## Classical Mechanics: Lecture 28 Notes

**Overview**

Cool lecture today on liquids. This material relates to chemistry. Walter Lewin has an interesting gesture of mussing his hair at certain points. It costs 49 minutes:

**Details**

A cylinder with length, surface area, density, and mass. It has a liquid line, fluid with density of height h. To float, there must be equilibrium from mg and the buoyant force.

P1 – P2 = d g h

F1 – F2 – mg = 0

F1 – F2 = bouyant force

F1 = area x p1

F2= area x p2

F buoyant = A d g h = weight of the displaced fluid

This is Archimedes principle. He tells the old crown/Archimedes story. Weight the crown in the normal way – W = V d g. Then throw it in water, W water = V dg – volume of the crown x fluid density x g.

W1/Weight loss = density crown/density water

This method is also used to compute body composition. Immerse in water, weight, then compare with regular weight.

Weight = Volume x density x gravity

An iceberg floats in water with mass m, density and volume. Density is .92 grams/cm.

mg = buoyant force = V total d ice g = V under d water g

V underwater/V total = d ice/d water = 0.9

*Floating conditioning*

buoyant force = mg

Density object < Density water

F b = mg

Ahdg = Alpg

If an object sinks, d object> d water.

In a swimming pool with a boat, there is a rock in the boat. Mark a line. Throw the rock in. The water line will rise.

*Stability*

An object floating in water with a center of mass. The gravity acts on the center of mass, the buoyant force is perpendicular to the surface, thus a torque is created. Either the cm becomes above or below the Fb.

Tilt an object with a low cm. The cm of the displaced fluid has a Fb up. This will be stable. If the cm is above the Fb, it is unstable. Build a ship with a very low cm. In the 17th century, cannons would throw off the cm and capsize the ship.

Balloons

A balloon is like a water floating in liquid. M is the mass of the air in the balloon with the string and the rubber. It has a volume and density.

To Float:

F b > mg

The weight of the displaced fluid must be larger than mg

V density air gravity = Fb

V density g + all the remaining mass

All the remaining mass>0.

The density of the gas must be < the density of air. It is necessary but not sufficient.

Air is made up of 78% N2, 21% O2, Argon, CO2, H2O.

An apple tied to a balloon. With no gravity, the apple would not fall, the balloon would not rise. He performs a demonstration with a cart containing an apple or balloon.

Moving fluids complicate things.

*Bernoulli’s Equation*

(1/2) p v1^2 + pgy + Py = C

This has to do with KE, PE and Pressure.

He then does another demonstration with a syphon. Swallow a little gas and you can empty someone’s gas tank. This begins at 35 minutes in.

Another demonstration with a funnel and ping pong ball. You cannot blow it up. The highest speed is the lowest pressure. You can turn it upside down to hold the ping pong ball up.

Fill a glass with cranberry juice. Put cardboard on top. The juice won’t fall out.

**Review**

F = ma

p = mv

U = mgh

K = .5 m v^2