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## Main Question or Discussion Point

Hello,

I am trying to get an understanding of work and energy conservation and am getting confused.

My thought experiment revolves around a mass hanging from a spring and appling a force to the resting mass.

Assume a 10kg mass hanging from a spring with k = 30 N/m. The mass will stretch the spring to x1 ~= -100/30 = -3.3m (-ve x is downwards). Given an equilbrium position of x1 = -3.3m I then "lift" the mass by applying an upwards force of 50N.

The total force acting on the mass will be 100N (due gravity) minus 50 N due to me lifting the spring. Therefore the mass will come to rest at x2 = -50/30 = 1.67m.

By lifting the mass I have done work on the spring by adding PE to the mass.

ΔPE to mass = mgΔh = 100*1.67 = 167J

I have also removed PE from the spring as I have moved it back towards its unstrained position.

Δ PE to spring = 0.5×(x2^2 - x1^2) = -125J

Does this mean the total work done by me lifting the mass is 167-125 = 42J

Or do I just use W = f×d = 50 x 1.67 = 83.5J

Or have I made a mistake somewhere? Do I need to account for the potential for the mass to oscillate?

Any help would be great!!

I am trying to get an understanding of work and energy conservation and am getting confused.

My thought experiment revolves around a mass hanging from a spring and appling a force to the resting mass.

Assume a 10kg mass hanging from a spring with k = 30 N/m. The mass will stretch the spring to x1 ~= -100/30 = -3.3m (-ve x is downwards). Given an equilbrium position of x1 = -3.3m I then "lift" the mass by applying an upwards force of 50N.

The total force acting on the mass will be 100N (due gravity) minus 50 N due to me lifting the spring. Therefore the mass will come to rest at x2 = -50/30 = 1.67m.

By lifting the mass I have done work on the spring by adding PE to the mass.

ΔPE to mass = mgΔh = 100*1.67 = 167J

I have also removed PE from the spring as I have moved it back towards its unstrained position.

Δ PE to spring = 0.5×(x2^2 - x1^2) = -125J

Does this mean the total work done by me lifting the mass is 167-125 = 42J

Or do I just use W = f×d = 50 x 1.67 = 83.5J

Or have I made a mistake somewhere? Do I need to account for the potential for the mass to oscillate?

Any help would be great!!