kinetic energy) remains constant (in the ideal, friction - free model). When the skater is at a higher height, there is more potential energy and less kinetic energy; as the height decreases, potential energy decreases and kinetic energy increases, with the total energy staying the same (or nearly the same in a real - world - like simulation with minimal energy loss). This shows that energy is conserved as it is transferred from one form to another.

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