Absolute pressure, buoyant force, tension problem

[jenn91890]

Homework Statement

A diving sphere has a mass of 150,000.0kg and an external diameter of 7.000 meters. The sphere is anchored with a cable on the bottom of an ocean, at a depth of .8000 km. The density of sea water is 1025.0kg/m3.
A) What is the absolute pressure at that depth in pascals?
B) What is the buoyant force felt by the sphere when it is completely submerged?
C) Calculate the tension of the cable.

Homework Equations

A) P = Ps+DgH
P=?
Ps=1.01E+5Pa
D=1.025E+3kg/m3
G=9.81m/s2
H=.8000km

B) P=F/A, A=pi R2
P=(from above)
BF=?
R=3.5m

C) WF=m*g
TF+WF=BF
m=150,000kg
g=9.81m/s2
TF=?
BF= (from above)

The Attempt at a Solution

A) P=(1.01E+5) + [(1.025E+3)*(9.81)*(800m)]
=8.145E+6Pa

B) 8.145E+6Pa = BF / (pi * 3.5)2
BF=3.135E+8N

C) WF=150000*9.81
WF=1471500
TF=313500000-1471500
TF=3.120E+8N

Is this correct? The numbers seem very high...

 

[TSny]

Hello and welcome to PF!

Is the depth .8000 hm or .8000 km?

Your method for part (a) is correct. For part (b) you have not calculated the BF correctly. Consider Archimedes' principle.

Your approach to part (c) looks correct.

 

[jenn91890]

Hello and welcome to PF!

Is the depth .8000 hm or .8000 km?

Your method for part (a) is correct. For part (b) you have not calculated the BF correctly. Consider Archimedes' principle.

Your approach to part (c) looks correct.

km, I have corrected the typo.

for part (b) density=mass/displaced volume
so displaced volume = mass/density
so displaced volume = 150,000/1025
so displaced volume = 146.341
BF = density * displace volume * gravity
BF=1025 * 146.341 * 9.81
=1.471E+6
?

 

[TSny]

so displaced volume = mass/density
so displaced volume = 150,000/1025
so displaced volume = 146.341

No, this isn't correct. 150,000 kg is the mass of the diving sphere, but 1025 kg/m³ is the density of sea water.

Try to think of another way to get the displaced volume. Hint: geometry.

 

[SteamKing]

km, I have corrected the typo.

for part (b) density=mass/displaced volume
so displaced volume = mass/density
so displaced volume = 150,000/1025
so displaced volume = 146.341
BF = density * displace volume * gravity
BF=1025 * 146.341 * 9.81
=1.471E+6
?

Your calculations become a lot more intelligible if you state the units after each result. It's a habit you should cultivate now.

 

[Chestermiller]

What is the volume of a sphere 7 m in diameter?

Chet