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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

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

5 answers

Based on the information given in the table, the skateboarder has the greatest potential energy at point A (which is 6m in height) because potential energy (PE) is directly related to height above a reference point (usually ground level). The formula for gravitational potential energy is:

\[ PE = mgh \]

where:

  • \( PE \) is the potential energy,
  • \( m \) is the mass of the skateboarder,
  • \( g \) is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and
  • \( h \) is the height above the ground.

At point A (6m), the skateboarder's height is the highest compared to the other points. Since potential energy increases with height, it naturally follows that the potential energy at 6m is greater than at 3m (where the potential energy is 2,352 Joules) and at 0m (where the potential energy is 0 Joules).

In summary, the skateboarder has the greatest potential energy at point A because it is at the highest elevation (6m), which results in the highest value for potential energy according to the formula provided.

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

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

This is because kinetic energy (KE) is given by the formula:

\[ KE = \frac{1}{2}mv^2 \]

where:

  • \( KE \) is the kinetic energy,
  • \( m \) is the mass of the skateboarder,
  • \( v \) is the velocity of the skateboarder.

As the skateboarder descends from a higher point (like point A at 6m) to point C (0m), potential energy (PE) is converted into kinetic energy (KE). At the highest point (point A), the skateboarder has maximum potential energy and minimal kinetic energy (0 Joules), as their speed is 0 m/s.

As the skateboarder moves to point B (3m), some potential energy is converted into kinetic energy, resulting in a velocity of 5.4 m/s and equal amounts of potential and kinetic energy (2,352 Joules each).

Finally, at point C (0m), all the potential energy (4,704 Joules) would have been transformed into kinetic energy, assuming no energy is lost to friction or air resistance. At this point, the skateboarder has the highest speed (10.8 m/s) and consequently the greatest kinetic energy.

So, the skateboarder has the greatest kinetic energy at point C because that is where they have converted the most potential energy into kinetic energy as they descend to the lowest point.

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 the height of the ramp is increased to 12 meters, this change would significantly affect both the potential energy and the kinetic energy throughout the investigation, particularly at points of descent.

Effects on Potential Energy

  1. Increased Potential Energy: The potential energy at the starting point (12 meters) can be calculated using the same formula:

    \[ PE = mgh \]

    Assuming the mass of the skateboarder remains constant and using \( g \approx 9.81 , \text{m/s}^2 \), the potential energy at 12 meters would be greater than the initial potential energy at 6 meters.

    For example, if the mass \( m \) is the same: \[ PE_{12m} = m \cdot 9.81 \cdot 12 , \text{Joules} \]

    This would yield a potential energy of \( 117.72m , \text{Joules} \), as opposed to the \( 4,704 , \text{Joules} \) at 6 meters.

  2. Greater Energy Available for Conversion: As the skateboarder descends the ramp from 12 meters, this increased potential energy can be converted into kinetic energy as they move downwards.

Effects on Kinetic Energy

  1. Increased Kinetic Energy at the Bottom: By the time the skateboarder reaches the lowest point (0 meters) after descending from 12 meters, they would convert a larger amount of their potential energy into kinetic energy. Assuming no energy is lost to friction or air resistance, the kinetic energy at the bottom would also increase:

    \[ KE_{\text{at bottom}} = \text{initial PE at 12m} = 117.72m , Joules \]

    This means the skateboarder would have more kinetic energy at the bottom compared to starting from a height of 6 meters.

  2. Increased Speed: With higher kinetic energy, the skateboarder would also have a higher speed at the bottom of the ramp. This can be calculated using the kinetic energy formula:

    \[ KE = \frac{1}{2}mv^2 \Rightarrow v = \sqrt{\frac{2KE}{m}} \]

    The skateboarder would achieve a greater velocity at 0 meters due to the additional potential energy converted to kinetic energy.

Summary

In summary, increasing the height of the ramp to 12 meters would result in:

  • Greater Potential Energy at the starting point due to the higher height.
  • Increased Kinetic Energy at the bottom of the ramp as more potential energy is converted to kinetic energy during the descent.
  • Higher Speed at the lowest point of the ramp as a result of the increased kinetic energy.

This illustrates the principle of conservation of energy, where potential energy at the starting height equals the kinetic energy at the lowest point, assuming an ideal situation with no energy losses.