Physics 1A
Lecture 9C
"All good things must come to an end.”
--Proverb
Buoyancy
If an object sinks to
the bottom of the
fluid (again taking
down as +y):
Then, ∑F = Fg – B – FN = 0
=>
FN = Fg – B
=>
apparent weight = weight – B
Things will appear to be lighter when compared to
being outside of the surrounding fluid.
Buoyancy
How do you make something like iron (ρiron > ρH2O)
float in water?
Change the shape to displace more water.
If you have a boat it
will displace enough
water to keep it afloat.
Add more weight to the
boat and it will lower
further into the water
to displace more water
and gain more buoyant
force.
In class Question
You are floating on a boat which is hauling iron on a
small lake. You get disgruntled and decide to unload
your iron into the water. What would happen to the
overall water level of the lake (as measured from
someone on the shore)?
A) The water level of the lake lowers slightly
compared to when the iron was on the boat.
B) The water level of the lake rises slightly compared
to when the iron was on the boat.
C) The water level of the lake will remain exactly the
same as when the iron was on the boat.
Buoyancy
The water level of the lake lowers.
The weight of the boat decreases so the water
that it displaces is much less.
The water that the volume of the submerged iron
displaces is not enough to keep it afloat.
So, even though the submerged iron displaces some
water, it was actually less displacement then when
it was being completely supported in the boat.
This leads to less overall displacement of water and
a lower water level in the lake.
Continuity Equation
An ideal fluid is one that is incompressible, has steady
constant motion, and contains no internal friction.
For an ideal fluid flowing through a pipe, as you
decrease the area you will have to increase the
velocity of the fluid through that section of pipe.
Equationally:
A1v1 = A2v2 = constant
A is cross-sectional area of
the pipe and v is velocity of
the fluid. Av is called the
volume flow rate.
Speed is high where the pipe
is narrow, speed is low the
pipe is wide.
Bernoulli’s Equation
Recall that pressure is:
We can apply this force
over a small distance to
get:
So we can think of pressure as an energy/volume
or otherwise known as an energy density.
What type of energies can a small amount fluid
contain?
Kinetic Energy.
Potential Energy.
Energy density (Pressure).
Bernoulli’s Equation
This is known as Bernoulli’s Equation.
It basically states that the total energy density
in any fluid is constant.
It relates pressure to fluid speed and elevation.
Swiftly moving fluids exert less pressure than do
slowly moving fluids (assuming their potential
energies are the same).
Bernoulli’s equation assumes that the fluid is
ideal.
Simple Example
A hose with negligible flow and gauge pressure of one
atmosphere or 100 kPa has a small hole.
Through the hole a “fountain” of water escapes straight
up.
How high is the fountain ?
P=ρgh
=> 100,000 N/m2 = (1000 kg/m3 ) ( 10m/s2 ) h
=> h = 10 m
Things We Have Learned
1) Math Techniques and Problem Solving:
Know how to pick an appropriate coordinate system.
Know how to use dimensional analysis and proper
unit conversion.
Know how to perform a simple estimate.
Know how to set up an equations from a word
problem.
Know how to add, subtract, and utilize vectors.
Know how to draw a properly labeled (extended)
force diagrams.
Things We Have Learned
2) Force and Motion:
Know how to apply the kinematic equations.
Understand the motion of objects (1D, 2D) under the
influence of various forces (Fg, FN, Ff, Fcent, FT...).
Be able to break forces, velocities, accelerations, or
any vectors into perpendicular components.
Know that perpendicular components are
independent of one another.
Understand how to apply Newton’s Laws to objects.
Understand differences between Newton’s 1st/2nd
Laws and Newton’s 3rd Law.
Things We Have Learned
3) Energy and Momentum:
Know the various forms of energy: PE (grav., spring...)
and KE (linear, rotational...).
Understand the conservation of energy: E1 = E2 if
Wnc = 0.
Know the difference between conservative forces and
non-conservative forces.
Know how to handle different collisions (elastic,
inelastic, 1D, 2D).
Know how to apply the conservation of linear
momentum to collisions.
Things We Have Learned
4) Rotational Motion and Equilibrium:
Know how to relate linear and rotational variables.
Know how to find centripetal acceleration (direction/
magnitude).
Know how to use the moment of inertia when dealing with
rotational motion.
Know how to calculate the torque on an object (magnitude
and direction).
Know how to apply equilibrium conditions for various cases
(∑τ = 0, ∑F = 0).
Know how to apply the conservation of angular momentum.
Things We Have Learned
5) Understanding Fluids:
density
pressure
buoyancy
continuity
Bernoulli’s equation
ALMOST THE END
Final is Friday, 11:30am - 2:30pm in this room
(2001 WLH).
Quizzes, HW, Lecture examples, in class Q’s,
Book examples, and maybe a few surprises.
Bring a Scantron and write your proper quiz
code number on your form.
For the most part, every quiz will be equally
represented on the final.
GOOD LUCK !!!
THE END
"Go forth and slay dragons.”
--Roderick Reid