What is the tension in the tether of a bomb tethered to the ocean floor?

  • Thread starter mailmas
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In summary, the conversation discusses a situation where a bomb is tethered to a cable on the ocean floor. The problem asks for the tension in the tether, assuming the bomb is a 300 kg sphere with a radius of 0.600 m, 4.00 m below the surface and the tether's mass is negligible. The conversation goes on to discuss the use of Archimedes' principle and the correct equations to solve for the buoyant force and the net force in the vertical direction. In the end, it is determined that the tension can be solved for by setting the net force equal to zero and solving for the tension.
  • #1
mailmas
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Homework Statement


A bomb is tethered to a cable on the ocean floor. Imagine one is a 300 kg sphere with a radius of 0.600 m. If it is 4.00 m below the surface and the tether is low mass enough to be negligible, what is the tension in the tether?

Homework Equations


Pbot = Ptop + density*g*h
P = F/A
Acircle = (pi)(r)^2

The Attempt at a Solution



Pbot = 101300 + (1030)(9.81)(4)
Pbot = 141717.2 Pa
F/A = 141717.2 Pa
F = 141717.2(pi)(.6)^2
= 160197 N
Is this the force I am looking for?
 
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  • #2
mailmas said:
Is this the force I am looking for?
No. That would be the weight of matter in a column radius 0.6m extending from 4m below the surface of the water, all the way to the top of the atmosphere!

You have heard of Archimedes, right?
 
  • #3
haruspex said:
No. That would be the weight of matter in a column radius 0.6m extending from 4m below the surface of the water, all the way to the top of the atmosphere!

You have heard of Archimedes, right?
Yeah but honestly don't really understand it. So the force I found is the force which acts upwards to an object that is being submerged? Then I should look at the weight force and the difference between those forces must be the force due to tension?
 
  • #4
mailmas said:
the force I found is the force which acts upwards to an object that is being submerged?
No, forget the force you found. It is not relevant to the question.
Can you state Archimedes' principle?

Edit: just noticed you correctly applied it to find the buoyant force in another thread.
So what is the buoyant force here?
 
  • #5
haruspex said:
No, forget the force you found. It is not relevant to the question.
Can you state Archimedes' principle?

Edit: just noticed you correctly applied it to find the buoyant force in another thread.
So what is the buoyant force here?
FBuoyancy = density*volume*g
(1030)(4/3)(pi)(.6)^3(9.81)

Then Fnety = 0 = FBuoyancy - Tension - mg
Could I solve for tension this way?
 
  • #6
mailmas said:
FBuoyancy = density*volume*g
(1030)(4/3)(pi)(.6)^3(9.81)

Then Fnety = 0 = FBuoyancy - Tension - mg
Could I solve for tension this way?
Yes.
 
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1. What is the "Tethered-Preasure Problem"?

The "Tethered-Preasure Problem" refers to the phenomenon where the pressure on a tethered object increases as it is moved closer to the surface of a planet or other celestial body. This increase in pressure can cause structural damage to the object or even lead to its destruction.

2. What causes the "Tethered-Preasure Problem"?

The "Tethered-Preasure Problem" is caused by the weight of the atmosphere or other gaseous environment pressing down on the object as it moves closer to the surface. This weight is known as atmospheric pressure and is dependent on the density of the atmosphere and the acceleration due to gravity of the celestial body.

3. How does the "Tethered-Preasure Problem" affect scientific research?

The "Tethered-Preasure Problem" can present challenges for scientists conducting experiments or observations on objects that are tethered to a spacecraft or other platform. The increased pressure can alter the behavior of the object and potentially interfere with the accuracy of the data being collected.

4. Are there any solutions to the "Tethered-Preasure Problem"?

There are a few potential solutions to the "Tethered-Preasure Problem". One approach is to design the tether and attached object to be strong enough to withstand the increased pressure. Another option is to use a device, such as a balloon or parachute, to create a barrier between the object and the atmosphere, reducing the pressure on the tethered object.

5. How is the "Tethered-Preasure Problem" being addressed in space exploration?

The "Tethered-Preasure Problem" is a consideration for engineers and scientists in the design of spacecraft and equipment for space exploration. It is important to carefully calculate the atmospheric pressure at different altitudes and design tethers and attached objects accordingly. In some cases, alternative methods of data collection or sample retrieval may be used to avoid the issue altogether.

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