in the menu at the bottom, click \measure\. this will take you to a different part of the simulation. in the…

Explanation:

Step1: Analyze energy - conservation principle

The skater's motion is governed by conservation of mechanical energy (kinetic + potential). At the start, the skater has potential energy $PE = mgh$ (where $m$ is mass, $g$ is gravitational acceleration, $h$ is height). As the skater moves, potential energy is converted to kinetic energy $KE=\frac{1}{2}mv^{2}$. To make it through the loop, the skater must have enough kinetic energy at the bottom - of the loop to overcome the centripetal force requirements at the top of the loop.

Step2: Consider ramp - height and loop

If the left - hand side of the ramp is taller than the loop but shorter than the right - hand side, the skater may have enough initial potential energy to make it through the loop. The skater's initial height gives enough energy to convert to the necessary kinetic energy at the bottom of the loop and then to the required potential and kinetic energy combination at the top of the loop.

Step3: Analyze reaching the right - hand side

To reach the top of the right - hand side, the skater needs enough initial potential energy to overcome the height difference and any energy losses (such as friction). If the initial height on the left - hand side is not high enough compared to the right - hand side height and energy losses are considered, the skater may not reach the top.

Step4: Analyze friction effect

When friction is increased to the maximum, friction dissipates the skater's mechanical energy as heat. This reduces the available energy for the skater to make it through the loop. The skater's initial potential energy is converted not only to kinetic and potential energy during motion but also to heat due to friction, reducing the energy available for loop - traversal.

Step5: Answer specific questions

1. Predict: Will the skater make it through the loop? Why do you think this?
   • If the left - hand side is taller than the loop, assuming no or low friction, the skater can convert enough potential energy to kinetic energy at the bottom to have enough speed to make it through the loop. The minimum speed $v$ at the bottom of the loop to make it through the top of the loop (radius $r$) is given by $v=\sqrt{5gr}$ (derived from centripetal force and energy - conservation equations).
2. Predict: Will the skater make it all the way to the top of the right side? Why do you think this is?
   • It depends on the height of the left - hand side compared to the right - hand side and energy losses. If the left - hand side is not high enough or there are significant energy losses (e.g., friction), the skater will not reach the top.
3. Were your predictions correct?
   • This requires actual simulation results. If the skater has enough energy based on initial height and energy - loss considerations, the predictions are correct.
4. Why was the skater able to make the loop but not all the way up the final ramp?
   • The skater had enough initial potential energy to convert to the necessary kinetic energy to make it through the loop. However, there was not enough remaining energy (after loop traversal and any energy losses) to reach the top of the higher right - hand side ramp.
5. Predict: Will the skater make it through the loop? Why do you think this? (when left - hand side is shortest)
   • Probably not. A shorter left - hand side means less initial potential energy. Without enough initial energy, the skater may not have enough speed at the bottom of the loop to make it through the top of the loop.
6. Was your prediction correct?
   • Depends on simulation results. If the skater doesn't have enough speed at the bottom of the loop, the prediction is correct.
7. Why was the skater NOT able to make the loop in this configuration, but WAS able to last time?
   • The initial potential energy was lower in this configuration (shorter left - hand side), resulting in less kinetic energy at the bottom of the loop and not enough speed to make it through the top of the loop.
8. Predict: will the skater be able to make it through the loop? Why do you think this? (when friction is maximum)
   • No. Maximum friction dissipates a large amount of the skater's initial potential energy as heat, reducing the available energy for loop - traversal.
9. Was your prediction correct?
   • Depends on simulation results. If the skater doesn't have enough energy due to friction - induced energy losses, the prediction is correct.
10. Why was the skater NOT able to make it through the loop this time, but WAS able to when there was no friction?

• Friction dissipates energy as heat. Without friction, all of the initial potential energy can be converted to kinetic and potential energy during motion. With maximum friction, too much energy is lost as heat, reducing the available energy for loop - traversal.

11. Looking at the bar chart, what kind of energy did the Potential and Kinetic turn into when there was friction?

• When there was friction, potential and kinetic energy were converted into thermal energy (heat). The friction force does work on the skater, dissipating the mechanical energy of the skater - Earth system as heat.

12. Think: A roller coaster does not use a motor or engine to run. Why should the first hill be the tallest part of the roller coaster?

• The first hill provides the roller - coaster (or skater in this case) with its initial potential energy. This initial potential energy is converted to kinetic and potential energy during the ride. To ensure that the roller coaster has enough energy to make it through all the subsequent parts of the track (loops, hills, etc.), the first hill must be the tallest to provide sufficient initial energy, considering energy losses due to friction and air resistance.

Answer:

The answers to each prediction and 'why' question are provided in the step - by - step explanations above. For example, for the first prediction "Will the skater make it through the loop?": If the left - hand side is taller than the loop and friction is low, the skater can make it through the loop because of sufficient initial potential energy for kinetic - energy conversion for loop traversal.