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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
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 dens
340
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
v
331
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
334
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 re
335
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 an
333
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
332
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 vert
330
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 yo
327
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
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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 equa
348
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
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 n
385
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 a
383
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
381
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 draw
380
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
367
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)
369
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 ge
356
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 consistin
355
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) =
329
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 hum
328
Week 7: Statics
Problem 3.
lift
pivot
In the gure above, three shapes (with uniform mass distribution and thickness) are drawn sitting
on a plane that can be tipped up gradually. Assuming that sta
326
Week 7: Statics
That is enough that we could almost guess the answer (at least, if we drew some very nice
pictures). However, we should work the problem algebraically to make sure that we all unde
269
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
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
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
266
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 revie
262
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 inerti
265
Week 5: Torque and Rotation in One Dimension
Homework for Week 5
Problem 1.
Physics Concepts: Make this weeks physics concepts summary as you work all of the problems
in this weeks assignment. Be