Where Did the Missing Energy Go in Stretching a Wire in Space?

[Iamtoast]

Homework Statement

I am in the vacuum of space. I carefully load a wire with a mass of 8kg, supporting the mass all the while with my hand. The wire stretches by 4.2 cm. What is the potential energy stored by the wire? What is the loss of potential energy of the mass?

Homework Equations

energy stored in the wire = work done in stretching the wire = 1/2 F.x
gpe lost by mass = mgh

The Attempt at a Solution

energy stored in the wire = work done in stretching the wire = 1/2 F.x = 1/2 mgx = 1.65 J
gpe lost by mass = mgh = 3.3 J

The wire gains exactly half the energy lost by the mass. A curious result. The wire's c of g is also lower and hence the wire loses gpe. My hand is also lower than at the start and loses gpe. The wire was loaded so carefully that there was no perceptible rise in temperature of any part of the apparatus. Where has my missing energy gone?

 

[anathema]

Thank you for your question. It seems like you have made some good progress in calculating the potential energy stored in the wire and the loss of potential energy of the mass. However, there are a few things to consider in this scenario.

Firstly, in a vacuum of space, there is no air resistance or friction to dissipate energy. This means that the total energy in the system should remain constant. In other words, the energy lost by the mass should be equal to the energy gained by the wire and your hand.

Secondly, when you carefully load the wire with the mass, you are doing work on the system. This work is what causes the wire to stretch and the mass to gain potential energy. However, when you release the mass, the wire will return to its original length and the mass will lose its potential energy. This means that the energy stored in the wire is only temporary and will be released as the wire returns to its original state.

So, to answer your question about the missing energy, it has not disappeared but has been temporarily stored in the wire as potential energy. Once the mass is released, this energy will be released and the wire, your hand, and the mass will return to their original states.

I hope this helps to clarify any confusion. Keep up the good work in your scientific studies!

 

[ogb p]

I would first double check my calculations to ensure they are correct. Then, I would consider other factors that may have contributed to the missing energy. It is possible that some energy was lost due to friction between the wire and my hand, or between the wire and the supports holding it in place. Additionally, there may be some small amount of energy lost due to air resistance, even in the vacuum of space. Another possibility is that some energy was lost as heat due to the stretching and deformation of the wire itself. Further experiments and data collection may be necessary to fully understand and account for the missing energy.