Solving Physics Problem: Calculating Net Stretch for 55.3kg Person

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In summary, the conversation discusses the calculation of the displacement of a fire net when a 55.3 kg person jumps into it from a window 21.9 m above. The net is assumed to behave like a simple spring and the calculation takes into account the conservation of energy, velocity, acceleration, force, and spring constant. However, there is an additional factor of gravitational potential energy that was not initially considered.
  • #1
ninjagowoowoo
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Q:
A 55.3 kg person jumps from a window to a fire net 21.9 m below, which stretches the net 1.04 m. Assume that the net behaves like a simple spring, and calculate how much it would stretch if the same person were lying in it.

Here's what I did:

using conservation of energy to get the velocity of the person right before it hits the net. (mgh = 0.5mv^2) Once I got the velocity, I found the acceleration caused by the net (deceleration if you will) (v^2=v^2 + 2ay). Then using that acceleration, I found the force of the net on the person (F=ma) Once I found that force, I used it to find the spring constant(k) of the "spring". (F=ky). Finally, using that k, I found the displacement of the "spring" caused by the force of just the person's weight (F=kx where F=55.3kg(9.8)) and got an answer, which was wrong.

Can anyone help me?
 
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  • #2
You forgot to take into consideration the gravitational potential energy difference while the person was on the trampolin.

So,

[tex]\frac{kx^2}{2}=mg(h+x)[/tex]
 
  • #3
hmm I don't quite understand the formula you came up with. I understand what you are saying, but perhaps you could elaborate a little more on how you came up with that formula. Thanks.
 
  • #4
oh by the way, thanks for the help.
 
  • #5
Law of conservation of energy. The gravitational potential energy is converted into the energy of the spring.

[tex]E=\frac{kx^2}{2}[/tex]

The person doesn't only fall 21.9 m, he also falls for an additional 1.04 m while he's streching the trampoline.
 
Last edited:

Related to Solving Physics Problem: Calculating Net Stretch for 55.3kg Person

What is the formula for calculating net stretch?

The formula for calculating net stretch is F=kx, where F is the force applied, k is the spring constant, and x is the displacement or change in length.

How do I determine the spring constant?

The spring constant can be determined by dividing the force applied by the displacement. This can also be found in the specifications of the spring itself if it is a pre-made spring.

What units should I use for the calculations?

The force should be measured in Newtons (N), the displacement in meters (m), and the spring constant in Newtons per meter (N/m).

Do I need to consider the weight of the person in the calculations?

Yes, the weight of the person should be included in the force applied. In this case, the force would be the weight of the person (55.3kg) multiplied by the acceleration due to gravity (9.8m/s^2).

What if I don't know the spring constant or the force applied?

If you do not have the spring constant or force applied, you can still calculate the net stretch by measuring the initial length of the spring and the length after the person is on it. The difference in length will be the displacement (x) in the formula.

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