Finding an increase in depth, pressure and thrust

In summary, the sphere increases the depth, the pressure, and the thrust by 2.25 cm, 360πg, and 9.8 N respectively.
  • #1
Woolyabyss
143
1

Homework Statement


A cylindrical tank of radius 4cm is partly filled with water.A solid metal sphere of radius 3cm is lowered into the water by means of a thin wire until it is totally immersed. Find the increase in
(i) the depth
(ii) the pressure at a point on the base
(iii) the thrust on the base(in terms of π )


Homework Equations


Pressure = (depth)(g)(density)

The Attempt at a Solution


(i)
h = depth of water before sphere added

Volume of water before sphere added = 16(π )(h)

volume after sphere added = 16(π)(h) + (4/3)(π)(64)

pressure = (1)gh (since the density of water is 1/cm^3)

I'm not sure what to do next I'd presume I have to get the depth(h) somehow?
 
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  • #2
Woolyabyss said:
1. volume after sphere added = 16(π)(h) + (4/3)(π)(64)


Check that second term on the right ...
 
  • #3
Oh sorry V = 16πh + (4/3)π(27) = 16πh + 36π

I'm still not sure how to get the height
 
  • #4
rude man said:
Check that second term on the right ...

Would this be correct?
(i)
V = volume after sphere is added

V = 16πh +36π

but V also = 16π(x+h) ... where x is the additional depth the water has risen)

16π(x+h) = 16πh + 36π

16πx + 16πh = 16πh +36π ... 16πh cancels

16πx = 36π

x = 36/16 =2.25 cm

(ii) convert to kg/m^3 and meters so our answer will be in pascals

1000g(0.0225+h) - 1000gh = 1000g(0.0225) +1000gh - 1000gh = 22.5g Pa

(iii) F = 22.5g(16π) = 360πg N

(these are the answers my book gives)
 
Last edited:
  • #5
Woolyabyss said:
Would this be correct?
(i)
V = volume after sphere is added

V = 16πh +36π

but V also = 16π(x+h) ... where x is the additional depth the water has risen)

16π(x+h) = 16πh + 36π

16πx + 16πh = 16πh +36π ... 16πh cancels

16πx = 36π

x = 36/16 =2.25 cm

(ii) convert to kg/m^3 and meters so our answer will be in pascals

1000g(0.0225+h) - 1000gh = 1000g(0.0225) +1000gh - 1000gh = 22.5g Pa

(iii) F = 22.5g(16π) = 360πg N

(these are the answers my book gives)

OK but you should include g = 9.8 in your answer.

I also advise using Rt and Rs for radius of the tank and sphere instead of the number, until the very end. That way you can check units term-by-term as you go along.
 

FAQ: Finding an increase in depth, pressure and thrust

What is the relationship between depth, pressure, and thrust?

The deeper an object is submerged in a fluid, the greater the pressure and thrust acting on it. This is due to the weight of the fluid above the object increasing with depth, creating a greater force pushing down on the object. The pressure and thrust also increase proportionally with the density of the fluid.

How can one determine an increase in depth, pressure, and thrust?

An increase in depth can be measured using a depth gauge or by calculating the distance from the surface to the object. Pressure can be measured using a pressure gauge or by using the equation P = ρgh, where P is pressure, ρ is density, g is the acceleration due to gravity, and h is the depth. Thrust can be determined by measuring the force acting on an object, which can be done using a force gauge or by using the equation F = ρVg, where F is thrust, ρ is density, V is volume, and g is the acceleration due to gravity.

What factors affect the increase in depth, pressure, and thrust?

The main factor that affects an increase in depth, pressure, and thrust is the density of the fluid. As mentioned before, depth, pressure, and thrust increase proportionally with density. Other factors that may affect these variables include the shape and density of the object, as well as any external forces or currents acting on the object.

How does an increase in depth, pressure, and thrust impact objects?

An increase in depth, pressure, and thrust can have different effects on different objects. For example, a submarine is designed to withstand high pressure and use thrust to maneuver at different depths. On the other hand, a human diver may experience discomfort or even injury if they descend too quickly to great depths, as their body is not adapted to withstand high pressures. In general, an increase in depth, pressure, and thrust can impact an object's buoyancy, stability, and ability to move or withstand external forces.

Can an increase in depth, pressure, and thrust be dangerous?

In certain situations, an increase in depth, pressure, and thrust can be dangerous. For example, diving to great depths without proper training or equipment can lead to serious injury or death due to the high pressure. In addition, objects or structures not designed to withstand high pressures may collapse or experience damage. It is important to understand and properly manage depth, pressure, and thrust to ensure safety in various environments.

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