Pebble Shot with Spring Constant - how to setup?

[Schoomy]

Homework Statement

You shoot a 49 g pebble straight up with a catapult whose spring constant is 320 N/m. The catapult is initially stretched by 0.30 m. How high above the starting point does the pebble fly? Ignore air resistance.

Homework Equations

Unsure?

The Attempt at a Solution

49g pebble = 0.049kg

 

[rock.freak667]

When the spring is stretched how much elastic potential energy does it have?

This is the energy that is converted to gravitational potential energy to raise it to the maximum height.

 

[Schoomy]

Uelastic = (.5)(320N/m)(0.3m²) = 14.4.

But then what? How do I turn this into a height?

 

[rock.freak667]

what is the formula for gravitational potential energy?

 

[Schoomy]

Ugrav = mg$$\Delta$$y

 

[Schoomy]

I can find U grav, but i don't see what that would get me?

Ug = (0.049kg)(9.8)(0.3)
= 0.144

 

[rock.freak667]

I can find U grav, but i don't see what that would get me?

Ug = (0.049kg)(9.8)(0.3)
= 0.144

0.3 is not the height. if y is the height and U=mgy, and you know the energy it has is equal to the elastic potential energy (which you found to be 14.4J) can you find the height y?

 

[Schoomy]

Yep. It was y that I was looking for...duh. So I just leave it blank, set Ug equal to 14.4, and solve for y, giving me roughly 30m as an answer.

Thanks!