Dropping a ball

[Hemichordate]

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[HopefulOncoDoc]

Yup. According to energy conservation; v^2 = 2gh so as long as the heights are the same, they should both have the same speeds at the bottom.

 

[ezsanche]

Whether or not you drop a ball off of a ledge straight down or you roll the ball off of a frictionless ramp, the speed at the bottom of both will be the same, right?

The balle will have the same speed. but which one will have more total energy?

 

[Hemichordate]

The balle will have the same speed. but which one will have more total energy?

The same?

 

[ezsanche]

The same?

Assuming they fall from the same height.


The ball that was drop straight down is not rotating. So there is no rotational kinetic energy. It only has potential energy and translational kinetic energy.

The ball that was ROLLED off the table has rotational kinetic energy, potential energy and kinetic energy.

So the ball that was rolled off should have more energy.

 

[wanderer]

Assuming they fall from the same height.


The ball that was drop straight down is not rotating. So there is no rotational kinetic energy. It only has potential energy and translational kinetic energy.

The ball that was ROLLED off the table has rotational kinetic energy, potential energy and kinetic energy.

So the ball that was rolled off should have more energy.

No it shouldn't. KEf total = PE initial. If the ball is rolling it would have a smaller linear velocity so it would have a lower linear KE than the dropped ball. The total KEf would be the same in both cases.

 

[ezsanche]

No it shouldn't. KEf total = PE initial. If the ball is rolling it would have a smaller linear velocity so it would have a lower linear KE than the dropped ball. The total KEf would be the same in both cases.

opps your right. I misread the original statement as a ball rolled of a table then falling straight down. and a ball that is just dropped from the same height. In which case then I would be right.

Now since we are talking about a ball rolled off a ramp. The speed would not be the same when it reaches the bottom.

here is a good link http://hyperphysics.phy-astr.gsu.edu/Hbase/sphinc.html#sph

that explains things a bit.

 

[pastryman]

i think the ball rolling off the ramp would have a lower final velocity because it had a lower acceleration than the ball that dropped straight down. (gsintheta vs. g)....

 

[HopefulOncoDoc]

i think the ball rolling off the ramp would have a lower final velocity because it had a lower acceleration than the ball that dropped straight down. (gsintheta vs. g)....

Yep. You're right. Sorry about that OP.

 

[pastryman]

Yep. You're right. Sorry about that OP.

Nope actually I am wrong. Even though the acceleration of the ball on the ramp is lower, it has a bigger displacement over which to accelerate so in the end, the final velocities are equal. My mistake, OP.

 

[ezsanche]

Nope actually I am wrong. Even though the acceleration of the ball on the ramp is lower, it has a bigger displacement over which to accelerate so in the end, the final velocities are equal. My mistake, OP.

No, the speed will be lower on a ramp. Since it is a ball that is rolling off a ramp it's potential energy will be converted into rotational kinetic energy and translational kintetic energy. Some energy goes to rotational kinetic energy hence the ball will have to have a lower translational kinetic energy which equates to a lower speed.

The velocity of a ball rolling off a ramp is about = (1.4gh)^1/2

The velocity of a ball that is dropped straight down will be v= (2gh)1/2


Now if it was a ball that was rolled off a table and then dropped, which I somehow mistook to be the question that hemi was asking, then the ball will have the greatest total energy because it has potential energy, kinetic energy, and rotational kinetic energy. Although the final vertical velocity will be the same as if the ball were dropped straight vertically down.

Now if it was a block -the velocity and the energy will be the same whether it was dropped from a ramp or dropped vertically from the same height. Why so? Because the block doesn't roll so all the energy goes to kinetic energy and nothing goes to rotational kinetic enegry. (This is only true for a frictionless ramp)


http://hyperphysics.phy-astr.gsu.edu/Hbase/sphinc.html#sph

 

[Hemichordate]

Sorry folks, I actually just meant a ball going down a ramp (no rolling) vs a ball being dropped straight down, in which case they would have the same velocity at the bottom.

 

[dragon529]

a ball going down a ramp with no rolling is slipping...

 

[pastryman]

ezsanche, if there is no friction, the ball would not roll. if there is no friction, for the purposes of finding a solution, the objects are not touching, thus the ball would not roll. friction causes the ball to roll. gravity exerts a force on the center of mass and not the surface so the ball does not have a net torque and will not roll. i looked it up in case i was wrong and here is a forum on a similar question.
http://www.physicsforums.com/archive/index.php/t-271692.html

 

[ezsanche]

ezsanche, if there is no friction, the ball would not roll. if there is no friction, for the purposes of finding a solution, the objects are not touching, thus the ball would not roll. friction causes the ball to roll. gravity exerts a force on the center of mass and not the surface so the ball does not have a net torque and will not roll. i looked it up in case i was wrong and here is a forum on a similar question.
http://www.physicsforums.com/archive/index.php/t-271692.html

Darn it. I concede. I read hemi's post and it said the ball was rolled down a ramp but I didn't know static friction between the ball and the surface of the ramp was essential for a ball to rotate. Thanks for clearing everything up. I learned a lot for this post. lol