Skateboard=80Kg

Question

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

Answer 1

To analyze the skateboarder's energy at different heights, let's clarify the energy types involved: potential energy (PE) and kinetic energy (KE). The total energy (TE) remains constant (assuming no energy losses), which is the sum of PE and KE.

Given Values:

• Mass of the skateboarder + skateboard: 80 kg
• Total Energy (TE): 4,704 Joules (constant throughout)

Energy Calculations:

1. Potential Energy (PE): It is calculated using the formula: \[ PE = m \cdot g \cdot h \] Where:

   • \( m \) = mass (80 kg),
   • \( g \) = acceleration due to gravity (approximately \( 9.81 , m/s² \)),
   • \( h \) = height (in meters).

2. Kinetic Energy (KE): It is calculated using the formula: \[ KE = \frac{1}{2} m v^2 \] Where:

   • \( v \) = speed (in m/s).

Given Data Analysis:

1. At 6m Height:

   • Height (h) = 6 m
   • Speed (v) = 0 m/s
   • Potential Energy (PE): \[ PE = 80 , \text{kg} \cdot 9.81 , \text{m/s²} \cdot 6 , \text{m} \approx 4,704 , \text{Joules} \]
   • Kinetic Energy (KE) = 0 Joules
   • Total Energy (TE) = PE + KE = 4,704 Joules (matches provided data).

2. At 3m Height:

   • Height (h) = 3 m
   • Speed (v) = (approximately 5.4 m/s)
   • Potential Energy (PE): \[ PE = 80 , \text{kg} \cdot 9.81 , \text{m/s²} \cdot 3 , \text{m} \approx 2,352 , \text{Joules} \]
   • Kinetic Energy (KE): \[ KE = TE - PE = 4,704 , \text{J} - 2,352 , \text{J} = 2,352 , \text{J} \]
   • Validation of KE: \[ KE = \frac{1}{2} \cdot 80 , \text{kg} \cdot (5.4 , \text{m/s})^2 \approx 2,352 , \text{Joules} \]
   • Total Energy (TE) = 4,704 Joules (consistent).

3. At 0m Height:

   • Height (h) = 0 m
   • Speed (v) = (approximately 10.8 m/s)
   • Potential Energy (PE): \[ PE = 0 Joules \]
   • Kinetic Energy (KE): \[ KE = TE - PE = 4,704 , \text{J} - 0 , \text{J} = 4,704 , \text{J} \]
   • Validation of KE: \[ KE = \frac{1}{2} \cdot 80 , \text{kg} \cdot (10.8 , \text{m/s})^2 \approx 4,704 , \text{Joules} \]
   • Total Energy (TE) = 4,704 Joules (consistent).

Summary of Energy States:

• At 6 m height: PE = 4,704 J, KE = 0 J, TE = 4,704 J
• At 3 m height: PE = 2,352 J, KE = 2,352 J, TE = 4,704 J
• At 0 m height: PE = 0 J, KE = 4,704 J, TE = 4,704 J

The analysis shows that the skateboarding system conserves energy as expected, transitioning between potential and kinetic forms as the height changes.

Answer 2

1. Based on the information given in the table, the skateboarder has the greatest potential energy at point A. Explain why

Answer 3

The skateboarder has the greatest potential energy at point A (at a height of 6 m) due to the relationship between height and gravitational potential energy. The potential energy (PE) is determined by the formula:

\[ PE = m \cdot g \cdot h \]

Where:

• \( m \) is the mass (80 kg in this case),
• \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s² \)),
• \( h \) is the height above a reference point (ground level).

Explanation of Potential Energy at Point A:

1. Height: At point A (6 m), the skateboarder is at the highest position compared to points B (3 m) and C (0 m). The greater the height, the more potential energy is stored due to gravity.

2. Mass: The mass of the skateboarder and the skateboard is constant throughout the scenario (80 kg). Since the mass is the same at all height levels, the factor that changes the potential energy is solely the height.

3. Gravitational Force: The force of gravity acts on the skateboarder, pulling them downwards. At a higher elevation, this force results in a larger amount of gravitational potential energy.

Conclusion: Therefore, at point A, where the height is at its maximum (6 m), the potential energy is also at its maximum (4,704 Joules). As the skateboarder descends to point B (3 m) and then to point C (0 m), the height decreases, which directly correlates to a decrease in potential energy. At point C (ground level), the height is zero, resulting in zero potential energy. Thus, point A represents the point of highest potential energy due to its greatest height above the ground.

Answer 4

At which point in the image, would the skateboarder have the greatest Kinetic Energy & Why?

Answer 5

The skateboarder would have the greatest kinetic energy at the lowest point, which is point C (0 m).

Explanation:

1. Kinetic Energy (KE) Formula: Kinetic energy is given by the formula: \[ KE = \frac{1}{2} m v^2 \] Where:

   • \( m \) is the mass (80 kg in this case),
   • \( v \) is the speed (in meters per second).

2. Conservation of Energy: The principle of conservation of energy states that the total mechanical energy (the sum of potential energy and kinetic energy) in the system remains constant, assuming there are no external forces (like friction) at work. Therefore, at any given point, the total energy can be expressed as: \[ TE = PE + KE \] Given that the total energy (TE) is constant at 4,704 Joules in this scenario, the relationship between potential and kinetic energy shifts as the skateboarder moves along.

