Solving a Physics Problem: Calculating Maximum Distance for Falling Fish

[pedro_infante]

Homework Statement

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.)

Homework Equations

F=-kx

The Attempt at a Solution

I do not remember my prof doing anything like this in class. Can anyone help?

 

[Chi Meson]

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?

 

[pedro_infante]

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

 

[bleedblue1234]

hint: what's 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...

 

[pedro_infante]

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?

 

[Chi Meson]

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

 

[dsol]

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?

In your case,
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?