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Grade: 10

                        

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?

5 years ago

Answers : (1)

Jitender Pal
askIITians Faculty
365 Points
							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.
5 years ago
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