Where Has the Missing Energy in a Stretched Wire Gone?

[Iamtoast]

Homework Statement

Perhaps a more provocative title will engage readers:

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. And it is not only the mass that loses energy. 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?

 

[Shooting Star]

Have a look at this and see if it's of any help. It discusses the same question.

https://www.physicsforums.com/showthread.php?t=197946

 

[TVP45]

Homework Statement

Perhaps a more provocative title will engage readers:

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. And it is not only the mass that loses energy. 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?

I suggest the following experiment:
Place perhaps 20 large rocks, cinderblocks, bags of sand, whatever on an elevated shelf, table, wall so that they are perhaps 50 cm or more above the floor.

Then allow them to sit quietly while you rest and put on clothing that is just a little warm for the ambient temperature.

Then lower each object smoothly to the ground, making sure none hit the ground with any appreciable speed. Don't pause till all are down.

Did any part of the system experience a temperature rise? If you're not sure, repeat with 100 objects (or have your weight-lifter brother keep replacing the objects back on the shelf).

 

[Shooting Star]

It's sweaty work! Would the increase in humidity contribute to temperature change?

Also, every object has to be lowered infinitely slowly...Otherwise the whole process has to be repeated until it's perfected.

 

[TVP45]

That is like one of those old movies where the cops find a message written on a bathroom mirror with lipstick,
"Stop me before I pun again"

Wish I had said it.

 

[Iamtoast]

Thanks y'all

Thank you TVP (textured vegetable protein?) 45 and Shooting Star. I like your response and the gently mocking humour with which it is laced. Priceless.

 

[Shooting Star]

But I do hope you also got a qualitative idea about the problem that you had posed.

 

[TVP45]

By the way, you could do your experiment with a constant force spring where, in the ideal case, the mass could be lowered by a baby's breath on it, and you would have no "missing energy". The equations come out a little different for constant force springs of course.

TVP (textured vegetable protein?) Ah, you've seen my latest brain MRI?