Question

A spring has a natural length of 20 meters. how do i find the work required to stretch the spring from 20 meters to 30 meters?

Answer 1

Given: \(\sf x_1 = 20\ m,\ x_2= 30\ m\)
Unknown: Work Done

What you should know:

Spring Force: F= -Kx , K is the spring constant
Work Done is:
\(\sf W= \int_{x_1}^{x_2} F• dx\\W= \int_{x_1}^{x_2} -kx• dx\\ W= -k \int_{x_1}^{x_2} x\ dx \\ \color{red}{\large W=\frac{1}{2}k[x_1^2-x_2^2]} \)

From the derived formula of the Work, you can now easily plug in your given values.

Answer 2

thank you for the help but there is no given values
for part 1 of the question it ask for the work required to stretch the spring from 20m to 30m
part 2 ask for the work to stretch the spring 30 to 40m
part 3 ask how is the work related
so I am not sure if the answer should include K(constant) or no

Answer 3

I assume you have to include the K on your answer.
The only givens are the initial and final positions of the the spring.
Same thing you have to do with part 2.

For part 3, how is work related to what? Is that the complete question or there is still a continuation?

[sorry, os took a long time to load]

Answer 4

that is the complete question. for part a, i got 50k N and part b 150K N
3W(a)=W(b)