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graph:

Skateboard=80Kg
Energy of Skateboarder
Height
Speed
Potential Energy
Kinetic Energy
Total Energy
6m
0 m/s²
4,704 Joules
0 Joules
4,704 Joules
3m
5.4 m/s²
2,352 Joules
2,352 Joules
4,704 Joules
0m
10.8 m/s²
0 Joules
4,704 Joules
4,704 Joules

at point C the skate baorder will have the most kinetic energy, Why?

7 answers

In the context of the energy of the skateboarder at different heights, it's important to understand how potential energy (PE) and kinetic energy (KE) convert into each other as the skateboarder moves.

Here's a breakdown of the scenario at each height:

  1. At 6 meters:

    • Potential Energy (PE) = 4,704 Joules
    • Kinetic Energy (KE) = 0 Joules
    • Total Energy = 4,704 Joules

    Here, all energy is in the form of potential energy since the skateboarder is at the highest point and is not moving.

  2. At 3 meters:

    • Potential Energy (PE) = 2,352 Joules
    • Kinetic Energy (KE) = 2,352 Joules
    • Total Energy = 4,704 Joules

    As the skateboarder descends, potential energy decreases while kinetic energy increases. The total energy remains constant.

  3. At 0 meters:

    • Potential Energy (PE) = 0 Joules
    • Kinetic Energy (KE) = 4,704 Joules
    • Total Energy = 4,704 Joules

    At the lowest point (0m), all the potential energy has been converted into kinetic energy. Here, the skateboarder has the highest speed (10.8 m/s²) and therefore the most kinetic energy.

Why the Most Kinetic Energy at Point C:

  • At point C (0 meters), the skateboarder has converted all of the potential energy from the height into kinetic energy as they descend. Since energy is conserved, the energy that was once potential has transformed into kinetic energy.
  • Kinetic energy is directly related to the speed of the skateboarder (KE = 1/2 mv²), meaning as they glide down, their speed increases and thus their kinetic energy increases.

Therefore, the point C features the greatest amount of kinetic energy because it corresponds to the lowest point in the potential energy profile, where all the potential energy has been converted to kinetic energy during the descent.

. Increase the Mass of the skater to Large by using the slider in the gray box for mass. How does the mass of the skater change the total amount of energy?

When the mass of the skateboarder (or skater) is increased while keeping the height and gravitational acceleration constant, it affects the potential energy and kinetic energy, but the total mechanical energy remains conserved.

Effects of Increasing Mass:

  1. Potential Energy (PE):

    • The potential energy is calculated using the formula: \[ \text{PE} = mgh \] where:

      • \(m\) = mass of the skateboarder,
      • \(g\) = acceleration due to gravity (approximately \(9.81 , \text{m/s}^2\)),
      • \(h\) = height above ground.

    • Increasing the mass will directly increase the potential energy at a given height. For example, if the mass of the skateboarder is doubled, the potential energy at any height will also double.

  2. Kinetic Energy (KE):

    • The kinetic energy is calculated using the formula: \[ \text{KE} = \frac{1}{2}mv^2 \]
    • If the mass increases, and if the skateboarder falls from the same height, the potential energy converts into kinetic energy. The total energy available is higher when the mass is increased, and if the skateboarder gains more speed due to the increased mass (while falling), kinetic energy will also increase.

  3. Total Energy:

    • The total mechanical energy (the sum of potential and kinetic energy) in a closed system remains constant if there are no outside forces (like friction).
    • However, the actual numerical values for potential and kinetic energy will depend on the mass. If the skater's mass is increased, both the potential energy at height and the kinetic energy at the lowest point will be higher, leading to a higher total energy compared to a lighter skater at the same height.

Summary:

  • Increasing mass increases both potential and kinetic energy at the same height and speed.
  • Total energy remains conserved but its numerical value will be higher if the skateboarder’s mass is increased since both forms of energy depend on mass.

In practical terms, if you were to slide the mass to a larger value, you would observe that at all heights mentioned, the potential energy would be proportionally higher, and thus, when descending, the total energy will also reflect this increase, keeping the principle of conservation of energy upheld.

If we could increase the height of the ramp to start at 12 meters. How would this affect the overall Kinetic & Potential Energy of the investigation? Explain why

If you increase the height of the ramp to start at 12 meters, it will significantly impact both the potential energy and kinetic energy of the skateboarder during the investigation. Here's how:

Potential Energy (PE):

  1. At the Starting Height (12m):

    • The potential energy of the skateboarder at the starting point can be calculated using the formula: \[ \text{PE} = mgh \] where:

      • \(m\) = mass of the skateboarder,
      • \(g\) = acceleration due to gravity (approximately \(9.81 , \text{m/s}^2\)),
      • \(h\) = height (in this case, 12 meters).

