How Do Incline Angles Affect the Speed of a Rolling Ball?

[nvez]

[RESOLVED] Speed in relation to angles

Homework Statement

You leave a ball roll down 3 different inclined plans with the same height. They each have 30, 45 & 60 degrees of incline respectively. Compare the sped of each of these plans

Height = constant, doesn't change
Angles of plans = 30, 45, 60

Homework Equations

None that I know of.

The Attempt at a Solution

I honestly do not see a way how to resolve this problem, if anyone can just shed any light, I know we're working in energy at the moment but I cannot find a way to get information with just an angle.

 

[LowlyPion]

That would be correct. Potential energy at the top will be kinetic energy at the bottom.

They will take different times to reach the bottom ... but at the bottom they will be going at the same speed. (Assuming there is no slipping at the steeper angle or bouncing on impact at the bottom etc.)

 

[nvez]

I _think_ I got it, this is what I did

$$mgh = 1/2mv^{2}$$

m = m therefore removed.

$$gh = 1/2v^{2}$$

take 1/2 on other side becomes 2

$$2gh = v^{2}$$

take the ^2 and make it sqrt the other side

$$\sqrt{2gh} = v$$

Therefore we conclude that the only variables that matter in it's speed is the gravity and height, which is the same in all 3 problems therefore it will arrive at the same speed because gravity and height are constant?

Thanks in advanced if I'm correct. :)

 

[LowlyPion]

That's correct.

 

[nvez]

That's correct.

Thank you very much again, I really appreciate it! :)