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

  • Thread starter Thread starter mailmas
  • Start date Start date
Click For Summary
The discussion revolves around calculating the tension in a tethered bomb submerged 4 meters below the ocean surface. The participant initially miscalculates the force by considering the weight of a water column instead of focusing on the buoyant force. They are guided to apply Archimedes' principle to find the buoyant force acting on the bomb. The correct approach involves using the buoyant force formula and setting up an equation for net force to solve for tension. Ultimately, the tension can be determined by balancing the buoyant force against the weight of the bomb.
mailmas
Messages
46
Reaction score
0

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?
 
Physics news on Phys.org
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?
 
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?
 
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?
 
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?
 
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.
 
  • Like
Likes mailmas

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Find the maximum safe depth of a submarine
  • · Replies 2 ·
Replies
2
Views
4K
What Are the Dynamics of a Motor Tethered to a Tower?
  • · Replies 1 ·
Replies
1
Views
2K
Absolute pressure, buoyant force, tension problem
  • · Replies 5 ·
Replies
5
Views
2K
What is the tension in the lift cable and in the string?
  • · Replies 19 ·
Replies
19
Views
4K
Just need an answer checked on a problem
  • · Replies 1 ·
Replies
1
Views
3K
What is the mass of the water in the stirrer supported by surface tension?
  • · Replies 2 ·
Replies
2
Views
3K
What is the pressure at 80 m below the surface of the ocean.
  • · Replies 2 ·
Replies
2
Views
7K
What is the power input of a motor pulling up an elevator?
  • · Replies 3 ·
Replies
3
Views
3K
Empty elevator with a max speed going down, find tension on cable.
  • · Replies 3 ·
Replies
3
Views
3K
What Is the Tension in the Rope When a Railroad Car Accelerates?
  • · Replies 15 ·
Replies
15
Views
3K