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Old Jan 31st 2018, 09:22 PM   #1
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Tension on 2 submerged objects

If 2 objects with different weigh is connected to each other by a string and both submerged to the water, how would i get the tension of the string?

Ive been searching all over the internet and they only gave me one object with the string attached to some sort of cable. Bouyant force is equal to the weight of the object and the tension is the weight minus the bouyant force but thats all i got. Nothing said anything about tension of a string connected to both submerged object

EDIT: I have to emphasise that the string connects them to each other and not outside of the water or anything.

Last edited by lazz; Jan 31st 2018 at 09:50 PM.
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Old Feb 1st 2018, 01:10 AM   #2
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This question is not as simple as first might appear....

Certainly if one object want's to float , and the other want's to sink there will tension in the string .... not dependent on weight ( m x g) ... but on density and volume ...one object must have a density greater than 1 , the other object less than 1 ....

If densities of the objects are different but both want to sink , but their size and shape are identical , then the denser will want to sink more than the other , there will be tension .

Same if densities are different but less than 1 ... and they have identical size and shape , both want to float the less dense will pull on the denser

But there can also be tension if the objects have the same density , but different size .

Consider two spheres made of solid plastic , both have same density 1.1 , but one is twice the size ... when first put in the water there is no tension ... they will both start to sink , but the bigger will fall faster than the smaller because the effect of the water resistance is less on the larger . The large object falling faster will drag the smaller with it , there will be tension ...

If the two objects have the same density and are less dense than water , the larger will float up faster and drag the smaller , there will be tension .

Last edited by oz93666; Feb 1st 2018 at 01:31 AM.
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Old Feb 1st 2018, 05:04 AM   #3
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I think oz93666 is over-complicating the answer.
I am guessing the question originates in a homework problem,
This style of question usually conveniently ignores the "side-issues"
These might be important in a "practical" or experimental situation,
but they are not what the tutor is looking for in a homework answer.

The key point will be the density difference leading to a difference in the rate that they sink down (or float up).

The density of (pure) water is one kilogram per litre,
If you buoyancy generated is equal to the amount of water displaced (pushed aside) by the object.
If the mass of the object is less than the mass of the water it displaces (it has a density less than 1kilogram per litre), then it will float.
If the mass of the object is greater than the mass of the water it displaces (it has a density greater than 1kilogram per litre), then it will sink.

If a sinker is tied to a floater, then you will get tension.

More generally if two objects of differing densities are tied together then one will sink (or rise) at a different rate to the other, and you will get tension.
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Old Feb 1st 2018, 07:38 AM   #4
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But HOW do i calculate for the tension?

Like if 2 object with the same volume but different (lets say X and Y) weight both submerged in water and connected to the string, HOW would i acquire the tension?
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Old Feb 1st 2018, 08:35 AM   #5
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The force on a mass due to gravity is given by F=mA
where:
F is the Force (Newtons)
m is the mass (kilograms)
A is the acceleration due to gravity (9.81 m/s/s).

The force exerted by buoyancy is F=d.A
where:
F is the Force (Newtons)
d is the mass of water displaced (kilograms)
A is the acceleration due to gravity (9.81 m/s/s).
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Old Feb 1st 2018, 07:45 PM   #6
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Originally Posted by lazz View Post
But HOW do i calculate for the tension?

Like if 2 object with the same volume but different (lets say X and Y) weight both submerged in water and connected to the string, HOW would i acquire the tension?
How did this question arise ??? Is it from a school book ???

If so give the whole question accurately !!!
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Old Feb 3rd 2018, 12:30 AM   #7
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The only thing is didnt say is the value of X and Y. But thats the entire question. no illustration either so no point in taking a picture of the problem.

I didnt say the actual weight of the two cause i dont wanna get "were not gonna do your homework for you" thing (which is right) so i made it like that so i know where to start solving on my own.

Apologies.
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Old Feb 3rd 2018, 02:05 AM   #8
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Originally Posted by lazz View Post
The only thing is didnt say is the value of X and Y.... cause i dont wanna get "were not gonna do your homework for you" thing (which is right) so i made it like that so i know where to start solving on my own.

Apologies.
It's very important you give the whole question with weights and ALL the information otherwise there are too many variables , and the answer is as in my first post.
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