why? why not?
2007-09-10 01:36:30 · 8 answers · asked by We don't fight fair. 1 in Science & Mathematics ➔ Physics
If you perform a dynamic/force analysis, you'll find that the mass term will always cancel off when you try to find the acceleration. Even with friction, the acceleration is independent of the mass.
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2007-09-10 01:52:03 · answer #1 · answered by Dr D 7 · 0⤊ 0⤋
I assume you mean the balls are rolled down the same ramp
(on Earth, or on the same planet with a uniform gravitational field, so that each ball experiences the same gravitational force).
Since the force of gravity upon each mass will be proportional to the mass, the acceleration due to gravity will be exactly the same for each mass. (F=ma and the greater the mass the greater the force, so acceleration is the same, regardless of mass -- if there are no other forces acting upon them.)
If they are rolling down a (straight) ramp, the ramp pushes back with a force that is also proportional to the mass, so the acceleration due to gravity is still the same for each mass.
That acceleration will cause them both to begin rolling down the ramp, but the resistance caused by friction might make them roll at different speeds. If the balls have exactly the same surface material, then the frictional force should also be proportional to mass, and the balls should roll down at the same rate regardless.
2007-09-10 09:13:17 · answer #2 · answered by bam 4 · 0⤊ 0⤋
The moment of inertia of hollow sphere is 2/3 m r^2
Assuming no friction,
The potential energy of the ball = sum of the kinetic energies of the ball.
mgh = 1/2mv^2 + 1/2 [2/3] m r^2 Ï ^2.
If the ball is not sliding v = r Ï.
Therefore, gh = [5/6] v^2
v^2 = 1.2 gh
When it has fallen through a vertical height h1 let its velocity be v1.
v1^2 = 1.2 gh1
Since the ball starts from rest
v1^2 = 2a h1 where a is the acceleration of the ball.
Comparing the two
2a = 1.2 g
a = 0.6 g. and this is a constant.
Hence the acceleration is independent of the mass or shape of the ball
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If friction is considered, since the friction depends upon the mass of the balls which are different, the velocities and hence the acceleration will be different for different balls.
2007-09-10 10:24:46 · answer #3 · answered by Pearlsawme 7 · 0⤊ 0⤋
They can't. Suppose that two were attached by a very thin thread. Does this make one larger ball, or two small ones? What happens to the thread? The only consistent result is that the acceleration must be the same, regardless of mass.
2007-09-10 08:46:09 · answer #4 · answered by Anonymous · 0⤊ 0⤋
All the other answers forget that there is rotational inertia in the ball. Therefore the acceleration depends on the material of the ball. Remember that there is a rotational acceleration as well. This is not free fall....
2007-09-10 09:15:45 · answer #5 · answered by janbbeck 2 · 0⤊ 0⤋
They have a different acceleration because the more mass, the more momentum it will gain going down the ramp and the faster it will roll.
2007-09-10 08:44:47 · answer #6 · answered by Anonymous · 0⤊ 0⤋
They have the same acceleration because the ratio of the net force acting on them to their mass (F/m) is a constant.
HTH
Doug
2007-09-10 08:48:58 · answer #7 · answered by doug_donaghue 7 · 0⤊ 0⤋
They have the same acceleration if they have the same surface properties. That means if friction is negligible. Gravity affect all objects uniformly.
2007-09-10 08:44:50 · answer #8 · answered by James H 3 · 0⤊ 0⤋