Use the ramp shaped like a U.

Question

→ 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).
→ Now use the phet, image below, and table to answer the following questions.

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

Answer 1

In the context of the scenario described, the skateboarder has the greatest potential energy at point A because potential energy is defined as the energy stored in an object due to its position relative to other objects, its condition, or its state.

At point A, which is the highest point on the ramp, the skateboarder has the maximum height compared to other points on the ramp. The potential energy (PE) of an object can be calculated using the formula:

\[ PE = mgh \]

where:

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

Since point A represents the highest vertical position of the skateboarder, the height \( h \) is at its maximum there. Consequently, since the mass \( m \) and gravity \( g \) remain constant, the potential energy is also at its maximum at this point.

As the skateboarder descends the ramp from point A to lower points (like point B or point C), the height decreases, which in turn decreases the potential energy. This energy is then transformed into kinetic energy as the skateboarder accelerates down the ramp, demonstrating the conservation of mechanical energy (where total energy remains constant if we ignore friction and air resistance).

In summary, the skateboarder has the greatest potential energy at point A due to its maximum height, making it the point where gravitational potential energy is highest.

Answer 2

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 3

When you increase the mass of the skater using the slider in the simulation, the total amount of energy, particularly the potential energy, increases. Here's how it works:

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

   \[ PE = mgh \]

   In this formula:

   • \( m \) is the mass of the skater,
   • \( g \) is the acceleration due to gravity (approximately 9.81 m/s²),
   • \( h \) is the height of the ramp.

   When you increase the mass (\( m \)), keeping height (\( h \)) and the acceleration due to gravity (\( g \)) constant, the potential energy will increase proportionally to the mass. For example, if the mass doubles, the potential energy will also double, assuming the skater is at the same height on the ramp.

2. Total Mechanical Energy: The total mechanical energy (which is the sum of potential energy and kinetic energy) should remain constant, assuming no energy losses due to friction or air resistance. When the skater is at the top of the ramp (point A), all the energy is in the form of potential energy. As the skater descends, potential energy is converted into kinetic energy.

3. Kinetic Energy (KE): When the skater descends, their kinetic energy can be calculated using the formula:

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

   If the mass increases, as long as energy conservation holds true, the kinetic energy at the bottom of the ramp will also reflect that increased mass. So, if the mass is larger, the skater will not only have more potential energy at the top but will also have more kinetic energy at the bottom, given that all potential energy is converted to kinetic energy during the descent.

In summary, increasing the mass of the skater will increase the total potential energy at the top of the ramp, and while the total mechanical energy remains constant, the distribution between potential and kinetic energy will change as the skater moves down the ramp.

Answer 4

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.
Type Answer HERE:

Answer 5

Increasing the height of the ramp to 12 meters would significantly affect both the potential energy (PE) and the kinetic energy (KE) during the investigation. Here’s how:

Effects on Potential Energy

1. Increased Potential Energy:
   • Potential energy is directly proportional to height (h) as per the formula: \[ PE = mgh \]
   • If you increase the height of the ramp to 12 meters, and the mass of the skater remains constant, the potential energy at the top of the ramp will increase substantially. For instance, if the mass of the skater is 50 kg, the potential energy at the top of the ramp (point A) can be calculated as: \[ PE = 50 \text{ kg} \times 9.81 \text{ m/s}^2 \times 12 \text{ m} = 5886 \text{ J} \]
   • This is much greater than the potential energy at lower heights (e.g., 6 meters, which would yield 2943 J for the same mass). Thus, increasing height leads to greater stored energy due to gravity.

Effects on Kinetic Energy

2. Increased Kinetic Energy:
   • If the skater starts from a higher position (12 meters), as they descend the ramp, all potential energy will be converted to kinetic energy (assuming no energy is lost to friction or air resistance). At the bottom of the ramp, the kinetic energy will be equal to the potential energy at the top.
   • Using the earlier example, when the skater reaches the bottom, their kinetic energy would also be 5886 J, as energy is conserved: \[ KE = PE , \text{at the bottom of the ramp} \]
   • This is again greater than the kinetic energy they would have at a lower height.

Summary

In summary, increasing the height of the ramp to 12 meters would lead to a significant increase in potential energy due to the higher elevation, which in turn results in a proportional increase in kinetic energy at the bottom of the ramp. The total mechanical energy of the system would remain constant throughout the motion (if we neglect friction), and would consist of a higher amount of energy available to the skater, allowing them to reach higher speeds at the bottom of the ramp. This concept demonstrates the essential principle of conservation of energy in mechanics.