Calculating Buoyancy Force & Tension in Cable for 6m Spherical Chamber

In summary, the chamber has a buoyant force of 9.8 * 10^6 N and a tension in the cable of 8.87 * 10^6 N.
An undersea research chamber for aquanauts is spherical with an external diameter of 6.0 m. The mass of the chamber, when occupied, is 75200 kg. It is anchored to the sea bottom by a cable.
(a) What is the buoyant force on the chamber?
N
(b) What is the tension in the cable?
N
What in am doing wrong? I assumed it's just the volume of the tank and then you find the weight of the water displaced. It's not working. I made sure that the diameter was changed into a radius for the volume of the sphere. Also as a sanity note, if you have a tank that sinks when it's empty it should still sink if it's full of air right?

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It's really simple.
a)[itex] F_ {APXIMN\Delta N\Sigma} = V_{sphere}\rho_{water} g [/tex]

That's the scalar.

For point b),apply Newton's second law for the sphere.How many forces act on the batiscaph?

Daniel.

It's really simple.
Yeah which is why I hate it when I get these problems wrong.:) I know that has to be the answer. I can't figure out why I am not getting the right number. Here is what I am getting. 1108353.888 Newtons.

dextercioby said:
[itex] F_ {APXIMN\Delta N\Sigma} = V_{sphere}\rho_{water} g [/tex]

Dex why are you writing hieroglyphs for very simple formulas .

Adam, $$F_B = \frac{4}{3}\pi r^3\rho_{w}g = F_B = \frac{4}{3}\pi (6m)^3(1000kg/m^3)(9.8m/s^2) = 8.87 * 10^6 N$$.
Right?

Right?
Yeah. Your equation is right. Though don't you need to divide the diamter by two to get the radius? I checked neither of those two possible solutions are correct.

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The problem I did like this used

$$\begin{multline*} \Sigma F_{y}=F_{b}-F_{t}-F_{g}\\F_{g}=ma \end{multline*}$$

with gravity and tension in the negative y direction.

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Hey,hieroglyphs are from ancient Egypt.Those were capital Greek letters...Hey,you are Greek!

Daniel.

1. How do I calculate the buoyancy force in a 6m spherical chamber?

To calculate the buoyancy force, you will need to know the density of the fluid inside the chamber, the volume of the chamber, and the density of the surrounding fluid. The formula for buoyancy force is Fb = (ρVg), where ρ is the density difference between the two fluids, V is the volume of the chamber, and g is the acceleration due to gravity.

2. Can I use Archimedes' principle to calculate the buoyancy force?

Yes, you can use Archimedes' principle to calculate the buoyancy force. This principle states that the buoyancy force on an object is equal to the weight of the fluid that the object displaces.

3. How do I calculate the tension in a cable supporting the 6m spherical chamber?

To calculate the tension in the cable, you will need to know the weight of the chamber, as well as the angle at which the cable is attached to the chamber. The formula for tension is T = mg/cosθ, where m is the mass of the chamber, g is the acceleration due to gravity, and θ is the angle of the cable.

4. What is the maximum weight that the cable can support?

The maximum weight that the cable can support depends on the strength and material of the cable, as well as the angle at which it is attached to the chamber. To determine the maximum weight, you will need to calculate the maximum tension that the cable can withstand without breaking.

5. How does the density of the fluid inside the chamber affect the buoyancy force and tension in the cable?

The density of the fluid inside the chamber affects both the buoyancy force and the tension in the cable. A higher density fluid will result in a higher buoyancy force, while a lower density fluid will result in a lower buoyancy force. The tension in the cable will also be affected, as a higher buoyancy force will result in a higher tension in the cable.

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