# Conservation of energy

1. Homework Statement [/b
I have 2 question

## Homework Equations

which one gets to point o earlier?we release them,both of them have the same conditions. the distance and mass every thing are the same.
I have attached the figures

## The Attempt at a Solution

I think in the first one because of the rotational motion that ball has ,the energy of it is divided, so ball get later,
Second one: In one figure on the way there is a hole and another one there isn't, I don't have any idea that which one get faster!

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stewartcs
1. Homework Statement [/b
I have 2 question

## Homework Equations

which one gets to point o earlier?we release them,both of them have the same conditions. the distance and mass every thing are the same.
I have attached the figures

## The Attempt at a Solution

I think in the first one because of the rotational motion that ball has ,the energy of it is divided, so ball get later,
Second one I don't have any idea that which one get faster!

Are the ramps frictionless?

What equations do you know?

CS

no,
Ei=0 Ef=1/2 Iω^2+mgLcosα
if α is the angle , L is distance

stewartcs
no,
Ei=0 Ef=1/2 Iω^2+mgLcosα
if α is the angle , L is distance
Did they tell you anything about the friction in the problem statement?

CS

No but I think because of frictional force the ball is rolling, if the plane is frictionless both of them get the same time

if we have friction we have rotational and translational motin. so for the ball
Ei=0 Ef=1/2 Iω^2+mgLcosα+1/2 mv^2 where I=2/5MR^2

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Am I right?

stewartcs
No but I think because of frictional force the ball is rolling, if the plane is frictionless both of them get the same time
You must know something about the frictional force between the objects and the ramp. Otherwise you can't determine the answer. For example, if the frictional force between the block and the ramp is high enough, the block will not even move. However, the cylinder will still roll down the ramp.

Also, if the ramp is frictionless and the cylinder has a pure rolling motion without slipping, the cylinder will reach the bottom last since it's Kinetic Energy has two components (1/2 mv^2 + 1/2 Iw^2 whereas the block only has 1/2 mv^2).

If the cylinder slips and doesn't roll, then they both will reach the bottom at the same time. Hence, it depends on what assumptions you make.

So you need more information. Did you post the entire problem statement?

CS

No, it didnt mention
for second figure could you help me?
(the figure: on the way there is a hole and another one there isn't)

stewartcs
No, it didnt mention
for second figure could you help me?
(the figure: on the way there is a hole and another one there isn't)
I don't understand your second drawing. If the two cylinders are at rest on a horizontal plane and no force acts on them, neither will move horizontally.

CS

Sorry its my fault,
We just hit the ball in the same way

stewartcs