Question

It takes 130 J of work to compress a certain spring 0.10m. (a) What is the force constant of this spring? (b) To compress the spring an additional 0.10 m, does it take 130 J, more than 130 J or less than 130 J? Verify your answer with a calculation.

Answer 1

Step-by-step explanation:

Given that,

Work done to stretch the spring, W = 130 J

Distance, x = 0.1 m

(a) We know that work done in stretching the spring is as follows :

`W=(1)/(2)kx^2\\\\k=(2W)/(x^2)\\\\k=(2* 130)/((0.1)^2)\\\\k=26000\ N/m`

(b) If additional distance is 0.1 m i.e. x = 0.1 + 0.1 = 0.2 m

So,

`W=(1)/(2)kx^2\\\\W=(1)/(2)* 26000* 0.2^2\\\\W=520\ J`

So, the new work is more than 130 J.