# Finding Force Constant of a Spring

1. Nov 12, 2009

### court2011

1. The problem statement, all variables and given/known data
A 1.80 kg block slides on a rough, horizontal surface. The block hits a spring with a speed of 1.95 m/s and compresses it a distance of 14.0 cm before coming to rest. If the coefficient of kinetic friction between the block and the surface is µk = 0.560, what is the force constant of the spring?

2. Relevant equations

k=2U/x^2

3. The attempt at a solution
k=2(0.560)/0.14^2

2. Nov 12, 2009

### rl.bhat

Hi court2011, welcome to PF.
The kinetic energy of the block is utilized to do the work to overcome the friction and compress the spring.
What is the frictional force?

3. Nov 12, 2009

### court2011

hi!! the problem doesn't say so im assuming i have to find it given the coefficient of kinetic friction?

4. Nov 12, 2009

### rl.bhat

Kinetic energy of the block = Potential energy of the spring + work done against the frictional force.

5. Nov 12, 2009

### court2011

ok so potential energy is = mgy but if its going horizontal isnt y=0 so the potential energy is 0?

6. Nov 12, 2009

### rl.bhat

Potential energy stored in the spring is 1/2*k*x^2.

7. Nov 12, 2009

### court2011

ok i need to find k so how do i get the potential energy without having k in the equation?

8. Nov 12, 2009

### rl.bhat

First of all find the frictional force.
Then using 1/2*m*v^2 = Fr*x + 1/2*k*x^2 find k.

9. Nov 12, 2009

### court2011

is Fr where i am supposed to insert the frictional force? because i did and I still got the problem wrong but equation seems right how do i find the frictional force isnt it fk=ukN?

10. Nov 12, 2009

### rl.bhat

I am refereeing Fr as fk which is equal to μk*N. Now what is the normal force?

11. Nov 12, 2009

### court2011

ma which is 1.8*1.95=3.51

12. Nov 12, 2009

### rl.bhat

The normal force is mg.
Frictional force is μk*mg.