Testing the effect of Gravity at home....

[PatrickR]

TL;DR

Would a ping pong ball fall to earth at the same time as a lead ball of exactly the same dimensions, when dropped from shoulder height in your own living room?

Hi ... air resistance is the reason that objects of different mass fall to Earth at different speeds. In a vacuum all objects fall to Earth at the same rate regardless of mass. OK - I get it but all the experiments that illustrate this tend to rely on tall buildings or massive vacuum chambers. Would a ping pong ball fall to Earth at the same time as a lead ball of exactly the same dimensions when dropped from shoulder height in your own living room?

 

[Doc Al]

Try it and see. This guy did:

 

[PatrickR]

Haha ... brilliant... thanks. It just seems so counter intuitive but if you can do it right in your own home there's no argument.

 

[kuruman]

Haha ... brilliant... thanks. It just seems so counter intuitive but if you can do it right in your own home there's no argument.

Not so fast. Air resistance is important, but its effects don't really show if you just release the two objects from rest at shoulder height. The higher release distance is needed to show that the ping-pong ball reaches terminal velocity long before the steel ball. If the same person pitched the two balls like a baseball, which one will travel farther out? Answer: The steel ball because the horizontal velocity of the ping-pong ball drops much faster than the steel ball. So the answer to your question,

Summary:: Would a ping pong ball fall to Earth at the same time as a lead ball of exactly the same dimensions, when dropped from shoulder height in your own living room?

is, the ping-pong ball will always lag the lead ball and will never hit the ground at exactly the same time unless you eliminate air resistance. The video demonstrates that the lag time is approximately zero to within the ability of your ear to discern the difference between the onset of the two sounds.

 

[Doc Al]

Would a ping pong ball fall to Earth at the same time as a lead ball of exactly the same dimensions when dropped from shoulder height in your own living room?

It all depends on how accurate you want to be. Please read @kuruman's post above.

 

[PatrickR]

... the ping-pong ball will always lag the lead ball and will never hit the ground at exactly the same time unless you eliminate air resistance...

Hmmm ... see now you've foxed me. Why would the air resistance be different if both balls were exactly the same shape/volume/surface area?

 

[Halc]

Why would the air resistance be different if both balls were exactly the same shape/volume/surface area?

Air resistance is the same, but acceleration is different.
F=ma. Air resistance (F) is the same, but the still ball has more mass, thus less change (acceleration) to its falling rate due to this force that is the same between both objects.

 

[Doc Al]

Hmmm ... see now you've foxed me. Why would the air resistance be different if both balls were exactly the same shape/volume/surface area?

Just because the air resistance is the same does not mean the effect is the same. Apply Newton's 2nd law to both balls and calculate the resulting acceleration (as a reasonable first step).

 

[PatrickR]

Just because the air resistance is the same does not mean the effect is the same. Apply Newton's 2nd law to both balls and calculate the resulting acceleration (as a reasonable first step).

Ha ... I knew there would be some kind of tricky caveat to this ... let me think about that :)

 

[PatrickR]

Ha ... I knew there would be some kind of tricky caveat to this ... let me think about that :)

Hmmm ... ok ... the rush (acceleration) to terminal velocity would be different due to the difference in mass ... I get that ... but from that point on they would be falling at exactly the same speed and therefore hit the ground very close together ... in this example anyway. If we had a 100 ton steel ball falling at the same time as a 100 picogram ping pong ball, the discrepancy would be more marked ... ok ... I can live with that. Ta :)

 

[etotheipi]

I suspect maybe the difficulty in dropping two balls at the same time (plus making sure they're at the same height, if you're holding them!) would be the largest cause of error for a demonstration like this. Assuming the height is small enough that neither reaches terminal velocity.

If you assume a model like linear drag, you can show that e.g. $v = \frac{mg}{k}(1-e^{-\frac{kt}{m}})$ is greater at all times $t$ if $m$ is greater. Same sort of thing goes for quadratic drag, and in real life drag is much more complicated but I would assume the general idea doesn't change.

 

[etotheipi]

but from that point on they would be falling at exactly the same speed

They will have different terminal velocities even if cross sectional area / drag coefficient etc. are the same, because one feels a larger weight force than the other.

 

[PatrickR]

They will have different terminal velocities even if cross sectional area / drag coefficient etc. are the same, because one feels a larger weight force than the other.

Hmmm ... nothing in this world is simple. OK but if we think about Galileo's experiment, which seems to be the seed upon which modern thinking on gravity has grown from, that would not have been different in essence from what we are discussing here with the living room experiment ... right?

 

[etotheipi]

Hmmm ... nothing in this world is simple. OK but if we think about Galileo's experiment, which seems to be the seed upon which modern thinking on gravity has grown from, that would not have been different in essence from what we are discussing here with the living room experiment ... right?

In reality they will hit at approximately the same time in the living room. You can try playing around with some differential equations (a more accurate model would be $F_D = \frac{1}{2}AC_d\rho v^2$) and work out some numerical results.

Of course, they only accelerate at exactly the same rate under extremely idealised conditions. That's pretty much impossible practically, but you can get fairly close. you mentioned earlier vacuum chambers:

 

[gmax137]

The clearest way to "think" about this, and fastest route to "understanding," is to follow the advice above; write out the equations and solve for the balls' positions and velocities vs. time. The mathematical approach provides clarity.

See the posts by @etotheipi

 

[PeroK]

Hmmm ... nothing in this world is simple. OK but if we think about Galileo's experiment, which seems to be the seed upon which modern thinking on gravity has grown from, that would not have been different in essence from what we are discussing here with the living room experiment ... right?

The action of gravity is simple. The gravitational force on an object is proportional to its mass, hence all objects have the same acceleration due to gravity.

