Question

If you cut a spring of stiffness constant k to two equal lengths, what is the spring constant for each of the two pieces. Hint: Use Newton’s Third Law and Hooke’s law in justifying your answer.

Answer 1

Answer:2k

Step-by-step explanation:

Given

Let K' be the new spring constant of each half

K is the original spring constant

If the original spring is formed using half piece with x_1 and x_2 extension in each spring when same force is applied as for the original spring

then

F=kx

for new spring

x=x_1+x_2

`(F)/(k)=(F)/(k')+(F)/(k')` [from hooke's law]

`(1)/(k)=(1)/(k') +(1)/(k')`

k'=2k