Height Speed potential Energy kinetic energy total

Question

6m 0 m/s^2 4,704 joules 0. joules 4,704
3m 5.4m/s^2 2,352 joules 2,352 joules 4,704
0m 10.8m/s^2 0 joules 4,704 joules 4,704
Based on the information given in the table, the skateboarder has the greatest potential energy at point a. Explain why

Answer 1

The potential energy of an object depends on its height above a reference point (usually the ground) and is calculated using the formula:

\[ \text{Potential Energy (PE)} = m \times g \times h \]

where:

• \( m \) is the mass of the object,
• \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) on Earth),
• \( h \) is the height above the reference point.

In the provided table, the skateboarder's potential energy is highest at a height of 6 meters, which corresponds to a potential energy value of 4,704 joules. At this height, the skateboarder has the maximum elevation above the ground, resulting in the greatest possible potential energy.

As the skateboarder descends to lower heights (3 meters and 0 meters), the potential energy decreases because the height \( h \) is decreasing. At 3 meters, the potential energy is reduced to 2,352 joules, and at the ground level (0 meters), the potential energy is 0 joules.

In summary, the skateboarder has the greatest potential energy at point A (6 meters) because potential energy is directly proportional to height, and the maximum height corresponds to the maximum potential energy.

Answer 2

Same thing different question
At which point in the image, would the skateboarder have the greatest Kinetic Energy & why

Answer 3

In the context of the skateboarder's motion, kinetic energy is the energy of an object due to its motion and is calculated using the formula:

\[ \text{Kinetic Energy (KE)} = \frac{1}{2} m v^2 \]

where:

• \( m \) is the mass of the object,
• \( v \) is the speed of the object.

From the information you provided in the previous table, we can observe the following points:

1. At a height of 6 meters, the speed is \( 0 , \text{m/s} \), resulting in a kinetic energy of \( 0 , \text{joules} \) (because \( KE = \frac{1}{2} m (0)^2 = 0 \)).
2. At a height of 3 meters, the speed is \( 5.4 , \text{m/s} \), giving a kinetic energy of \( 2,352 , \text{joules} \).
3. At a height of 0 meters, the speed is \( 10.8 , \text{m/s} \), resulting in a kinetic energy of \( 4,704 , \text{joules} \).

From this analysis, it is clear that the skateboarder has the greatest kinetic energy at the height of 0 meters. This is because, at this point, the skateboarder is moving with the highest speed (10.8 m/s), leading to the maximum kinetic energy.

In summary, the skateboarder has the greatest kinetic energy at the lowest point (0 meters) in the image due to the highest velocity, which significantly contributes to the overall kinetic energy calculated using the formula for kinetic energy.

Answer 4

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 5

When you increase the mass of the skateboarder while keeping the height and speed constant, the total amount of energy increases because both potential energy and kinetic energy are dependent on mass.

1. Potential Energy (PE): As previously mentioned, potential energy is calculated using the formula

   \[ \text{Potential Energy (PE)} = m \times g \times h \]

   If you increase the mass (\( m \)), the potential energy at any given height (\( h \)) increases proportionally. For example, if the mass of the skateboarder is doubled, the potential energy at a specific height will also double.

2. Kinetic Energy (KE): Kinetic energy is calculated using

   \[ \text{Kinetic Energy (KE)} = \frac{1}{2} m v^2 \]

   Increasing the mass (\( m \)) also increases the kinetic energy at any given speed (\( v \)). Similar to potential energy, if the mass is doubled, the kinetic energy at a specific speed will also double.

3. Total Energy: The total mechanical energy (which is the sum of potential energy and kinetic energy) is:

   \[ \text{Total Energy} = \text{Potential Energy} + \text{Kinetic Energy} \]

   Consequently, increasing the mass of the skateboarder results in an increase in both potential energy and kinetic energy, leading to a higher total mechanical energy.

In summary, as you use the slider to increase the mass of the skateboarder, both the potential energy (at any height) and the kinetic energy (at any speed) increase proportionally. Therefore, the total amount of energy will also increase as a result of the increased mass.