The complexities relate to the medium in which the experiment takes place. An object falling through air, water or quicksand are all different. The difference is not related to gravity, as such, but to the properties of the object in relation to the medium. In air you may also have winds, hot air currents and aeronautical effects (that birds and aeroplanes make use of) that produce outcomes other than falling!

This is one reason Newton's laws were not discovered sooner. No one saw the elementary, fundamental laws through the complexities of everyday phenomena.

 

[PatrickR]

The action of gravity is simple...

So in essence the experiment with the balls in the living room I have described here, is the same as Galileo's where he threw objects off of The Tower of Pizza ... is that correct?

 

[etotheipi]

I wasn't actually aware of this, but apparently Galileo did notice that the heavier ball hit the ground sooner than the lighter ball when he performed the experiment. I don't know if was aware that the discrepancy was due to air resistance, though.

This is one reason Newton's laws were not discovered sooner. No one saw the elementary, fundamental laws through the complexities of everyday phenomena.

A good example of this is $F =mv$. Poor Aristotle knew that objects in a fluid (eventually) fell at a constant velocity approximately proportional to their weight and inversely proportional to the density of fluid, but there was no notion in his model of an opposing force from the fluid .

 

[Stephen Tashi]

If you drop a steel ball and a ping pong ball of the same dimensions in water, you will see different results. Objects in air have a degree of buoyancy just as they do in water. Air resistance and gravity aren't the only forces acting on falling objects.

 

[PeroK]

So in essence the experiment with the balls in the living room I have described here, is the same as Galileo's where he threw objects off of The Tower of Pizza ... is that correct?

Yes, except that it was the Tower of Pisa. Pizzas hadn't been invented in Galileo's time.

 

[kuruman]

The clearest way to "think" about this, and fastest route to "understanding," is to follow the advice above; write out the equations and solve for the balls' positions and velocities vs. time. The mathematical approach provides clarity.

See the posts by @etotheipi

One doesn't need to do that. What @Doc Al suggests in post #8 is sufficient for a qualitative comparison. One can assume a power law for the speed and write Newton's 2nd law for the falling mass $$m\frac{d^2x}{dt^2}=-g+\kappa v^n$$where $n$ is some exponent (usually set equal to 1 or 2) and $\kappa$ is a constant that depends on air density, shape of the object, etc. When terminal velocity is reached, the acceleration is zero and from the equation above we get $$v_{ter}^n=\dfrac{mg}{\kappa}~~~(1)$$. Put this back in Newton's 2nd law to get$$\frac{d^2x}{dt^2}=g\left(\frac {v^n}{v_{ter}^n}-1\right).~~~(2)$$Assuming that $\kappa$ is the same for both objects, equation (1) says that the larger mass (lead ball) has the larger terminal velocity; equation (2) says that the object with the larger terminal velocity (lead ball) has the smaller acceleration. Over the same distance, the object with the smaller acceleration (lead ball) will hit the ground first. Q.E.D.

 

[gmax137]

One doesn't need to do that.

Well, OK. But the point I was trying to make is, the mathematical formulation provides a good bit more clarity than any "hand waving" line of reasoning.

 

[PatrickR]

Yes, except that it was the Tower of Pisa. Pizzas hadn't been invented in Galileo's time.

Haha ... yes - thanks - that was a typo ... honest ... I've been there :)

 

[etotheipi]

Customary Thursday Meme (please don't ban me , I swear it's on topic...)

 

[gmax137]

1869?
That's the kind of little mistake that makes me question the whole thing...

 

[Vanadium 50]

Everyone knows real pizza was invented in 1943 by Ike Sewell.

Back on topic, DFoc Al's #8 is good advice. You don't have to calculate the exact form of the air resistance. As far as dropping the balls together, it takes about a half-second for the balls to fall, and human reaction time is about a tenth of a second. So it will be very hard to see anything less than about a 20% effect.

 

[jbriggs444]

Everyone knows real pizza was invented in 1943 by Ike Sewell.

Back on topic, DFoc Al's #8 is good advice. You don't have to calculate the exact form of the air resistance. As far as dropping the balls together, it takes about a half-second for the balls to fall, and human reaction time is about a tenth of a second. So it will be very hard to see anything less than about a 20% effect.

I do not think that "reaction time" is the correct figure of merit here. We are not interested in the time delta between stimulus and response. We are interested in the time delta to notice a discrepancy in two stimuli.

Depending on the stimulus, that can be something on the order of 3 ms or better. We just had a thread here about direction sensing with the ears. The time delta between signals received at the two ears are about 3 ms apart. The actual time delta can be used to obtain direction information.

[I doubt that we can consciously sense distinct clicks at the 3ms level -- that'd be in the delta t range used for direction indication, not the delta t range used to sense delta t]

 

[russ_watters]

If such a time delay applied to coordinated movements, consistently making coordinated movements beyond practiced muscle-memory would be impossible. And forget about even attempting music.

 

[Vanadium 50]

I do not think that "reaction time" is the correct figure of merit here. We are not interested in the time delta between stimulus and response

I'm not thinking of the detection events - we can obviously tell if too events are simultaneous to better than that (Russ gives a good example). I am thinking about the release event - or rather ensuring that the two release events happen at the same time.

 

[jbriggs444]

I'm not thinking of the detection events - we can obviously tell if too events are simultaneous to better than that (Russ gives a good example). I am thinking about the release event - or rather ensuring that the two release events happen at the same time.

Again, that does not involve reaction time. The release is planned. We can plan to a delta t far tighter than we can react.

We do not wait to see the left hand open before opening the right.

Edit: just tested this by snapping the fingers of both hands as near simultaneously as I could. Sometimes I can detect a delta t. Some times I cannot. No way was it ever as much as a tenth of a second delta -- well, maybe a couple times when my right finger got held up a bit longer than usual.