3. At Point C (Lowest Point):

   • Potential Energy (PE): At this point, the height is 0 m, which means the potential energy is zero: \[ PE = m \cdot g \cdot 0 = 0 \text{ Joules} \]
   • Kinetic Energy (KE): Because total energy is conserved, the kinetic energy at this lowest point can be calculated as: \[ KE = TE - PE = 4,704 \text{ Joules} - 0 \text{ Joules} = 4,704 \text{ Joules} \]
   • Therefore, at point C, the skateboarder has the maximum speed, resulting in the highest kinetic energy.

Conclusion:

The skateboarder would have the greatest kinetic energy (4,704 Joules) at point C because this is the point where the height is lowest, maximizing speed and thereby kinetic energy, while all gravitational potential energy has been converted into kinetic energy as they have descended from point A (6 m).

Answer 6

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?

Answer 7

To understand how increasing the mass of the skateboarder affects the total amount of energy, let's break down the key concepts involved:

Total Mechanical Energy

The total mechanical energy (TE) of the skateboarder-skateboard system can be represented as:

\[ TE = PE + KE \]

Where:

• PE is the potential energy given by the formula: \[ PE = m \cdot g \cdot h \]
• KE is the kinetic energy given by the formula: \[ KE = \frac{1}{2} m v^2 \]

Effect of Increasing Mass

1. Potential Energy (PE):

   • As the mass \( m \) increases, the potential energy at a given height will also increase because it is directly proportional to mass: \[ PE \text{ increases as } m \text{ increases} \]

2. Kinetic Energy (KE):

   • Similarly, the kinetic energy at a given speed will increase as mass increases because it is also directly proportional to mass: \[ KE \text{ increases as } m \text{ increases} \]

3. Total Energy (TE):

   • The total energy of the system, however, is only determined by the initial conditions of the system, assuming no external work is done and no energy is lost. In an ideal system, the total mechanical energy remains constant regardless of changes in mass.
   • If you increase the mass of the skateboarder but still want to maintain a constant total energy, the potential and kinetic energies associated with that mass will also change correspondingly to keep the total energy the same.

4. Practical Implications:

   • If you simply double the mass of the skateboarder but keep height and speed constant, then:
     • At maximum height, \( PE \) will increase, resulting in a different energy distribution.
     • At the lowest point, if that mass is moved with the same speed, \( KE \) would increase significantly, and one would expect at least double the kinetic energy if speed remains constant.

Conclusion

Increasing the mass of the skateboarder affects the distribution of energy between potential energy (at height) and kinetic energy (at speed). While the absolute values of potential and kinetic energy will change with mass, in a closed system with no external work done or energy lost to friction, the total mechanical energy of the system will remain constant.

If you are assessing a simulation that limits the total energy to a certain value, increasing mass would require the skateboarder to be at a lower height or have reduced speed to maintain that total energy constant, thereby revealing the interplay between mass, height, and speed.

To summarize:

• Increasing the mass of the skateboarder increases both potential and kinetic energy proportionately, provided that external constraints do not force changes in the total energy available to the system.

Answer 8

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?

Answer 9

When the skateboarder is placed at the 6-meter mark and allowed to descend, several physical phenomena occur based on the principles of mechanics, specifically the conservation of mechanical energy. Here’s what happens during the "investigation" and the reasoning behind it:

1. Initial Conditions:

• Height: The skateboarder starts at a height of 6 meters, which means they have maximum potential energy (PE).
• Speed: At this starting position, the skateboarder is momentarily at rest (0 m/s), resulting in zero kinetic energy (KE).

2. As the Skateboarder Starts to Descend:

• Potential Energy Decrease: As the skateboarder descends, their height decreases, leading to a reduction in potential energy: \[ PE = m \cdot g \cdot h \]
• Kinetic Energy Increase: Simultaneously, as the height decreases, the skateboarder's speed increases due to the gravitational force acting on them. The kinetic energy increases as they accelerate: \[ KE = \frac{1}{2} m v^2 \]

3. Conservation of Mechanical Energy:

• Throughout the descent, the total mechanical energy remains constant (assuming no external forces such as friction or air resistance): \[ TE = PE + KE \]
• Initially, all energy is in the form of potential energy. As the skateboarder moves downward, potential energy is converted into kinetic energy. At the moment of reaching the ground (0 m), all potential energy has been converted into kinetic energy.

4. At the Lowest Point (0 meters):

• Minimum Potential Energy: At ground level, the height (h) is zero, resulting in: \[ PE = 0 \text{ Joules} \]
• Maximum Kinetic Energy: The skateboarder reaches the maximum speed, and therefore, the kinetic energy is at its highest value: \[ KE = TE - PE = 4,704 \text{ Joules} - 0 \text{ Joules} = 4,704 \text{ Joules} \]
• The skateboarder accelerates due to gravity as they descend, continually transferring potential energy into kinetic energy.

Summary of What Happened:

• Energy Transformation: The skateboarder starts with all gravitational potential energy at the height of 6 meters. As they descend, this energy is transformed into kinetic energy as they pick up speed.
• Conservation Principle: The total energy remains constant, showcasing the principle of energy conservation throughout the process.
• Speed Increase: The skateboarder accelerates continuously as they fall, reaching the maximum speed (and thus maximum kinetic energy) just before hitting the ground (point C).

Conclusion:

The investigation illustrates how gravitational potential energy is converted into kinetic energy during free fall due to gravity, reinforcing fundamental principles of physics such as energy conservation and the interchangeability of energy forms. The behavior of the skateboarder as they descend highlights the interplay between these forms of energy in a gravitational field.