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

Question

Use the ramp shaped like a U.
→ Click and drag the skater to the top of the ramp’s left side. Release the skateboarder.
→ The first time, just watch prior to collecting data & answering the questions.. Observe the changes of energy with the pie chart. After observing with the pie chart, observe the changes of energy on the bar graph (make sure there is a check).

Answer 1

To explain why the skateboarder has the greatest potential energy at point A, we need to understand the concepts of potential energy and kinetic energy, especially in the context of a ramp shaped like a U.

1. Definition of Potential Energy: Potential energy is the energy stored in an object due to its position relative to other objects. In the context of gravity, it is primarily influenced by the height of the object above the ground. The formula for gravitational potential energy (PE) is given by: \[ PE = mgh \] where \(m\) is mass, \(g\) is the acceleration due to gravity, and \(h\) is the height above the reference point.

2. Position on the Ramp: At point A, which is at the top of the left side of the U-shaped ramp, the skateboarder is at the highest point on the ramp. At this height, the skateboarder has maximum potential energy because the height \(h\) is greatest at this position.

3. Conversion of Energy: As the skateboarder starts to move down the ramp from point A, potential energy is converted into kinetic energy (the energy of motion). The skateboarder speeds up as they descend, which means kinetic energy increases while potential energy decreases.

4. Observations from the Energy Graphs:

   • In the pie chart and bar graph showing energy changes, you would notice that at point A, the portion of energy shown as potential energy would be at its maximum while kinetic energy would be at its minimum, because the skateboarder is momentarily at rest before descending.
   • As the skateboarder moves down the ramp, the potential energy would decrease and the kinetic energy would increase, illustrating the conservation of mechanical energy; the total energy remains constant if we neglect friction and air resistance.

In summary, the skateboarder has the greatest potential energy at point A because that is the highest position on the ramp. As the skateboarder descends, potential energy decreases and kinetic energy increases, demonstrating the conversion of energy from potential to kinetic as the skateboarder moves.

Answer 2

(the answer is c, the dip of the U)
At which point in the image, would the skateboarder have the greatest Kinetic Energy & Why?

Answer 3

The skateboarder would have the greatest kinetic energy at the lowest point of the U-shaped ramp, which is at the dip (let's refer to this point as point C). Here’s why:

1. Kinetic Energy Definition: Kinetic energy (KE) is the energy of an object due to its motion. It is defined by the formula: \[ KE = \frac{1}{2}mv^2 \] where \(m\) is the mass of the object and \(v\) is its velocity. As the velocity increases, the kinetic energy increases.

2. Energy Conversion: When the skateboarder is at the top of the ramp (such as at point A), they have maximum potential energy and minimal kinetic energy (assuming they are momentarily at rest). As the skateboarder descends the ramp, potential energy is transformed into kinetic energy.

3. Lowest Point of the Ramp: At the lowest point of the U-shaped ramp (point C), the skateboarder is moving the fastest due to gravity pulling them downwards. At this point, the potential energy is at its minimum (because height is zero) and all the energy has converted into kinetic energy. Thus, here, the kinetic energy is maximized.

4. Graphical Representation: If you were to observe the energy changes using a pie chart or bar graph, you would see that as the skateboarder moves toward the dip of the U, potential energy decreases and kinetic energy increases. At the lowest point (point C), kinetic energy is at its highest while potential energy is at its lowest.

In summary, the skateboarder would have the greatest kinetic energy at the dip of the U (point C) because this is where they are moving the fastest, having converted most of their potential energy into kinetic energy as they descended from the higher points of the ramp.

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 using the slider, it affects the total amount of mechanical energy in the system in the following ways:

1. Potential Energy: The potential energy (PE) is calculated using the formula: \[ PE = mgh \] where \(m\) is the mass, \(g\) is the acceleration due to gravity, and \(h\) is the height. If you increase the mass of the skateboarder, the potential energy at any given height also increases. For example, if the skateboarder is at the top of the ramp, a larger mass would result in a higher potential energy compared to a smaller mass.

2. Kinetic Energy: The kinetic energy (KE) is calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] Here, if the mass increases while the velocity remains constant, the kinetic energy will also increase. However, the speed of the skateboarder when descending the ramp may vary based on the mass and the force acting on it.

3. Total Mechanical Energy: The total mechanical energy (TME) of the system is the sum of the potential energy and kinetic energy: \[ TME = PE + KE \] While conserving mechanical energy in the absence of friction or other non-conservative forces, the total mechanical energy will still remain constant. However, increasing the mass of the skateboarder will raise the baseline for both potential and kinetic energy — meaning that at any height or point in motion, the absolute values of these energies will be larger when the mass is greater.

4. Conclusion on Total Energy: By increasing the mass, you essentially increase the total mechanical energy present in the system. However, as long as the skateboarder is moving only under the influence of gravity and no energy is lost to friction or air resistance, the total energy remains constant throughout the motion. The distribution of energy between potential and kinetic forms will adjust based on the skateboarder's height and speed, but the total amount of mechanical energy will be higher if the mass is larger.

In summary, increasing the mass of the skateboarder increases both the potential and kinetic energy at any point in the motion, thus increasing the total mechanical energy of the system when measured in absolute terms.

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

When you increase the mass of the skateboarder to "Large" using the slider, the total mechanical energy of the system behaves as follows:

1. Potential Energy (PE): The potential energy is calculated by the formula: \[ PE = mgh \]

   • Effect of Increased Mass: When you increase the mass of the skateboarder, the potential energy at any given height (e.g., at the top of the ramp) increases proportionally with the mass. This means that if the skateboarder is at a certain height \(h\), a larger mass will lead to higher potential energy.

2. Kinetic Energy (KE): Kinetic energy is given by: \[ KE = \frac{1}{2}mv^2 \]

   • Effect of Increased Mass: If the skateboarder descends the ramp under the influence of gravity, their speed may change as they fall. While the kinetic energy depends on both the mass and the square of the velocity, if we assume the skateboarder reaches the same speed as a lighter skater at the lowest point of the ramp, the increasing mass will result in increased kinetic energy.

3. Total Mechanical Energy (TME): The total mechanical energy in the system is still defined as the sum of potential and kinetic energy: \[ TME = PE + KE \]

   • Total Energy Change: If the system is closed, meaning no energy losses due to friction or air resistance, the total mechanical energy will remain constant throughout the skateboarder's motion. However, when the mass is increased, the absolute values of potential energy at the top of the ramp and kinetic energy at the bottom of the ramp will increase. Therefore, while the total mechanical energy remains constant (due to the conservation of energy), the baseline of energy you can observe in the system becomes higher with a larger mass.

Summary

• With Increased Mass: The potential energy at the top of the ramp increases. As the skateboarder moves down, kinetic energy at the bottom also tends to increase because of increased mass.
• Conservation of Energy: The total mechanical energy remains constant if you’re neglecting external forces. While the total amount of energy stays the same, the total values of kinetic and potential energy increase, leading to more substantial observable energy changes during the skateboarder’s motion.

In conclusion, increasing the mass of the skateboarder leads to higher potential and kinetic energies, increasing the total observable energy measurement. However, the fundamental principle of conservation of energy means that total mechanical energy remains constant throughout the motion.