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
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 =
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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
z
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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
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 t
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-d
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
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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
ind
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
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
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Introduction
Formative
Summative
*an average grade of 50% on the laboratory component
is required in order to receive credit for the course
Me
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
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
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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
Physics 117 Equation Sheet For Fall 2014 Midterm
MECHANICS
For constant acceleration, ax:
(same for y-motion)
(
)
Quadratic equation:
Relative velocity:
Dynamics:
Friction:
(kinetic),
Newtons law of g
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 a
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
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 Princi
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.
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
9
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
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 flyin
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 s
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 leav
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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
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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
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Free Fall