The tennis ball has the smallest moment of inertia. The moment of inertia is the rotational analogue to mass when it comes to kinetic energy. A ball's angular speed is inversely proportional to the moment of inertia when kinetic energy is constant (the earth does a set amount of work over a given time).
In plain English, the tennis ball's mass is less spread out, so it's easier to get rolling. The moment of inertia is a way of measuring how "spread out" an object's mass is.
It has nothing to do with friction or density. All of the balls only touch the ground at a single point (ideally, assuming they are perfectly inflated spheres). Even still, contrary to what others have said, friction is what actually makes the balls spin, much like a tire. Friction does not slow the balls down.
This problem is very important. Understanding this problem shows that you understand how rotations work. The above people do not know how rotational motion works. This is often used as a trick question when students are starting the rotations unit. A similar situation is to compare a bowling ball and a ping pong ball. The bowling (solid) ball will always go farther than the hollow ping pong ball.
Full explaination:
All of the balls start out with the same potential energy: mgh. Their masses may be different, but this will not matter in the end. Now you may know that the PE at the top is equal to the KE at the bottom (potential energy and kinetic energy). Since we are talking about rotations, you must account for both rotational and translational kinetic energy.
So far we have:
PE = KE
mgh = (mv^2)/2 +(Iv^2)/(2r^2)
Where I = kmr^2, and k is determined by the shape of whats rotating.
So:
mgh = (mv^2)/2 + (kmv^2)/2
and solving for v:
v = sqrt[ 2gh/(k+1) ]
So you can see that a larger k means a smaller velocity. Now a tennis ball is closer to a solid sphere, where k = 2/5. The larger balls are closer to perfectly hollow spheres, k = 2/3.
Since 2/3 > 2/5, the larger balls go slower. It doesn't matter if any of the balls are made of lead or styrofoam, because mass does not matter. Friction, density, nor anything else matter. Only the shape of whats rolling matters.
2007-02-06 10:17:50
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answer #1
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answered by Tony O 2
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The tennis ball has a smaller diameter and means less of the tennis ball in in contact with the surface. Less surface area means smaller the force of friction can act.
2007-02-06 10:11:40
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answer #2
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answered by T C 3
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i think if we think according to physics i think the rolling of an object from a ramp depends on the coefficient of static friction so the tennis ball must be having the value of static friction coefficient greater than other balls so it rolls the farthest because static friction coefficient is what starts an object rolling
2007-02-06 10:44:48
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answer #3
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answered by rohan1985 2
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I am thinking that maybe the tennis ball has a greater density compared to those other two items and is therefore slowed down less quickly by air resistance.
2007-02-06 10:09:04
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answer #4
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answered by bruinfan 7
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If that does actually happen, I would have to guess it has something to do with centripetal force.
The smaller the object, the more times it rolls and gains centripetal force.
Compare it to a figure skater. When their arms are out, they spin slower. But, when the bring their arms and legs inward, they spin faster.
2007-02-06 10:15:11
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answer #5
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answered by Anonymous
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Because it's the lightest and has more density. It can travel the fastest because the smaller and denser the object is, the faster the speed and the furthest distance.
2007-02-06 10:10:19
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answer #6
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answered by Agent319.007 6
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basketball and soccer ball have more friction acting on them bc of the greater surface area
NOT BECAUSE ITS DENSER... ITS NOT
2007-02-06 10:13:36
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answer #7
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answered by Mr. Primetime 3
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It depends..
2016-08-23 17:15:35
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answer #8
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answered by Anonymous
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smaller
2007-02-06 10:08:24
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answer #9
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answered by flonkas 3
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