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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.

Respuesta :

Answer:2k

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

[tex]\frac{F}{k}=\frac{F}{k'}+\frac{F}{k'}[/tex]  [from hooke's law]

[tex]\frac{1}{k}=\frac{1}{k'} +\frac{1}{k'}[/tex]

k'=2k  

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