# Final velocity of a ball down a ramp.

1. Jan 16, 2015

### HHH

1. The problem statement, all variables and given/known data
If a ball is dropped down a ramp of any shape, will the acceleration always be 9.8 assuming there is no friction.

2. Relevant equations
I know you can use mgh = 1/2mv^2 to solve for velocity, but can you use vf^2 = vi^2 + 2(a)(d)

3. The attempt at a solution
If you use both equations you get the same answer for final velocity at the bottom of the ramp. However is the acceleration always 9.8 no matter what the shape of the ramp is?

2. Jan 16, 2015

### haruspex

I don't see any attempt to answer the question here. Think about forces.

3. Jan 16, 2015

### HHH

Does it have to do with the normal force decreasing the force of gravity?

4. Jan 16, 2015

### haruspex

Well, it doesn't decrease it, but it does partially oppose it.

5. Jan 16, 2015

### HHH

so the acceleration would not be 9.8? if not why can you use both equations?

mgh = 1/2mv^2
(2)x(9.8)x(3) = 1/2 (2) v^2
v = 7.6m/s

vf^2 = vi^2 + 2ad
vf^2 = 0 + 2(9.8)(3)
v = 7.6m/s

6. Jan 16, 2015

### haruspex

Ignoring the fact that it's a ball for the moment, just treating it as a zero friction ramp, those (that) equation only tells you the final velocity. It doesn't tell you how long it takes to get there. The final velocity is the same whether dropped straight down or going down a ramp. It only depends on the PE lost. But it takes longer down the ramp, so the acceleration is less.

If it is a rolling ball, that starts off not rotating, then there is another issue. At the end some of the KE will be in rotational energy, so the linear velocity will be less.

7. Jan 16, 2015

### HHH

Thank you.

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