# Weight And Falls

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### #1 hazelm

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Posted 08 February 2018 - 07:12 AM

Am I right in what I think I remember?  The longer the distance that an object falls the more speed it will pick up as it drops.  Ex:  Drop a 50-pound weight from the third floor.  Drop another 50-pound weight from the tenth floor.  The second weight will pick up more speed before it hits the ground than will the first weight.

Do I have it right?   Conversely, what if you drop two different weights from the same floor?  Will the heavier weight fall any faster than the lighter weight?  Seems to me it would but  I think it has been shown not to do so.

Thank you.

### #2 exchemist

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Posted 08 February 2018 - 08:44 AM

Am I right in what I think I remember?  The longer the distance that an object falls the more speed it will pick up as it drops.  Ex:  Drop a 50-pound weight from the third floor.  Drop another 50-pound weight from the tenth floor.  The second weight will pick up more speed before it hits the ground than will the first weight.

Do I have it right?   Conversely, what if you drop two different weights from the same floor?  Will the heavier weight fall any faster than the lighter weight?  Seems to me it would but  I think it has been shown not to do so.

Thank you.

Newton's Second Law: F=ma. Force = mass x acceleration.

The force here is the force of gravity on the object. This is constant so will cause a constant acceleration in a dropped object. So something dropped from the 10th floor will have longer to accelerate before hitting the ground than something dropped from the 3rd, and will thus be moving faster when it strikes.

However, the force of gravity on an object is also proportional to its mass. For example the force of gravity on a 2lb mass is double the force on a 1lb mass.

However, if you drop it, this force has to accelerate double the mass. So the two doubling effects cancel and it accelerates at the same rate as the 1lb mass would if you dropped that.

(This analysis neglects air resistance, of course. Air resistance depends on the shape of the object, not its mass.)

### #3 hazelm

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Posted 08 February 2018 - 11:22 AM

Newton's Second Law: F=ma. Force = mass x acceleration.

The force here is the force of gravity on the object. This is constant so will cause a constant acceleration in a dropped object. So something dropped from the 10th floor will have longer to accelerate before hitting the ground than something dropped from the 3rd, and will thus be moving faster when it strikes.

However, the force of gravity on an object is also proportional to its mass. For example the force of gravity on a 2lb mass is double the force on a 1lb mass.

However, if you drop it, this force has to accelerate double the mass. So the two doubling effects cancel and it accelerates at the same rate as the 1lb mass would if you dropped that.

(This analysis neglects air resistance, of course. Air resistance depends on the shape of the object, not its mass.)

Thank you, exchemist.  It is that second which keeps puzzling me.  I do not know how to explain it but it seems to me that this would not always be true.  I keep thinking there would be variable based on the difference in both the weights and the distance falling.  The ratios should not always be the same.  All right.  Let's see if it keeps me awake another night.  <g>  Thanks

### #4 exchemist

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Posted 08 February 2018 - 11:55 AM

Thank you, exchemist.  It is that second which keeps puzzling me.  I do not know how to explain it but it seems to me that this would not always be true.  I keep thinking there would be variable based on the difference in both the weights and the distance falling.  The ratios should not always be the same.  All right.  Let's see if it keeps me awake another night.  <g>  Thanks

It will be the air resistance effect that you have trouble setting aside, I think, as it so pervasive here on Earth.

In a vacuum, a hammer falls at the same speed as a feather. They actually demonstrated this on one of the later moon shots, here:

Edited by exchemist, 08 February 2018 - 11:56 AM.

### #5 hazelm

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Posted 08 February 2018 - 12:17 PM

In a vacuum, yes, and I do keep forgetting that.  But this doesn't happen in a vacuum regularly.  The test from the leaning tower of Pisa was not in a vacuum.  As you mentioned, air resistance has to be considered.   But there is more there.  I know it is I who am not understanding.  Too many brighter brains than mine say it is true.  I am missing something.    Remember, I am considering only mass in that second instance.  I had not thought of the two instances cancelling each other out.  More to consider there.

Hmmm?  "It will be the air resistance effect that you have trouble setting aside, I think, as it so pervasive here on Earth."

Maybe that is it.  Won't air resistance vary according to weight and size (which equals mass, I think.)?

Edited by hazelm, 08 February 2018 - 12:22 PM.

### #6 Farming guy

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Posted 08 February 2018 - 05:55 PM

In a vacuum, yes, and I do keep forgetting that.  But this doesn't happen in a vacuum regularly.  The test from the leaning tower of Pisa was not in a vacuum.  As you mentioned, air resistance has to be considered.   But there is more there.  I know it is I who am not understanding.  Too many brighter brains than mine say it is true.  I am missing something.    Remember, I am considering only mass in that second instance.  I had not thought of the two instances cancelling each other out.  More to consider there.

