How to Calculate Tension in a Hanging Block Supported by a Rubber Cord

[feelau]

Homework Statement

So a 2kg block hangs from a rubber cord and it's being supported so that the cord is not stretched. The unstretch length of the cord is .500 meters and its mass is 5.3 grams. The spring constant for the cord is 105 N/m. The block is released and stops at the lowest point. a)Find the tension b),c) I know how to solve, I only need tension...

Homework Equations

I set up Newton's second law equation when it's at the bottom but I have two variables T and x. I also looked at the osciallation way of approaching this problem but could not think of how I can relate everything together. I know there's only like one equation I'm missing and that's all I need but I don't know what.
Thanks

 

[OlderDan]

I assume they only want the tension when the block is at the lowest point. The tension will not be exactly uniform, since the cord has mass, but the cord's mass is so small compared to that of the block I am assuming you can ignore that. What you need to find is how far the cord has stretched when the block comes to rest and use the spring constant to find the force the cord is providing at that time. That will be the tension. You should be able to use energy principles to find it.

 

[feelau]

hm...part b asks how far it stretches so I thought there would be some other way to approach this. I'm having some troubles trying to visualize the energy equation since at the beginning it has potential energy, but no kinetic right? Then at the lowest point, it is another potential energy. So would it be just mgh=.5kx^2? then h is basically the x correct? so we get 2mg/k=x?

EDIT: Yay I got the answer correct! Thank you soooo much!