Understanding the Impact of Tensile Force on Objects of Different Lengths

[cowgomoo]

Hello guys!

Please can someone answer my dilema.

Lets say we have two apples on tree. Apple A and apple B. And on those apples are attached same weight object. Only difference is length of string.

Here is the link to the image:

http://postimg.org/image/oayj18nk7/

Which one will fall first? I am mean on what apple gravity/tensile force will effect more.

Or length of string is irelevant and tensile force/gravity will have same effect in both cases.

Thanks.

 

[cowgomoo]

Question two what if string is flexible string of rubber for example?

 

[UltrafastPED]

Assuming a constant gravitational force near the Earth's surface, g=9.8 m/s^2, they would be the same. The string simply transmits the "weight" of the mass to the apple.

Using a more detailed model, we would note that Newton's Universal Law of Gravitation says that gravity varies with distance; then the apple with the longer string will feel slightly more force, depending upon the lengths of the strings.

Finally, if you actually do the experiment, in an apple orchard, you will be limited by the assumption that the apples are bound to the tree with the same strength; as an old apple picker, I assure you that apples will not have quite the same bonding force! But aside from that, on a windy day the longer string will generate more torque, and will dislocate its apple more quickly.

PS: The stretchy string won't matter unless you start the weight bobbing up and down.

 

[cowgomoo]

Lets assume that both apples are bound to the tree with same strenght and there is no wind.
Just gravity.

Im little confused with your answer. In first two lines you say that effect will be the same. Then that gravity varies with distance.

Is it true that gravity varries with distance in the first place?
If so on what level? In our non quantum world? Let's use examples of apples...

Thanks in advance.

 

[Nugatory]

Is it true that gravity varies with distance in the first place?

Yes. The easiest way to see this is to look at Newton's law: $F=Gm_1m_2/r^2$ where $r$ is the distance between (the center of mass of) the two masses; clearly the gravitational force will be different if $r$ is different.

However, we don't worry about this when we're working with apples in a tree, or anything else that's within many kilometers of the surface of the earth. For example, suppose the apple tree is ten meters tall (which is a very tall apple tree indeed)... The radius of the Earth is about 6300 kilometers, so we're talking about the ratio between $(6300)^2$ and $(6300.01)^2$ for the difference in strength of gravity at the top and bottom of the tree. This is far too small to notice or care about.

So... when you're solving problems near the surface of the earth, save yourself some unnecessary work and do all your calculations as if the force of gravity does not vary with distance. Just remember that when you move on to satellites in orbit and the like, you won't be able to make this simplifying assumption.

 

[cowgomoo]

Thanks guys!

One more thing...

But aside from that, on a windy day the longer string will generate more torque, and will dislocate its apple more quickly.

Are we talking about momentum force?
Longer distance higher momentum force?

How strechy string fits into this story?