Two Balls Dropped: Separate or Together?

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In summary, the conversation discusses the problem of two balls being dropped on top of each other and how to calculate the height of the top ball's bounce. The solution assumes that the bottom ball hits the ground first, but the questioner wonders if the balls would ideally stay on top of each other since they experience the same acceleration. The responder explains that splitting the equations into two stages makes it easier to solve the problem and that the balls actually deform and take a short amount of time to "know" that the bottom ball has hit the ground. In the end, the questioner thanks the responder for their help.
  • #1
darkSun
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Hello,

In this problem: http://www.physics.harvard.edu/academics/undergrad/probweek/prob1.pdf

Two balls are dropped, one on top of each other. When figuring out how high the top ball bounces, the solution assumes that the bottom ball hits the ground first, without the other ball on top of it.

I thought that ideally the two balls would stay on top of each other, since they experience the same acceleration, and would both "hit" at the same time. Is something wrong with my thinking?
 
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  • #2
darkSun said:
I thought that ideally the two balls would stay on top of each other, since they experience the same acceleration, and would both "hit" at the same time. Is something wrong with my thinking?

Hello darkSun! :smile:

No, you're right …

but it doesn't make any difference to the result if we split the equations into two stages …

and since that's easier, that's exactly what we do! :wink:

(technically, of course, the balls deform, and the top of the lower ball doesn't "know" that the bottom has hit the ground until shortly afterwards!)
 
  • #3
Oh, I see!

It really doesn't make a difference? Seems weird, but I'll try that.

Thank you for the help tiny-tim.
 

Related to Two Balls Dropped: Separate or Together?

1. How does the height of the drop affect whether the two balls will land together or separately?

The height of the drop does not affect whether the two balls will land together or separately. As long as both balls are dropped at the same time and from the same height, they will land at the same time.

2. Will the weight of the balls have an impact on whether they land together or separately?

No, the weight of the balls will not affect whether they land together or separately. As long as both balls are dropped at the same time and from the same height, they will land at the same time.

3. What is the scientific explanation for why the balls land together or separately?

The scientific explanation for why the balls land together or separately is based on the Law of Inertia and the Law of Gravity. The Law of Inertia states that an object at rest will stay at rest, and an object in motion will stay in motion, unless acted upon by an external force. The Law of Gravity states that all objects in the universe are attracted to each other with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them. When the balls are dropped at the same time and from the same height, they experience the same external forces (gravity and air resistance) and therefore land at the same time.

4. What other factors could affect whether the balls land together or separately?

Other factors that could potentially affect whether the balls land together or separately include air resistance, wind, and temperature. However, as long as these factors are controlled and both balls are dropped from the same height at the same time, they should still land together.

5. Is there a limit to the height from which the balls can be dropped and still land together?

No, there is no limit to the height from which the balls can be dropped and still land together. As long as both balls are dropped at the same time and from the same height, they will land together regardless of the height.

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