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Spring problem? Physics/Calc?
A spring has a natural length of 20 cm. If a 25 N force is required to keep it stretched to a length of 30 cm, how much work is required to stretch it from 20 cm to 25 cm?
F = spring constant * d
So:
25N = const * .1 (20cm to 30cm is .1m)
const = 250
F = spring constant * d again
F = 250 * .05m (from 20cm to 25cm)
F = 12.5
Work = F * d
12.5 * .05 = .625J
Obviously that is way too small, and not correct. Also, WebAssign tells me it isn't correct. Why? What is correct?
1 Answer
- 8 years agoFavourite answer
This is a very weak spring, and the answer is actually a half of what you got.
You have Work Done = F * d = k * d * d = k* d^2
But actually WD = Potential Energy of spring = 0.5 * k * d^2
The 0.5 appears when you integrate the Force and d becomes 0.5*d^2
So the answer will be 0.5 * 250 * 0.05^2 = 0.312 J
