F10L2, Work energy - Bernoulli
A
B
1. PA > PB
2. PB > PA
Bernoullis equation is derived using the work-energy
theorem and relates the velocity and height of a moving
fluid to its pressure.
P2
y1
P1
m v1
m v2
y1
y2
P2
y2
m V
Bernoullis Equation
2
P 1 v12
Kinematic Equations
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v
x,v,a
a
t
v
t
a
v
a
x
t
v
a
t0
x
t
v
t
a
a
a
t0
v = v0+at
x = (v0+v)t
Kinematic Equations
v = v0+at
x = (v0+v)t
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t
v = v0+at
x = (v0+v)t
x = v0t + at2
v2 = v02 + 2a x
x
Clear communication & Clear thinking
1. D
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Impulse and Momentum
p
mv
impetus
p
F
a
F
m
F t
I
p
t
v
t
p
p
ma
v
t
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Impulse and Momentum
A
B
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Impulse and Momentum
p
t
F
Collapsible steering
column
Front
crumple
zone
Flexible
bumpers
Air bags
m
t
F
p
t
F
m
v
t
follow
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More Newton's Laws Problems
F
v
v
F
fk
fk
N
b F
c F
d F
e
fk
fk
fk
F
x
W
a F
y
fk
W
N
W
N W
N W
N W
m
m
M
M
m
M
m
M.
N
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More Newton's Laws Problems
s
k
x = v0 t +
s
k
fsmax
at2
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More Work, Power
KE mv2 PEG=mgy PES=kx2
E = KE + PE
W
F d
F
d
Wnc increases or decreases the mechanical energy of the system
Wc rearranges the mechanical energy of the system
Wnc
Ef Ei
Wnc = m(vf2 - vi2) + mg y + k(xf 2 - xi 2)
d
v
v
d
Page 2
Kinematics in 1 dimension
DISPLACEMENT
Displacement is a vector that points from an objects initial position to its final position. The magnitude
of the displacement is the shortest distance between the two positions.
SPEED AND VELOCITY
The average speed
THE CONCEPTS OF FORCE AND MASS
A force is a push or a pull and is a vector quantity. Contact forces arise from the physical contact
between two objects. Noncontact forces are also called action-at-a-distance forces, because they arise
without physical con
Kinematics in 2 dimensions
DISPLACEMENT, VELOCITY, AND ACCELERATION
The position of an object is located with a vector
drawn from the coordinate origin to the object. The
displacement
of the object is defined as
, where
and
specify its final and
initial p
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Newton's Three Laws
Constant velocity means no change in speed or direction
F ma
Fx ma x
Fy ma y
kg
m
s
Fz ma z
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Newton's Three Laws
FAB
FAB
FBA
FBA
y
x
tart with a FBD
w
Fg
indicate magnitude and direction
Gmbody mobj
r
w mg
g
n
F
Projectiles and Relative Velocity
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Projectiles
y
vo
yfinal
y
vo
h
h
R
R
y
yfinal
y
vo
h
R
yfinal
yfinal
vo
Projectiles and Relative Velocity
o=oreo, b=bus, g=ground, m=mom
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c=car
v AB
vob=
vbg=
v AE
v AB
vog=
A
vom=
B
vEB
vBE
vmg=
v
Pulleys and Inclined Planes
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FAB
FBA
Pulleys and Inclined Planes
g
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Pulleys and Inclined Planes
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F ma
v = v0+at
x=
(v0+v)t
x = v0 t +
at2
v2 = v02 + ax
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Introduction
117
Professor Topper
Page 2 of 4
Introduction
Formative
Summative
*an average grade of 50% on the laboratory component
is required in order to receive credit for the course
Measure x so you can determine y where y=f(x).
