Week 8: Fluids
379
two aspects of this extra pressure to consider one is the increase in pressure differential across the
valve, but perhaps the greater one is the increase in pressure differential between the inside of the
vein and the outside tissue. Th
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Week 8: Fluids
Impulse
Figure 101: A large number of atoms or molecules are confined within in a box, where they bounce
around off of each other and the walls. They exert a force on the walls equal and opposite the the
force the walls exert on them as
Week 8: Fluids
345
bulk modulus of water is 2.2 109 Pa, which means that even deep in the ocean where pressures
can be measured in the tens of millions of Pascals (or hundreds of atmospheres) the density of
water only varies by a few percent from that on
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Week 8: Fluids
It is worth noting that this is the fluid-flow version of Ohms Law, which you will learn next
semester if you continue. We will generally omit the modifier dynamical from the term
viscosity in this course, although there is actually ano
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Week 7: Statics
Problem 7.
m
M
T
L
P
This problem will help you learn required concepts such as:
Force Balance
Torque Balance
Static Equilibrium
so please review them before you begin.
A small round mass M sits on the end of a rod of length L and m
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Week 7: Statics
Optional Problems
The following problems are not required or to be handed in, but are provided to give you
some extra things to work on or test yourself with after mastering the required problems and concepts
above and to prepare for q
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Week 7: Statics
*
Optional Problem 11.
F
M
R
h
A cylinder of mass M and radius R sits against a step of height h = R/2 as shown above. A
force F~ is applied parallel to the ground as shown. All answers should be in terms of M , R, g.
a) Find the minim
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Week 7: Statics
Problem 9.
M
m
s
h
This problem will help you learn required concepts such as:
Torque Balance
Force Balance
Static Equilibrium
Static Friction
so please review them before you begin.
In the gure above, a ladder of mass m and length
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Week 7: Statics
Problem 8.
Ft
d
H
M
Fb
d
W
A door of mass M that has height H and width W is hung from two hinges located a distance
d from the top and bottom, respectively. Assuming that the vertical weight of the door
is equally distributed between
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Week 8: Fluids
Note well that this says nothing about the tangential force exerted by fluids in relative motion
to the walls of the confining container. We already know that a fluid moving across a solid surface
will exert a drag force, and later this
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Week 8: Fluids
8.2: Pascals Principle and Hydraulics
We note that (from the above) the general form of P of a fluid confined to a sealed container has
the most general form:
Z z
gdz
(728)
P (z) = P0 +
0
where P0 is the constant of integration or value
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Week 8: Fluids
We recall that the pressure changes only when we change our depth. Moving laterally does not
change the pressure, because e.g. dP/dx = dP/dy = 0. We can always find a path consisting of
vertical and lateral displacements from z = 0 to a
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Week 8: Fluids
static pressure in the liquid is in balance with the vacuum that forms at the top of the tube and the
ambient pressure of the surrounding air on the uid surface of the reservoir at the bottom.
a) Suppose the uid is water, with w = 1000
Week 9: Oscillations
387
Optional Problems: Start Review for Final!
At this point we are roughly four weeks out from our nal exam170 . I thus strongly suggest
that you devote any extra time you have not to further reinforcement of uid ow, but to a gradual
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Week 8: Fluids
c) Evaluate the answers to a) and b) for A = 0.25 m2 , P = 2 atmospheres, a = 0.25 cm2 , H = 50
cm, h = 1 meter and beer = 1000 kg/m3 (the same as water).
Problem 12.
m
M
The gure above illustrates the principle of hydraulic lift. A pai
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Week 8: Fluids
T?
W?
A block of density and volume V is suspended by a thin thread and is immersed completely
in a jar of oil (density o < ) that is resting on a scale as shown. The total mass of the oil and jar
(alone) is M .
a) What is the buoyant f
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Week 8: Fluids
a) A 1 = 30 cm 2, v1 = 3 cm/sec, A
2
= 6 cm 2
b) A 1 = 10 cm 2, v1 = 8 cm/sec, A
2
= 5 cm 2
c) A 1 = 20 cm 2, v1 = 3 cm/sec, A
2
= 3 cm
2
H
In the figure above three flasks are drawn that have the same (shaded) cross sectional area of
t
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Week 8: Fluids
Problem 2.
A small boy is riding in a minivan with the windows closed, holding a helium balloon. The van
goes around a corner to the left. Does the balloon swing to the left, still pull straight up, or swing
to the right as the van swin
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Week 8: Fluids
8.4.2: Work-Mechanical Energy in Fluids: Bernoullis Equation
Daniel Bernoulli was a third generation member of the famous Bernoulli family157 who worked on
(among many other things) fluid dynamics, along with his good friend and contemp
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Week 8: Fluids
from high pressure to low pressure just enough to overcome drag/friction and keep the fluid flowing
at a constant speed.
To correctly derive all of this, even for the simplest of geometries, is beyond the scope of this
course. It isnt h
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Week 7: Statics
Problem 6.
w/2
d
w/3
m
d/3
w
Top view
This problem will help you learn required concepts such as:
Force Balance
Torque Balance
Static Equilibrium
so please review them before you begin.
The figure below shows a mass m placed on a ta
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Week 7: Statics
Homework for Week 7
Problem 1.
Physics Concepts: Make this weeks physics concepts summary as you work all of the problems
in this weeks assignment. Be sure to cross-reference each concept in the summary to the problem(s)
they were key
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Week 7: Statics
Problem 5.
T?
m
M
D
F?
d
This problem will help you learn required concepts such as:
Static Equilibrium
Force and Torque
so please review them before you begin.
An exercising human person holds their arm of mass M and a barbell of ma
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Week 5: Torque and Rotation in One Dimension
Problem 9.
m,r
H
R
This problem will help you learn required concepts such as:
Newtons Second Law
Moments of Inertia
Rotational Kinetic Energy
The Rolling Constraint
Conservation of Mechanical Energy
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Week 5: Torque and Rotation in One Dimension
Problem 4.
M,R
H
This problem will help you learn required concepts such as:
Newtons Second Law for Translation and Rotation
Moment of Inertia
Conservation of Mechanical Energy
Static Friction
so please
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Week 5: Torque and Rotation in One Dimension
Problem 6.
I (about cm)
mass m
R
r
F
F
F
This problem will help you learn required concepts such as:
Direction of torque
Rolling Constraint
so please review them before you begin.
In the gure above, a spo
270
Week 5: Torque and Rotation in One Dimension
Problem 7.
R
M
m1
m2
H
This problem will help you learn required concepts such as:
Newtons Second Law
Newtons Second Law for Rotating Systems (torque and angular acceleration)
Moments of Inertia
The Rol
268
Week 5: Torque and Rotation in One Dimension
Problem 5.
m,R
rough
H
icy
H
This problem will help you learn required concepts such as:
Conservation of Mechanical Energy
Rotational Kinetic Energy
Rolling Constraint.
so please review them before you b
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Week 5: Torque and Rotation in One Dimension
Problem 3.
This problem will help you learn required concepts such as:
Denition/Evaluation of Moment of Inertia
Parallel Axis Theorem
so please review them before you begin.
a) Evaluate the moment of iner
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Week 5: Torque and Rotation in One Dimension
pivot
M
R
Figure 77: A hoop of mass M and radius R is pivoted on the side think of it as being hung on a
nail from a barn door.
is the moment of inertia of the hoop about this new axis parallel to the one t