Answer 6

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

Answer 7

Increasing the height of the ramp to start at 12 meters would have a significant impact on both the potential energy and kinetic energy of the skateboarder at various points during the investigation. Here's how:

Effect on Potential Energy

1. Potential Energy (PE): The potential energy at a certain height is given by the formula:

   \[ \text{PE} = m \times g \times h \]

   • Since the mass (\(m\)) and gravitational acceleration (\(g\)) remain constant, increasing the height (\(h\)) to 12 meters will directly increase the potential energy of the skateboarder at that starting position.
   • For example, if we assume the mass of the skateboarder is constant, the potential energy at 12 meters would be greater than it was at 6 meters (which was 4,704 joules). The new potential energy would be calculated as:

   \[ \text{PE}_{12m} = m \times g \times 12 , \text{m} \]

2. Increased Total Energy: Since potential energy is greater at a height of 12 meters, the total mechanical energy at the top of the ramp will also increase. As the skateboarder starts from this height, they will have more energy available for conversion into kinetic energy as they descend.

Effect on Kinetic Energy

As the skateboarder travels down the ramp:

1. Conversion of Potential Energy to Kinetic Energy: As they descend from the higher starting point (12 meters), gravitational potential energy is converted into kinetic energy. The kinetic energy at the bottom of the ramp (0 meters height) can be determined using energy conservation principles:

   \[ \text{Total Energy at the top} = \text{Potential Energy at the top} = \text{Kinetic Energy at the bottom} \]

2. Kinetic Energy at the Bottom: If the skateboarder starts at 12 meters, their kinetic energy at the bottom of the ramp will be:

   \[ \text{KE}_{\text{bottom}} = m \times g \times 12 , \text{m} \]

   This will be greater than the kinetic energy they would have had if they started at 6 meters.

Summary

• Increased Potential Energy: Starting at 12 meters height increases the initial potential energy due to the greater height.
• Increased Kinetic Energy: As the skateboarder descends, more potential energy is converted into greater kinetic energy at the bottom of the ramp. In simple terms, the skateboarder will be moving faster at the bottom compared to a scenario where they only started at 6 meters, assuming no energy losses due to friction or air resistance.

Overall, increasing the ramp height to 12 meters will lead to an increase in both potential energy at the start and kinetic energy at the bottom of the ramp, resulting in greater speeds and energy levels throughout the skateboarder's motion.

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

If the skateboarder is placed at the 6 meters mark on the ramp and allowed to roll down, here's what happens and the reasoning behind it:

Initial Conditions

At the 6-meter mark, the skateboarder starts with a certain amount of potential energy determined by their height (6 meters) and mass. As discussed earlier, the potential energy (PE) at this height is calculated as:

\[ \text{PE} = m \times g \times h \]

where \( h = 6 , \text{m} \).

As the Investigation Plays Out

1. Descent: As the skateboarder starts from the 6-meter height, they begin to accelerate down the ramp due to gravity. During this descent, the potential energy is converted into kinetic energy.

2. Energy Conversion:

   • At the top (6 meters), the skateboarder has maximum potential energy and zero kinetic energy (if starting from rest).
   • As they roll down, the height decreases, and the potential energy decreases while the kinetic energy increases. The total mechanical energy (the sum of potential and kinetic energy) remains constant, assuming no friction or air resistance.

3. Speed Increase: As the skateboarder descends the ramp, their speed increases due to the conversion of potential energy into kinetic energy. At different points down the ramp:

   • At halfway (3 meters), they would have lower potential energy, which gets converted to kinetic energy. The skateboarder speeds up as they get closer to the bottom.
   • Finally, at the bottom (0 meters), nearly all the potential energy will have been converted to kinetic energy, and the skateboarder will be moving at their highest speed.

Observations

• Acceleration: You would observe that the skateboarder accelerates as they move down the ramp. This is because the force of gravity is acting on the skateboarder, pulling them downwards.
• Highest Speed at Bottom: When the skateboarder reaches the bottom of the ramp (0 meters), they would have reached their maximum speed because they have converted the maximum amount of potential energy into kinetic energy.

Conclusion

Observing the skateboarder from the 6-meter mark illustrates the principle of energy conversion in a gravitational field. As they descend, potential energy is transformed into kinetic energy, leading to an increase in speed and demonstrating the conservation of mechanical energy in the absence of external forces (like friction). If the investigation is conducted without any energy losses, the total mechanical energy remains constant throughout the skateboarder's descent.