y
y
y
ybes
WORK DONE BY A CONSTANT FORCE
The work W done by a constant force acting on an object is
cos
where F is the magnitude of the force, d is the magnitude of the displacement, and is the angle
between the force and the displacement vectors. Work is a scalar q
Scaling
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l=linear dimensions
Ax =
As =
l=x
V=
Ax =
As =
V=
l=2x
s=scaling factor
Ax =
As =
V=
l=sx
T
s
_
Scaling
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Consider strength of the supports vs. load
load x23
w mg
l
wbig
s
strength x22
l
wsmall
_
s
s s
s
s
s s
s
_
_
s
s
Scali
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Spring Potential Energy
d
FApplied
kx
d
Fs
keq =
Units:
Fs
kx
F
F
W
x
F
Fd
x
xf
xi
W
F
F
kx
F dd
W
xf
kx f
xi
kx
W
x
W
x
kx
kx
W
kx f
kxi
kxi
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Spring Potential Energy
PE
WS
PE s
WC
kx f
kx f
kxi
kxi
Wnc = mvf2 mvi2 + mg y + kxf2 - k
THE IMPULSEMOMENTUM THEOREM
The impulse of a force is the product of the average force
which the force acts:
and the time interval during
Impulse is a vector that points in the same direction as the average force.
The linear momentum of an object is the
F10L3, Torricelli, Fluids Review
An ice cube floats in a glass of water filled to
the brim. As the ice melts which of the
following is true:
1. the water level stays constant
2. the water overflows
Ex. A ship floating on a lake has a 80 cm2 hole in the hu
F9L2, Pascal's Principle, Measuring Pressure
Fluids -materials that can flow
m
V
Density
Pressure
P = F/A
gauge pressure = P- Patm
Pressure variations with depth of fluid
P0
P P0 gh
h
P
Pascals Principle
Pressure applied to a confined fluid increases the
F10L1 Equation of Continuity
A solid piece of plastic of volume V, and
density plastic would ordinarily float in
water, but it is held under water by a string
tied to the bottom of bucket as shown.
1. Zero
2. water V g
3. plastic V g
A solid piece of plas
F10L2, Volume thermal expansion
L
V0 L
3
0
L L0 T
L
L
V
Volume thermal expansion
V V0 T
where is the coefficient of volume
expansion in (C0)-1.
3
Water
Density (kg/m3)
1000.00
999.95
999.90
999.85
999.80
999 80
999.75
999.70
999.65
999.60
999.55
0
2
4
6
Page1of7
Part I Multiple Choice Questions (answer on Scantron card)
1. A parachutist jumps out of an airplane and falls freely under the influence of gravity alone to a maximum
velocity of 58.8 m/s in 6.00 seconds. At this time, she opens her parachute an
Phys 117 Dec 99
1. An object weighs 10 N on the earth's
surface. What is the weight of the object on a
planet which has one tenth the earth's mass
and one half the earth's radius?
2. An airplane flying at 115 m/s due east
makes a gradual turn following a
1. A steel ring of inner diameter 1.0020 cm at 200C is placed around a copper rod of diameter
1.0000 cm at 200C. At what temperature will the ring fit tightly? The coefficient of linear
expansion of steel is 12x10-6 K-1 and that of copper is 16x10-6 K-1.
Physics 107 December 2007
Page 2
Section A Multiple Choice. Choose the one alternative that best completes the statement or answers
the question. Mark your answer on the Scantron card.
1. A skier leaves the ramp of a ski jump with a velocity of 10 m/s, 15
Page 1 of 3
Conservation of Momentum
from just before
to just after
define system so
there are no net
external forces
vBE
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Conservation of Momentum
vb1
vb2
vb2
vb1
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Conservation of Momentum
Fext
M,
Pi
vA
vC
x
x
Pf
Fext
Pi
y
y
Pf
x
y
Page 1 of 3
Free Fall
a, v
When is an object in Free Fall?
y
y
a
t
a
v
t
y
t
v = v0+at
x=
(v0+v)t
x = v0t + at2
v2 = v02 + 2a x
v = v0+at
x=
(v0+v)t
x = v0t + at2
v2 = v02 + 2a x
Page 2 of 3
Free Fall
v = v0+at
v = v0+at
x=
x=
(v0+v)t
x = v0t + at2
v2 = v