# Spring constant?

1. Jan 4, 2010

### lking226

1. The problem statement, all variables and given/known data
A ball is dropped from rest at a height of 50.0m above a spring. After the ball hits, it compresses the spring .340m. Ignoring any non-conservative forces, find the spring constant if the mass of the ball is 4.50 kg.

2. Relevant equations
Hooke's law: k = mg/x

3. The attempt at a solution
I'm not sure what to do.
k = 4.50 kg x 9.8 m/s / 0.340 m = 129.71
That doesn't seem right.
Help?

2. Jan 4, 2010

### rock.freak667

Conservation of energy would work very well here.

3. Jan 4, 2010

### lking226

but how do you use conservation of energy with springs?

4. Jan 4, 2010

### rock.freak667

The potential energy stored in a spring is given by 1/2kx2. So what type of energy is being converted into the elastic potential energy in the spring?

5. Jan 4, 2010

### lking226

the kinetic energy of the ball?

6. Jan 4, 2010

### rock.freak667

The energy is possesses at rest 50m above the spring.

7. Jan 4, 2010

### lking226

so the gravitational potential energy of the ball at 50m converts to the elastic potential energy in the spring?

8. Jan 4, 2010

### rock.freak667

That would be correct. Can you now form an equation and solve for the spring constant 'k'?

9. Jan 4, 2010

### lking226

mghi + kxi^2 = mghf + kxf^2 ??

10. Jan 4, 2010

### rock.freak667

Initially the spring is not extended, so what does the left side reduce to? At the final stage, the final height is zero. So the entire equation simplifies to?

11. Jan 4, 2010

### lking226

so then just

mghi = kxf^2

12. Jan 4, 2010

### rock.freak667

Right, so what is k equal to now?

13. Jan 4, 2010

### lking226

4.50 kg x 9.8 m/s x 50.0 m = k x 0.340m
k = 6485.3 ?

14. Jan 4, 2010

### rock.freak667

That should be

$$4.5 kg \times 9.81 m/s^2 \times 50m = \frac{1}{2}k(0.34m)^2$$

Solve again for k

15. Jan 4, 2010

### lking226

38187.71?

16. Jan 4, 2010

### rock.freak667

That looks correct to me

17. Jan 4, 2010

### lking226

Thank you so much!

18. Jan 4, 2010

### Phrak

To nit-pick, the ball doesn't fall 50.0 meters, it falls 50.34 m after compressing the spring.