Find the distance that a force stretches a spring.

[student34]

Homework Statement

A mass of 6.40 kg is hung from a spring with aforce constant of 7.80*10^3 N/m. The spring unstretched is 0.120m long. Find the distance that the spring stretches.

Homework Equations

F = k*x is the way that gives the answer in my textbook.

I tried W = 0.5*k*x^2.

The Attempt at a Solution

What is wrong with the following? I used W = 0.5*k*x^2 = 0.5*7800N/m*x^2 . Then made W = m*g*x. So, m*g*x = 0.5*7800N/m*x^2. Then I canceled out the x from both sides, and isolate the remaining x, so x = (m*g)/(0.5*78000N/m) = 0.136m. My answer is close to the correct answer of x = 0.128m, but I would really like to know what I don't understand which led me to the wrong answer.

 

[TerraForce469]

Use Newton's 2nd law. Draw your FBD and correctly set up your terms for ƩF, knowing that the system is at static equilibirum. You'll be able to find the change in x of the spring from its unstretched length this way.

The x in your 'mgx' term (which in this case is also the gravitational potential energy) isn't the same as the x in your '.5mgx^2' term. Energy methods aren't always so convenient in these types of problems.

 

[tiny-tim]

hi student34!

A mass of 6.40 kg is hung from a spring with aforce constant of 7.80*10^3 N/m. The spring unstretched is 0.120m long. Find the distance that the spring stretches.

you're using conservation of energy, which (correctly) gives you the lowest point of the motion if the mass is released from rest in the unstretched position, and allowed to oscillate up and down

but the question is about carefully lowering the mass until the system is in equilibrium

 

[student34]

Thanks for both of these answers!

 

[Hush]

If I know the spring constant, I can calculate the displacement given the mass,
mg=kx
x=mg/k

6400*.00980665=62.76256N
62.76256N/7800N=.008046482m.
This must be wrong if the textbook wants exactly .008m as displacement.
So I fail. A for effort.

 

[Hush]

...and the units in the last expression all must be labeled N/m.
I am a disgrace to the profession.