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You cut a spring in half. What is the relation of the force constant k for the original spring to that for either of the half-springs?
You cut a spring in half. What is the relation of the force constant k for the original spring to that for either of the half-springs?

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5 years ago

```							The new force constant (kʹ) for either of the half springs will be doubled of the force constant k for the original spring.By Hooke’s law, in one dimension, the x component of the force exerted by the spring (F) on the body attached to it as,F = -kx …… (1)Where, k is the force constant.So the force constant (k) will be,k = F/x …… (2)When you cut a spring in half, so length of the each new spring (xʹ) will be,xʹ = x/2 …… (3)If the same force is applied then, the new force constant (kʹ) will be,kʹ = F/xʹ …… (4)To find the new force constant (kʹ), substitute xʹ = x/2 in the equation kʹ = F/xʹ,kʹ = F/xʹ = F/(x/2) = 2F/x= 2k (Since, from equation (2), k = F/x) …… (5)From equation (5) we observed that, the new force constant (kʹ) for either of the half springs will be doubled of the force constant k for the original spring.
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5 years ago
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