Energy conservation used to predict speed?

[chops369]

Homework Statement

I don't know if anyone can help me with this without having done the lab, but I thought I'd give it a shot. Ok, so I did a lab in my physics class where we used little rollercoasters to find the PE and KE of a marble at various heights and speeds. Here is the question in my lab write-up that has me stumped.

How can you use energy conservation to predict the speed of the marble from the height?

Homework Equations

PEi + KEi = PEf = KEf

The Attempt at a Solution

I know that you can obtain the equation Vf = √2gh_i from energy conservation, but that doesn't seem to be working when I plug in the height. It isn't coming out to the correct speed which I already calculated.

 

[rock.freak667]

Well from the top of the roller coaster it would have 0 KE, and max PE. (At height h₁). So the PE here is mgh₁.

When it moves from the initial height, h1 to another height, h₂. The PE is mgh₂. This change in PE, mg(h₁-h₂). Gives the change in kinetic energy.

EDIT:

So by conservation of energy:

1/2 mv²=mg(h₁-h₂)

 

[wiggler115]

you can use the equation 1/2mv^2+mgh=1/2mv^2+mgh

 

[LowlyPion]

For one thing you have the angular kinetic energy of the marble.

KE = 1/2*I*ω²

For a sphere - the marble - I = 2/5*m*r²

So the √2gh is really (2gh/(1+2/5*r))^1/2

 

[chops369]

So by conservation of energy:

1/2 mv²=mg(h₁-h₂)

Wouldn't that simplify to Vf = √2g(h_i - h_f) ?

And @ LowlyPion, idk how to do angular KE, you're making it harder than it actually is.

 

[LowlyPion]

And @ LowlyPion, idk how to do angular KE, you're making it harder than it actually is.

I understand. But your marble rolls without slipping. That means as the speed increases, some of the PE is going to KE_r.

If you are wanting to determine why observation doesn't match the math, that's where some of your error is coming from.