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Phy 121
Your 'cq_1_17.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A steel ball rolls down a ramp and collides with a marble, as in the video. The marble is slightly smaller and quite a bit less massive than the ball.
• If they both experience the same force, which will have the greater acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
The greater accleration will belong to the smaller ball. We can see this principle by looking at the equation F = m / a. If F (force) is the same for both sized balls, and the mass is larger on one then the other, the the acceleration of the smaller ball would have to be greater than the larger ball in order for the two forces to be equivalent.
Example: force of both is equal to 100 N. If the mass of the larger ball is 50 kg and the mass of the smaller ball is 25 kg, then the accleration of the larger ball would be:
100 N = 50 kg * a
a = 2 m/s^2
...and the acceleration of the smaller ball would be:
100 N = 25 kg * a
a = 4 m/s^2
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• If the forces were exerted during identical time intervals, which would have the greater change in velocity?
answer/question/discussion: ->->->->->->->->->->->-> :
We can reason that because the smaller ball had a higher rate of acceleration, its change in velocity over a specific time period would have to be greater than the larger ball that had a lesser rate of acceleration.
We can prove this by looking at the equation: a = 'dv / dt.
If the 'dt was identical - knowing that the acceleration of the smaller ball was greater - we can see that it would take a larger change in velocity ('dv) to equal the change in velocity of the larger ball (which had less acceleration).
Example:
'dv = 4 m/s^2 * 5 s = 20 m/s <--- smaller ball
'dv = 2 m/s^2 * 5 s = 10 m/s <--- larger ball
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