Homework Help: Stretching of a spring: calculate force constant of spring in terms of distance and m

1. Oct 25, 2009

pedro_infante

1. The problem statement, all variables and given/known data
If a fish is attached to a vertical spring and slowly lowered to its equilibrium position, it is found to stretch the spring by an amount d.
If the same fish is attached to the end of the unstretched spring and then allowed to fall from rest, through what maximum distance does it stretch the spring? (Hint: Calculate the force constant of the spring in terms of the distance d and the mass m of the fish.)
2. Relevant equations
F=-kx

3. The attempt at a solution
I do not remember my prof doing anything like this in class. Can anyone help?

Last edited: Oct 25, 2009
2. Oct 25, 2009

Chi Meson

Re: stretching of a spring: calculate force constant of spring in terms of distance a

In this case, you need to use the conservation of energy principle. Do you know the equation for the energy in a compressed/extended spring?

3. Oct 25, 2009

pedro_infante

Re: stretching of a spring: calculate force constant of spring in terms of distance a

yeah I just don't know where to start really. it's F=-kx

4. Oct 25, 2009

bleedblue1234

Re: stretching of a spring: calculate force constant of spring in terms of distance a

hint: whats the force provided by the fish?

how would i go about getting k after I have found F and x...

I have a feeling you are missing something in your problem statement....

5. Oct 25, 2009

pedro_infante

Re: stretching of a spring: calculate force constant of spring in terms of distance a

well that's all the mastering physics website states as the problem statement.
so F=ma so F= mg
so mg=-kx
so k=mg/x?

6. Oct 26, 2009

Chi Meson

Re: stretching of a spring: calculate force constant of spring in terms of distance a

yes, and now you need the equation for the energy in a compressed/extended spring.

7. Nov 12, 2009

dsol

Re: stretching of a spring: calculate force constant of spring in terms of distance a

sumF=mg-kx=0
at x=d, mg=kd --> k=mg/d

To find the maximum distance the spring stretches, you need to use an energy perspective (@Chi Meson)

sum E=mgx-(k*x^2)/2-(m*v^2)/2=0
The first term is the potential energy of the mass.
The second term is the potential energy of the spring.
The third term is the kinetic energy of the mass (These problems ignore the kinetic energy of the spring).

Solve the energy equation for x.
Hint: When the spring is at its maximum stretch, what is your velocity v?