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ilovebio ilovebio
wrote...
11 years ago
I am trying to figure out the acceleration of a ball rolling down a ramp as a science project, but I don't know how to do it. Please help.
Thank You
I am trying to calculate the acceleration of a ball rolling down a ramp in a certain amount of time..but I don't know how to do it. Please help.
Thank you!
ps..I am only a Freshman in highschool, so no crazy science things please.
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wrote...
11 years ago
Acceleration can be calculated in different ways depending on what you know.

If you assume the ball is of uniform density and no energy is lost to sliding friction, then the moment of inertia is 2/5 mr^2 and the ball's energy is
1/2 m v^2 + 1/2 I w^2 = 1/2 m v^2 (1 + 2/5)
Therefore 5/7 of the ball's energy goes into linear motion (instead of angular).

The gravitational force on the ball is mgsin(theta). 5/7 of that goes into linear acceleration, while the other 2/7 is offset by friction to make the ball rotate.

Therefore, ma = 5/7 mg sin(theta)
a = 5/7 g sin(theta)


EDIT: the force on the ball is constant. If you know the height of the ramp and the total time it takes, use:
h = 1/2 a t^2
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