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?
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?