How Do You Calculate Spring Constant with Friction Involved?

[rileyjah]

Friction/Springs/HELP!
An object of mass m=2.6 kg is traveling on a horizontal surface. The coefficient of kinetic friction between the object and the surface is µk=0.16. The object has speed v=0.65 m/s when it reaches x=0 and encounters a spring. The object compresses the spring a distance d/2, stops instantaneously, and then travels back to x=0 where it stops completely. Eventually you will be asked to find the spring constant, k.

1.What is the total distance, d, that the object moves after first touching the spring?
2.When the object reaches d/2 and stops instantaneously, what is the energy stored in the spring?
3.What is the spring constant, k, of the spring?

I just tried to post w/ my entire attempt at a soln ad somehow lost it- so here's a quick version.

1. I got this correct- Wfriction=mv^2/2=-mgukd, solve for d gives correct answer
2. KEspring+Espring=KEi+ Wfriction
Espring= KEi- KEspring+Wfriction=.5mv2-0-mgukd
not correct answer, this is where I feel very confused
3. Espring=-k*d ?

DO I have to use Kf+Uf+deltaEth=Ki+Ui+Wext to solve this problem beacuse friction is non-conservative... if so how?

 

[rileyjah]

Ok, I know how to get 2. So how do I get the spring constant, F=-k*X, but what is F??/

 

[krausr79]

The work required to compress a spring is (1/2)kx² where x is the compression in meters and k is the spring constant. If you figured the energy to compress the spring then you can solve for it, yes?

 

[PhanthomJay]

Ok, I know how to get 2. So how do I get the spring constant, F=-k*X, but what is F??/

the energy stored in the spring is equal to the work done on it, (F_avg)(displacement). F is 0 when it just starts to compress, and F is kx when it's compressed to its maximum. So calculate (F_avg), and multiply it by the spring displacement, to get the stored energy, a well known equation.

 

[rileyjah]

Thank you all I got it now ;)