Force due to Gravity Question

[4563728]

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This is a question from Kaplan's Q bank:

Two identical objects are released in mid air, at rest, one object one meter above the other. How does the separation between the two change as they fall?

They said the separation of the two increase since the low object feels a greater force due to gravity than the higher one. But don't both objects undergo an acceleration of 9.8m/s^2 so wouldn't their separation stay constant?

Thank you!

 

[DrknoSDN]

9.8 m/s^2 is a rounding approximation of F=GMm/r^2 that is useful only at the surface of earth.

The Kaplan answer is thinking about things on much larger more infinite scale (immeasurable). If you have 2 balls 1 meter apart that were millions of miles from a gravitational source and it would take them years to reach it,,, over that large timeframe the very minute difference in gravity due to the differences in the force applied to each ball would cause them to separate. [You couldn't observe a difference on earth.]

This is also why black holes theoretically produce hawking radiation. The gravity of a black hole is so massive that it can rip apart the very components of atoms because there is more gravity on one side of the atom than the other.

 

[ahisma]

You are right that they both undergo the same acceleration and experience the same force. But acceleration is not linear. As the units denote it's m/s^2. Checkout this nice demonstration and explanation.

Have you taken Physics I yet?

 

[chenzt]

F = Gm1m2/r2

Technically, the distance between the earth/object 1 is slightly smaller than earth/object 2. So force is slightly less on object 2. In practical sense, there isn't.

 

[DrknoSDN]

You are right that they both undergo the same acceleration and experience the same force. But acceleration is not linear. As the units denote it's m/s^2. Checkout this nice demonstration and explanation.
Have you taken Physics I yet?

Unfortunately not true. Srs...? Have you taken physics? lol j/k, sorry i couldn't resist.
The whole point of the problem is trying to explain that they don't experience the same force... as radius increases, force decreases. The difference in distance is small but it wasn't asking for you to measure a difference in acceleration, just asking if there was one. Regardless, this question is a bad analogy to demonstrate the point they were trying to make. (Kaplan...)

 

[ahisma]

No I haven't taken physics yet, I am taking it right now! Maybe I misread the question but it just reminded me to one we were asked at the beginning of class. Perhaps this is an over-simplification but couldn't the difference also be explained by the exponential relationship of acceleration to velocity?

I was just curious if the OP took physics yet because I've heard of folks putting it off till after the MCAT. If you have a strong mathematical foundation you might be able to teach yourself or maybe remember high school but for the rest of us it probably wouldn't bode well for your scores.

 

[milski]

Who writes these questions? The difference in acceleration due to the difference in distance from the center of Earth in what they describe is about 0.003%!!! Yes, it is non-zero, but there is no way to answer this correctly without knowing why you are being asked. On the bright side, I have never seen anything so ambiguous originating from AAMC.

 

[DrknoSDN]

Who writes these questions? The difference in acceleration due to the difference in distance from the center of Earth in what they describe is about 0.003%!!! Yes, it is non-zero, but there is no way to answer this correctly without knowing why you are being asked. On the bright side, I have never seen anything so ambiguous originating from AAMC.

Kaplan books are garbage, classes I hear are the only thing of benefit.

No I haven't taken physics yet, I am taking it right now! Maybe I misread the question but it just reminded me to one we were asked at the beginning of class. Perhaps this is an over-simplification but couldn't the difference also be explained by the exponential relationship of acceleration to velocity?

The exponential increase in displacement vs time (acceleration) your talking about is not an explanation for this one because they were dropped at the same time. If two objects are experiencing the same force and acceleration but there is a delay in the release time then yes, they would drift apart over time due to the exponential portion of the equation:
X=Xo + VoT + 1/2aT^2

You can also see that if two objects were dropped from different heights but T and A are identical, the displacement between them would not change over time.
You could actually reverse engineer the problem and find delta(x) at time(T), and determine the difference in gravitational force. Would be a fun MCAT problem... (-.-)