This is a four part question, I need help with the fourth part.
1. I found the Gravitational Potential Energy of a gymnast at her maximum height above a trampoline to be 400J.
2. I found the Kinetic Energy of her just before she makes contact with the trampoline to also be 400J.
3. At maximum stretch of the trampoline (at the bottom of the motion) i found the sum of the elastic and gravitational energy of her to also be 398.75J. (And the kinetic energy at this point is 1.25J to make a total of 400J)
4. What conclusions can you draw from the answers found above.
Any ideas?
Thanks in advance.
And what exactly does Conservation of Energy mean?
hahaa.. funny.
I had to show the calculations for each step. So are you suggesting that I just state that this proves the Conservation of Energy?
yes, that is the point of the problem.
To draw conclusions from the given information, we can analyze the energy transfers involved in the motion of the gymnast on the trampoline.
From the given data, we can start by looking at the total mechanical energy of the system. Mechanical energy is the sum of the potential energy and kinetic energy.
In the first situation, at the maximum height, the gravitational potential energy is 400J. At this point, the kinetic energy is zero since the gymnast is at rest. Therefore, the total mechanical energy is equal to the gravitational potential energy, which is 400J.
In the second situation, just before making contact with the trampoline, the kinetic energy of the gymnast is 400J. At this point, the gravitational potential energy becomes zero since the gymnast is at the lowest point of the motion. Therefore, the total mechanical energy is equal to the kinetic energy, which is 400J.
In the third situation, at the maximum stretch of the trampoline, the sum of the elastic potential energy and gravitational potential energy is 398.75J. The kinetic energy at this point is 1.25J, making a total of 400J.
Now, let's analyze the conclusions we can draw:
1. Conservation of mechanical energy: In the absence of external forces, the total mechanical energy (sum of potential and kinetic energy) remains constant. This is evident in situations 1 and 2, where the total mechanical energy (400J) remains the same.
2. Energy transformation: The energy transformation occurs when the gymnast is on the trampoline. In situation 3, the elastic potential energy of the trampoline is storing energy as the trampoline gets stretched, and the gravitational potential energy of the gymnast decreases. The kinetic energy of the gymnast also increases as it gets closer to the trampoline.
3. Energy transfer: The energy transfer between the gymnast and the trampoline can be seen in the change of kinetic energy. In situation 4, the kinetic energy decreases from 400J to 1.25J as the gymnast's downward motion is inhibited by the trampoline.
In summary, the conclusions from the answers found above indicate that energy is conserved within the system, and there is an exchange of energy between potential and kinetic forms as the gymnast interacts with the trampoline.