Hmmm?  "It will be the air resistance effect that you have trouble setting aside, I think, as it so pervasive here on Earth."

Maybe that is it.  Won't air resistance vary according to weight and size (which equals mass, I think.)?

I think that in the test from the leaning tower of Pisa, air resistance was negligible.  You would need a big difference in surface area or you would have to be dropping the objects from a much higher elevation.  If you want more to consider, and possibly lose sleep over, there is the subject of terminal velocity, where the force of air resistance would cancel out the acceleration when you got to a high enough velocity.

### #7 exchemist

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Posted 09 February 2018 - 02:18 AM

I think that in the test from the leaning tower of Pisa, air resistance was negligible.  You would need a big difference in surface area or you would have to be dropping the objects from a much higher elevation.  If you want more to consider, and possibly lose sleep over, there is the subject of terminal velocity, where the force of air resistance would cancel out the acceleration when you got to a high enough velocity.

I had always understood the story of the test from the leaning tower of Pisa was merely apocryphal. They used an inclined plane, to slow the whole process down enough to be able to detect any differences. As this reduced the speeds, it would also have virtually eliminated any confounding effects from air resistance.

### #8 Farming guy

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Posted 11 February 2018 - 12:01 PM

I had always understood the story of the test from the leaning tower of Pisa was merely apocryphal. They used an inclined plane, to slow the whole process down enough to be able to detect any differences. As this reduced the speeds, it would also have virtually eliminated any confounding effects from air resistance.

I didn't remember the inclined plane part of the story.  Maybe I was looking out the classroom window on a nice day...

### #9 A-wal

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Posted 23 March 2018 - 03:43 PM

People love to make this seem way more complicated than it actually is. I've even come across claims that objects falling at the same rate tells us something profound about the universe. Look at it like this, you drop two objects from a tall building and they stick together during the fall. Would you expect the (now one) object's rate of acceleration to increase because it's heavier than it was before? Of course not, so obviously an object's weight doesn't matter, until it hits something.

### #10 DaveC426913

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Posted 22 April 2018 - 02:12 PM

A heavy sphere will fall at the same rate as a light sphere for the following reason:

While the heavy sphere is pulled toward the Earth with a greater force than the light sphere is, the heavy sphere also has more inertia, meaning it is essentially harder to get it started. These two are both dependent on the object's mass m, and therefore the forces exactly cancel out, resulting in both spheres accelerating at the same rate.

### #11 hazelm

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Posted 22 April 2018 - 02:21 PM

A heavy sphere will fall at the same rate as a light sphere for the following reason:

While the heavy sphere is pulled toward the Earth with a greater force than the light sphere is, the heavy sphere also has more inertia, meaning it is essentially harder to get it started. These two are both dependent on the object's mass m, and therefore the forces exactly cancel out, resulting in both spheres accelerating at the same rate.

I have read that explanation but it just doesn't make sense to me.  But never mind. It probably involves physics and math.  I'll just trust that it is true.    Thank you.

Edited by hazelm, 22 April 2018 - 02:21 PM.

### #12 JMJones0424

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Posted 23 April 2018 - 03:08 AM

Never trust that something is true.  I think we can easily show that the explanations given above must be appropriate descriptions of reality, without math.

Take a sled of any type, say a skateboard.  Place a weight on the skateboard, say a small child, and shove it. Then place more weight on the skateboard and shove it.  I think you should be able to understand that the more massive weight is harder to move than the less massive weight.  This is a description of inertia

Now, imagine instead of shoving various weights, you drop them.  In this case, the only force involved is gravity.  We can demonstrate that surface area is what is most important in air resistance rather than weight, as a sail boat that is tacked appropriately moves more quickly than a sail boat with the same weight of sails turned into the wind rather than catching the wind.  A good way to negate air resistance without requiring a vacuum is to make similarly sized spheres of different weight.  Imagine two similar bowling balls but one has been hollowed out so that it weighs significantly less than the other.  Both balls would fall when dropped at the same rate.  Alternatively, roll them down a ramp rather than dropping them.  Their speed when hitting the bottom would be the same.  The acceleration they encounter, which is the change in speed over time, would be the same.  You could measure the difference in velocity (velocity is speed in a particular direction) when they hit the ground depending on the height that they were dropped from.  If you made repeated experiments, you would notice that velocity at impact is proportional to the time to impact squared.  It is repeated observations such as these that led to Newton's description of gravitational interactions.

In the skateboard tests, we showed that it takes more force to move a heavier weight than a lighter weight.  In the drop tests, we showed that regardless of weight, similarly shaped objects fall at the same rate.  Inertia is the key to why these two seemingly contradictory statements are correct.  It makes sense to think that a heavy object will fall faster than a light object.  But, it takes more force to accelerate a heavy object as observed in the skateboard tests.  It turns out that after careful measurements, the two things cancel out.  The amazing thing is that this was discovered more than three centuries ago.

