12.2 - Density, Pressure and Floatation

Question 1

What do fluids do more than solids when heated?

Answer 1

Expand

Question 2

What does this mean for a fixed mass of fluid?

Answer 2

It occupies a bigger volume than solid form

Question 3

What does this mean about its density?

Answer 3

It is reduced, compared to the solid form

Question 4

Are liquids generally compressible?

Answer 4

No

Question 5

Can gases be compressed?

Answer 5

Yes, it is done all the time

Question 6

What is fluid pressure?

Answer 6

The weight of fluid pressing down on an object

Question 7

Derive the equation for fluid pressure at height h, density p and cross-sectional area A:

Answer 7

Pressure at base = Weight of Column / Area
Pressure at base = mg/A
Pressure at base = Vpg/A
But V = Ah
So Pressure = hpg

Question 8

For large values of h, what do gases do?

Answer 8

Compress

Question 9

What does this mean for the Earth’s atmosphere?

Answer 9

It is less dense at higher altitudes

Question 10

What is the adopted value for atmospheric pressure?

Answer 10

100kPa

Question 11

What name is given to the buoyancy force that enabled us to float in water?

Answer 11

Upthrust

Question 12

What is upthrust a consequence of?

Answer 12

Water pressure being greater below an immersed object than above it

Question 13

What is upthrust equal to?

Answer 13

The weight of the fluid displaced

Question 14

What is this result often known as?

Answer 14

Archimedes’ principle

Question 15

How is this derived?

Answer 15

Consider a cylinder immersed in liquid
The upthrust is the difference between the force due to water pressure at the bottom, F2, and that at the top, F1
F1 = p1A = h1ρgA
F2 = p2A = h2ρgA
U = F2 - F1
U = h2ρgA - h1ρgA
U = (h2-h1)ρgA
U = Vρg = mg

Question 16

When will an object float in fluid?

Answer 16

When the upthrust is equal to its weight

Question 17

How would a ship floating in cold salt water be different from warm fresh water?

Answer 17

It would lie deeper in the fresh water, as fresh water is less dense than salt water, so it must displace more of it in order to float