Liquids - Lecture Slides - Basic Concepts of Physics, Slides of Physics

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-- Finish Atomic Structure of Matter (a fewslides)-- Liquids (Ch. 13)

Antimatter

-^

Composed of atoms with

negative nuclei

and

positive electrons

(called

positrons

Positrons

: (1932), first discovered in

cosmic rays bombarding earth. Samemass as electron, equal but oppositecharge. Antiprotons:

same mass as proton, equal

but opposite charge. Antiparticles

: now made in labs with

nuclear reactors. The first anti-atom (anti-hydrogen) made in 1995. Every particle has an antiparticle – every quark has an antiquark.Antiparticles of neutral particles like neutron have same mass, butdifferent other properties (eg spin..we’re not getting into this…)

Clicker Question

A movie-maker runs this idea by you – that if an antimatter

alien set foot upon the earth, the whole world wouldexplode into pure radiant energy. What would you say?

A) Great idea!B) No, the amount of matter annihilated would only have the

mass of the alien, a pair of particles at a time.

C) No, the alien would survive but generate energy through

interactions with humans.Answer: BThe amount of matter annihilated would be the same as theamount of antimatter, a pair of particles at a time. Thewhole world could only be annihilated if the mass of thealien were at least equal to the mass of the earth.

Dark Matter

•^

Light emitted from stars contains info about the elements insidethem – stars and other bodies out in universe contain same particleswe have on earth.

-^

But there is a lot more mass out there in the universe than we cansee – called

dark matter

• pulls on stars and galaxies that we can

see.

-^

Deduced gravitational forces in galaxies are far greater than whatvisible matter can account for.

-^

Estimated to be 90% of mass of universe!

A little more on density…

•^

Some densities:– Osmium (bluish-white metal) is the densest substance on earth.

It’s an element (atomic # 76), whose crystalline form has veryclosely packed atoms. Density 22.6 g/cm

Used e.g. in fountain pen tips, electrical contacts, where extremedurability/hardness needed.

• Water has density 1 g/cm

3

• Ice has less density, 0.92 g/cm

3 , because when water freezes, it

expands.

• Seawater has greater density, 1.03 g/cm

Clicker Question

Question:Which has greater density, 1 liter of water or 1 liter of ice?

And which weighs more?

A) The water has greater density and weighs moreB) The water has greater density but weighs lessC) The water has less density but weighs moreD) The water has less density and weighs lessAnswer: A Any

amount of water has greater density than

any

amount of ice (it doesn’t

depend on amount, since density is the ratio of mass to volume).Since water has greater density, it weighs more than an equal volume of ice.

Pressure in a liquid

•^

A liquid is composed of molecules that move constantly and bounce offthe sides of the container it is in and or bounce off objects (like aswimmer) in the liquid.Bouncing creates a force (recall momentum-impulse) – hence a

pressure.

Liquid Pressure = weight density x depth

“Proof”: Pressure =

forcearea

=^

weightarea

=^

weight density x volume

area

area x depth

= weight density x depth

due to liquid’s weightdirectly above

Pressure in a liquid: dependence on depth.• Pressure at a point twice as deep, is twice as much.

-^ Consider swimming:

Near top surface of the water, don’t feel much

pressure (depth is near 0). (More precisely, need to add air pressure ofthe atmosphere but since it’s there all the time, we don’t notice that).Go deeper - you feel more pressure (e.g. in your ears). The deeper yougo, the more weight of water is above you, so more pressure you feel.•^

It does

not

depend on the volume, only on the

depth

• Eg. Same water pressure felt when swimming 2m deep in a backyardpool than when swimming 2m deep in a huge freshwater lake.

Eg. Different shaped vases all connected – the level of the water ineach is the same. Why?^ Because, if not, the pressure would be more at the bottom of the vasewith higher water level (from eqn, larger depth). This increasedpressure would then force water sideways to lower pressure, and thenup the vase with lower level. Eventually pressures equalize – whichmeans same water level in each.This gives rise to the saying water “seeks it’s own level”.

Eg. Hold a garden hose filled with water, and hold both ends at same

height, water stays. Now if raise one end, water flows out lower end,even through an “uphill” path. Question:

Which pot holds more

tea? (They are identical except thatthe left one is taller)The both hold the same! The watercannot be no deeper than thespouts, which are at the sameheight. Relevant to the unnecessarily elaborateacqueducts the Romans made, verycarefully ensuring water would flowdownhill at all points – but actually water can

flow upwards in between.

Liquid Pressure: Direction

-^ Liquid pressure is exerted

equally

in

all

directions.

Eg Swimming underwater, pressure on eardrum is same if tilthead in any direction.Eg. Water spurts

sideways

from holes in the side

Eg. Boat on water – water pressure acts

upward

on the boat surface

• Although force has direction, pressure does not (it’s a scalar)At any point on the triangular block shown, force frombouncing molecules are in all directions, but only thatnormal to the surface doesn’t get cancelled out.

Net

force is normal (perpendicular) to (any) surface.

Buoyancy

Buoyant force = upward force acting on an object in liquid, due to pressureon lower part of object being higher than pressure on upper part

:

Why? Because liquid pressure islarger for larger depths.

Question:

If there’s an upward buoyant force on a submerged object, then

how come it doesn’t accelerate upwards (N’s 2

nd

law) ??

There are also other forces acting – downward gravitational force andwater resistance. So whether it accelerates or not, and in which direction(up or down) depends on how these balance.Eg, if push a light ball under water, it accelerates up once you let go due tobuoyant force being dominant.But if you push a boulder under water, it will sink, as weight (grav force) islarger than the buoyant force.

Aside: Archimedes and the King’s Crown

• This concept of displacement of water is really useful if you want to measure thevolume of odd-shaped objects.• There is a story of how Archimedes (circa 250 BC) discovered this.King Hiero II had given a goldsmith a lump of pure gold of a certain weight to makehim an elaborate crown. He then wanted to verify that the goldsmith did in fact useall the gold, and didn’t substitute part of a cheaper metal like silver, taking some ofthe gold for himself instead. How to determine this without destroying the crown?^ Can measure that thecrown and gold ingothave the same weight.

When put in water, the king’scrown displaced more water thanthe gold ingot



larger volume



lower density, i.e. not pure gold

While taking a bath, Archimedes realized when object is put in water, the waterlevel rises an amount equal to the object’s volume (displacement principle).So:

Buoyancy: Archimedes’ Principle

An immersed body is buoyed up by a force equal to the weight of thefluid it displaces.

-^ Applies to liquids and gases• Applies to either partially submerged objects or fully submerged objects• So buoyant force depends on object’s

volume

Eg. What is the buoyant force on a 1-liter container of anything in waterso that just

half

of it is in the water?

Same volume, 0.5-liter, of water is displaced, so the buoyant

force on it is the weight of 0.5-liters of water = 0.5 x 9.8 N = 4.9 N.

Recall 1-liter of anything is 1000 cm

3. Recall mass

density of water is 1g/cm

3 , so weight density is 1x

g

= 9.8 N/cm

3. So weight of 1 liter of water is 9.8 N.

If fully submerged, the buoyant force is greater – equal to 9.8 N in the caseof (any) 1-liter object.