    • Increasing the height to 12 meters will result in a greater potential energy than at lower heights, assuming the mass of the skateboarder remains the same. For example, if the mass of the skateboarder is 80 kg, then: \[ \text{PE} = 80 , \text{kg} \times 9.81 , \text{m/s}^2 \times 12 , \text{m} = 9,408 \text{ Joules}. \]

Kinetic Energy (KE) at the Bottom:

As the skateboarder descends from the ramp, the potential energy will convert into kinetic energy. Assuming there are no energy losses (like friction or air resistance), the total mechanical energy remains conserved.

  1. At the Bottom (0m):
    • When the skateboarder reaches the bottom of the ramp (0 meters), all of the potential energy will have been converted into kinetic energy. Therefore:
      • The kinetic energy at the bottom will equal the potential energy at the top: \[ \text{KE} = \text{PE}_{\text{initial}} = 9,408 \text{ Joules}. \]

Overall Impact on Kinetic & Potential Energy:

  • Increased Potential Energy: By starting at a height of 12 meters, the skateboarder begins with higher potential energy compared to lower heights, such as 6 meters. This higher initial energy means that there is more energy available to convert into kinetic energy as the skateboarder descends.

  • Increased Kinetic Energy: When the skateboarder reaches the bottom of the ramp, their kinetic energy will also be higher than it would be from a lower starting height because the potential energy converted is greater.

Key Takeaway:

  • Height and Energy Relationship: There is a direct relationship between height and energy. The greater the height, the greater the potential energy and, upon descending, a correspondingly greater amount of kinetic energy. This reflects the conservation of energy principle, whereby the total mechanical energy remains constant but the forms of energy change as the skateboarder moves.

Conclusion:

Increasing the ramp's height to 12 meters will result in increased potential energy at the start and, assuming no losses, will convert to increased kinetic energy at the bottom, allowing the skateboarder to have more speed and energy through the descent.

Now place your skateboarder at the 6 meters mark and let the investigation play out. You can play it at Normal Speed. What happened and why?

When you place the skateboarder at the 6-meter mark and let the investigation play out at normal speed, the following happens, and here's the reasoning behind it:

Observations:

  1. Initial Position at 6 Meters:

    • At the beginning of the descent from the 6-meter mark, the skateboarder has a substantial amount of potential energy because of their height. The potential energy at 6 meters can be calculated using the formula: \[ \text{PE} = mgh \] If we assume a mass of 80 kg, the potential energy would be: \[ \text{PE} = 80 , \text{kg} \times 9.81 , \text{m/s}^2 \times 6 , \text{m} = 4,704 \text{ Joules}. \]

  2. Descent Begins:

    • As the skateboarder begins to descend, that potential energy starts converting into kinetic energy. Initially, the skateboarder is not moving at the top, so kinetic energy is zero.

  3. At 3 Meters:

    • When the skateboarder reaches the halfway point (3 meters), some of the potential energy has been converted into kinetic energy while remaining total mechanical energy is conserved. At this point, the potential energy would be: \[ \text{PE} = 80 , \text{kg} \times 9.81 , \text{m/s}^2 \times 3 , \text{m} = 2,352 \text{ Joules}. \]
    • The kinetic energy at this point would also be: \[ \text{KE} = \text{Total Energy} - \text{PE} = 4,704 \text{ Joules} - 2,352 \text{ Joules} = 2,352 \text{ Joules}. \]

  4. At the Bottom (0 Meters):

    • When the skateboarder reaches the bottom of the ramp (0 meters), all the potential energy has been converted to kinetic energy:
      • The potential energy at the bottom is 0 Joules, and the kinetic energy is equal to the total potential energy that was present at the start (4,704 Joules).
    • The skateboarder should be moving at a maximum speed at this point due to the conversion of energy.

Explanation of What Happened:

  • Energy Conversion: Throughout the entire investigation, the skateboarder demonstrates the principle of energy conversion. The potential energy (based on height) converts into kinetic energy (based on speed) as they descend the ramp.

  • Conservation of Energy: The total mechanical energy remains constant throughout the motion (neglecting air resistance and friction). Therefore, whatever potential energy is lost as height decreases is equal to the kinetic energy gained as speed increases.

  • Motion Dynamics: At the highest point, the skateboarder gains speed as they descend due to the gravitational force acting on them. Their acceleration is influenced by the gravitational force, which results in an increase in speed as potential energy is converted to kinetic energy.

Conclusion:

When you play out the scenario with the skateboarder starting at the 6-meter mark, you observe a clear transition of energy types—potential energy is converted to kinetic energy as the skateboarder descends. This illustrates core principles of physics such as energy conservation and the relationship between height, potential energy, and speed, allowing for a better understanding of how energy transforms in a gravitational field.