Physics 1A
Lecture 9B
"There is nothing like returning to a place that
remains unchanged to find the ways in which you
yourself have altered.”
--Nelson Mandela
Matter
There are four basic states of matter:
Solids - definite volume and definite shape.
Liquids - definite volume but no definite shape.
Gases - no definite volume and no definite shape.
Plasmas - high temperature matter with electrons
freed from their respective nuclei.
You can deform all of the above states of matter.
Solids are the hardest to deform, but it is possible
through the application of external forces.
Solids
Stress is the force per unit area causing the
deformation.
Strain is a measure of the amount of deformation.
The elastic modulus is a measure of the stiffness
of the given material. An object with a large
elastic modulus is hard to deform.
stress = (Elastic modulus) x (strain).
Units are:
stress [N/m2], modulus [N/m2], strain[unitless].
This deformation can occur in many ways:
tensile stress, elastic stress, volume stress.
Fluids
A fluid is a substance that can conform to the
boundaries of any container.
Liquids and gases fall into this category.
Two important quantities for dealing with fluids
are density and pressure.
Density, ρ, is given by:
Density is measured in units of:
kg/m3.
The specific gravity of a substance is the ratio
of its density to the density of water at 4oC.
The density of water at 4oC is 1000kg/m3.
Fluids
Pressure, P, is given by:
Pressure is measured in SI units
of: N/m2 = Pascal = Pa.
There are plenty of units for
pressure:
atm, torr, psi, mm of Hg, kPa, bar...
Because of this be aware of the
basic conversions:
1atm = 1.01x105Pa = 760torr = 14.7psi.
Pressure is a scalar quantity, it
doesn’t have a direction.
Fluids
When discussing pressure in a fluid, it is important to
measure with respect to a reference point.
So, in reality you are measuring a change in pressure or
ΔP.
As you go deeper into the fluid, your pressure will
increase (there is more mass on top of you pushing down
on you).
If the fluid is static (i.e. at
rest) then we can say that:
ΔP = P2 – P1 = ρg(y2 – y1)
For a height h,
P2 = P1 + ρgh
P2 > P1
Fluids
The pressure at any point in a fluid which is in static
equilibrium depends on the depth of that point.
The pressure does not depend upon the shape of the
container.
There are two types of pressure: Gauge and
Absolute.
Absolute Pressure is the total
pressure at a location.
Gauge Pressure is the
measured pressure compared
to a reference point (this
reference is nearly always
atmospheric pressure).
Pascal’s Principle
One of the most useful aspects of fluids is the
incompressibility of liquids (gases are quite
compressible).
Pascal’s Principle takes advantage of this
effect:
“A change in the pressure applied to an
enclosed incompressible fluid is transmitted
undiminished to every portion of the fluid.”
Applied pressure is felt throughout the fluid
not just at the point of contact.
This idea helped to develop the hydraulic lever.
Pascal’s Principle
If I apply a force to a small area of a liquid (F1 and
A1), this in turn will exert a different force, F2, on a
different area of the fluid (A2).
By Pascal’s Principle,
But you don’t get
something for nothing!
The distance you need
to push down on A1
(Δx1) needs to be much
greater than how much
A2 raises (Δx2).
P1 = P2
Archimedes Principle
When an object is submerged in a fluid (even if only
partially) it will be given an upward force by the
fluid.
This upward force is called the buoyant force, FB or B.
The physical cause of the
buoyant force is the
pressure difference between
the top and the bottom of
the object.
Archimedes determined that
this force depends upon the
amount of fluid that the
object has displaced.
Archimedes Principle
Equationally this becomes:
where ρf is the density of the
displaced fluid and Vi is the
volume of the object that is
immersed in the fluid.
If the entire object is immersed
in the fluid then you just use
the volume of the object for Vi.
But if the object is only
partially immersed just use the
volume that is immersed as Vi.
Buoyancy
Example
A ball is floating in a pool of water. 25% of its
volume is immersed in the water. What is the
density of the ball?
Answer
First, define a coordinate system.
Let’s choose down as the positive y-direction.
Buoyancy
Answer
Next, draw a force diagram for the ball:
Fbuoyancy, water on ball
ball
+y
Fgravity, Earth on ball
Since the ball is in equilibrium, we can say that in
the y-direction:
Answer
Buoyancy
Somehow we need to find the density of the ball,
we can use: m = ρV.
70+ As
roughly 120 Bs
roughly 50 Cs
about 10 Ds and Fs
0
More
91.14585938
85.06946875
78.99307813
72.9166875
66.84029688
60.76390625
54.68751563
48.611125
42.53473438
36.45834375
30.38195313
24.3055625
18.22917188
12.15278125
6.076390625
Quiz grades
Frequency
Histogram
80
70
60
50
40
30
20
10
0
Frequency
Bin
Based on the quiz grades alone we would have:
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