A spring with a spring constant of 38N/cm has a cage attached to one end. How mu

Question

A spring with a spring constant of 38N/cm has a cage attached to one end. How much work does the spring force do on the cage if the spring is stretched from its relaxed length by 7.6 mm?

How much additional work is done by the spring force if it is stretched by an additional 7.6 mm?

A spring with a spring constant of 38N/cm has a cage attached to one end. How much work does the spring force do on the cage if the spring is stretched from its relaxed length by 7.6 mm? How much additional work is done by the spring force if it is stretched by an additional 7.6 mm?

Explanation / Answer

potential energy of a spring = 1/2 kx^2
k = 3800 N/m
x = 0.0076 m

then by puting the values

PE = 0.5 * 3800 * 0.0076 * 0.0076

PE = 0.1097 J

for the additional 0.0076m

so the total allongation is 0.0076 + 0.0076 = 0.0152 m

for this allongation potential energy is

PE1 = 0.5 * 300 * 0.0152 * 0.0152

PE1 = 0.4389 J

so the additioanl work is

PE1 - PE = 0.4389 - 0.1097 = 0.3292 J

the addtional work is done by the spring is 0.329 J

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