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What will hit the ground first?by BMcN
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#1
Jun2104, 04:30 PM

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Ok, classic old question. Two tennis balls dropped from a very high height. One normal, one filled with lead, for example.
So what will hit first? I am certain that they will hit together (theoretically) by looking at the equation v = u + at so no mention of weight or mass. However equally there is no mention of air resistance. Now I know these are the same shape however when arguing my point someone said that the heavier ball would cut through the drag better. I can't really see this being true however I would like this confirmed.... So, basically my question is, in the real world what would happen? 


#2
Jun2104, 04:33 PM

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#3
Jun2104, 04:40 PM

P: 11

Well the way I was thinking about it was that if I had a car in a wind tunnel and tested it with the engine in and then with the engine out, the results will be the same. Also, if the extra weight helped then surely the skydivers (the ones that dive for speed) would strap weights to their jump suits?



#4
Jun2104, 04:52 PM

P: 991

What will hit the ground first?
The force air resistance should be the same for both. However, you'll note that the force of gravity is larger for the heavier ball than the lighter one. Thus, air resistance is comparatively smaller for the heavier one.
Alternatively, you could look at it from a terminal velocity standpoint. Drag must negative gravity at terminal velocity. Gravity depends on m, drag depends on v (all other things being equal), so larger m yields a larger v. cookiemonster 


#5
Jun2204, 04:02 AM

P: 11

So the heavier ball has a greater terminal velocity, so if the balls fell long enough to reach terminal velocity then the heavier ball would hit the ground first?



#6
Jun2204, 07:47 AM

P: 7

The heavier ball would land first on Earth because of air resistance. Although, if you dropped them in a vacuum they would fall at an equal rate and hit the ground at the same time.
Ravenlock 


#7
Jun2204, 11:09 AM

P: 71

The heavier ball would hit the ground first. By Newton's second law the differential equation governing the motion of a ball of mass m in a uniform g field will be (aproximately)
x''+(b/m)x'+g=0 the second term on the left represents the air resistence. THe constant b is called aerodynamic coefficient or something and is determined experimentaly. Hence if the shape of the balls are equal their bs will be the same and the air resistance will be larger for the lighter ball, because the term proportional to the velocity is divided by m and hence larger when m is smaller. 


#8
Jun2204, 06:42 PM

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This requires changing your frame of reference, but from the balls' point of view, the ground is rushing toward them. This big wall of dirt rushing toward them is preceded by a gust of wind. Both balls are blown away from the approaching ground by this wind, but the lighter one is blown away faster. Therefore, the ground strikes the heavier one first and catches up with the lighter one later. 


#9
Jun2204, 07:00 PM

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#10
Jun2204, 10:13 PM

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If you think of it as the ball colliding with air particles, you will see that the ball with greater mass will retain more momentum than the lighter ball will.



#11
Jun2404, 07:14 AM

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#12
Jun2404, 01:07 PM

P: 609

If the balls where in a vacuum they would both hit at the same time. In air the heavy ball would hit first because it has a greater terminal velocity.



#13
Jun2404, 03:13 PM

P: 5

Imagine if you had 3 one pound metal balls, and when you droped them they all hit at the same time. Now take 2 of them and weld them together, and drop the 1 one pound and the now 1 two pound ball... What would happen? Are you saying the one little weld made the 2 balls, welded together, drop faster? That is kind of like saying if you were skydiving and you grab another skydivers hand, your weight would double so now you would instantly fall faster?



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Jun2404, 06:07 PM

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#15
Jun2404, 07:56 PM

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#16
Jun2404, 11:47 PM

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#17
Jun2804, 07:32 PM

P: 181

Anyone think of having one ball made of lead one one made of bismuth? At the same weight, in a vacuum, which one would hit the ground first? ;)
(hint: bismuth repells magnetic fields) 


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