A 650N man jumps out of a window into a fire net 8m below. The net stretches 1.5m before bringing the man to rest and tossing him back into the air. What is the maximum potential energy of the net compared to its unstretched potential energy?
When the man stopped at the bottom he had minimal potential energy and no kinetic energy.
He had gone down 9.5 meters
so the total energy he lost was m g h = 650*9.8*9.5
The net is also not moving then so all that potential the man had went into potential energy of the net. When the net starts the man moving it will have to use up that potential so that is the max.
To find the maximum potential energy of the net compared to its unstretched potential energy, we need to calculate the change in potential energy.
The potential energy of an object is given by the equation U = mgh, where U is the potential energy, m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
In this case, we are dealing with a person, so we need to calculate the potential energy both when the person is at rest on the net and when the net is stretched.
1. Unstretched Potential Energy:
The unstretched potential energy is given by U_unstretched = mgh. Since the person is at rest on the net, the height is simply the height from the ground to the window, which is 8 m. So we have:
U_unstretched = m * g * h_unstretched
2. Stretched Potential Energy:
When the net stretches, it brings the person to rest and then tosses the person back into the air. At the maximum stretch, the height of the person from the ground is zero (the person is back at the same level as the window).
At this point, all the potential energy has been converted into kinetic energy and then back into potential energy again. So, the maximum potential energy of the net is equal to the original potential energy before the person jumped.
U_stretched = U_unstretched
Therefore, the maximum potential energy of the net compared to its unstretched potential energy is equal to 1.
In other words, at the maximum stretch, the potential energy of the net is the same as its original potential energy before the person jumped.