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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 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
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
viscosity in this course, although there is actually ano
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 round mass M sits on the end of a rod of length L and m
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 required problems and concepts
above and to prepare for q
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 answers should be in terms of M , R, g.
a) Find the minim
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 begin.
In the gure above, a ladder of mass m and length
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 vertical weight of the door
is equally distributed between
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 you begin.
The figure below shows a mass m placed on a ta
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 concept in the summary to the problem(s)
they were key
341
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
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 a solid surface
will exert a drag force, and later this
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
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 above illustrates the principle of hydraulic lift. A pai
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 the oil and jar
(alone) is M .
a) What is the buoyant f
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 drawn that have the same (shaded) cross sectional area of
t
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 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
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 geometries, is beyond the scope of this
course. It isnt h
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 consisting of
vertical and lateral displacements from z = 0 to a
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) = P0 +
0
where P0 is the constant of integration or value
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 human person holds their arm of mass M and a barbell of ma
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 static friction is great enough that all
of these shapes w
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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 understand
it. Let us assume that F = Fm , the desired mini
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 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
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 review them before you begin.
a) Evaluate the moment of iner
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 inertia of the hoop about this new axis parallel to the one t
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 sure to cross-reference each concept in the summary to
Physics 1A
Spring 2015
Challenge Problem 6
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A 4-kg block rests on top of a 5-kg block, which rests on a frictionless
table. The coefficient of friction between the two blocks is such that the
Physics 11 Assignment
Chapter 3
Physicist: KEY
1. Define the following terms:
Vector - a physical quantity that has a magnitude and a direction
Scalar - a physical quantity that has only a magnitude or size
Vector diagram - a diagram, with a coordinate
Physics 1A
Week 5 Questions
Fall 1998
1. A flywheel rotates with constant angular velocity. Does a point on its rim have a tangential acceleration? A
radial acceleration? Are these accelerations constant in magnitude? In direction? In each case, give the
Physics 1A
Spring 2015
Challenge Problem 12
sh is
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aC s
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The pulleys in the diagram below are massless and have frictionless axles.
The cables are massless and have constant length. The top pulley is atta
Page |1
Chapter 8: Momentum, Impulse, and Collisions
1.) When a large, heavy truck collides with a passenger car, the occupants of
the car are more likely to be hurt than the driver. Why?
2.) A net force of 4 N acts on an object initially at rest for 0.25