Edited by JMJones0424, 23 April 2018 - 03:22 AM.

### #13 hazelm

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Posted 23 April 2018 - 04:16 AM

Never trust that something is true.  I think we can easily show that the explanations given above must be appropriate descriptions of reality, without math.

Take a sled of any type, say a skateboard.  Place a weight on the skateboard, say a small child, and shove it. Then place more weight on the skateboard and shove it.  I think you should be able to understand that the more massive weight is harder to move than the less massive weight.  This is a description of inertia

Now, imagine instead of shoving various weights, you drop them.  In this case, the only force involved is gravity.  We can demonstrate that surface area is what is most important in air resistance rather than weight, as a sail boat that is tacked appropriately moves more quickly than a sail boat with the same weight of sails turned into the wind rather than catching the wind.  A good way to negate air resistance without requiring a vacuum is to make similarly sized spheres of different weight.  Imagine two similar bowling balls but one has been hollowed out so that it weighs significantly less than the other.  Both balls would fall when dropped at the same rate.  Alternatively, roll them down a ramp rather than dropping them.  Their speed when hitting the bottom would be the same.  The acceleration they encounter, which is the change in speed over time, would be the same.  You could measure the difference in velocity (velocity is speed in a particular direction) when they hit the ground depending on the height that they were dropped from.  If you made repeated experiments, you would notice that velocity at impact is proportional to the time to impact squared.  It is repeated observations such as these that led to Newton's description of gravitational interactions.

In the skateboard tests, we showed that it takes more force to move a heavier weight than a lighter weight.  In the drop tests, we showed that regardless of weight, similarly shaped objects fall at the same rate.  Inertia is the key to why these two seemingly contradictory statements are correct.  It makes sense to think that a heavy object will fall faster than a light object.  But, it takes more force to accelerate a heavy object as observed in the skateboard tests.  It turns out that after careful measurements, the two things cancel out.  The amazing thing is that this was discovered more than three centuries ago.

Thank you, JM.  I shall have to read the description of the dropped balls a few times and see what clicks.  By the way, are feathers eliminated from this experiment because they float?  Air resistance out-weighs gravity?  This is what confuses me.  If a feather is eliminated because of its very light weight, this resistance should change proportionately as you change to a larger and heavier weight which is still lighter than the other object.  Try a ping pong ball and a bowling ball.  Then try a baseball and a bowling ball.  There should be a gradual decrease in the timing with the change in weights.  No?

Anyway, this will take some re-reading when I get home later.  Thank you.

### #14 JMJones0424

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Posted 23 April 2018 - 05:24 AM

Feathers have a very small mass when compared to their surface area.  Therefore, air resistance is far more of a consideration when describing the motion of a dropped feather when compared to the motion of a dropped hammer on the surface of the Earth.  You can't do it, but this experiment has been done on the moon.

Simple physics experiments work best when you eliminate all variables except the one you are testing.  We don't want to test the fluid mechanics of different objects falling through the air if all we are trying to do is understand how gravity works on different masses.  The best way to do this is to have to similarly shaped spheres of different masses.  You might try dropping a ping pong ball and a golf ball, as I think these are pretty close to the same diameter, though the shape isn't entirely the same.  This is a far better test than comparing a ping pong ball and a bowling ball.

Another way to look at this is to consider what would happen if more massive objects did actually accelerate more rapidly in a gravitational field.  This is something similar to a proof by contradiction.  Imagine that you have three identical golf balls and drop them individually from a given height.  Being identical, all three of them individually accelerate at the same rate and hit the ground at the same velocity.  Now, attach two of these balls together and drop them at the same time as the third.  There is no logical reason why the doubled golf ball will fall faster then it did when they were separated, or faster than the remaining single golf ball.  If you can understand that two golf balls attached by a gossamer thread fall at the same acceleration as they did individually, then you can see that the mass of the falling object alone is not the determining factor in the acceleration due to gravity.

Hell, drop a baseball and a bowling ball.  Unless you're doing it from a flying vehicle or in a hurricane, they will hit the ground at the same time.

### #15 EinsteinIsUseless199

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Posted 25 April 2018 - 09:28 AM

the object with the biggest mass will touch the ground for about 10^-12 faster

### #16 EinsteinIsUseless199

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Posted 25 April 2018 - 09:30 AM

earlierI wanted to say

### #17 exchemist

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Posted 25 April 2018 - 09:33 AM

the object with the biggest mass will touch the ground for about 10^-12 faster

In what units? Minutes?