Momentum

1
Momentum Energy conservation
2
Momentum
3
Newtons 2nd law (shorthand version)
F ma
change in v time
a
change in v time
F m
4
Car truck collision
Fc
Ft
Ft mt
change in vt time
Fc mc
change in vc time
Fc t mc change in vc
Ft t mt change in vt
Fc t Ft t mc change in vc mt change in vt
(Fc Ft)t change in mcvc change in mtvt
(Fc Ft)t change in (mcvc mtvt)
5
Car truck collision
Fc
Ft
(Fc Ft)t change in (mcvc mtvt)
Newtons 3rd law Fc -Ft
(Fc Ft)t 0
0 change in (mcvc mtvt)
mcvc mtvt stays constant!
6
Momentum mv
mcvc momentum of car
this changes
this changes
Mtvt momentum of thruck
mcvc mtvt total momentum
this stays constant
Before -40
After -40
Momentum is conserved!
7
True for all collisions
before 20
after 20
visit www.physicsclassroom.com/mmedia/index.html
8
Revisit the canoe at the dock
Initial momentum canoe 0 boy 0 Total 0
final momentum canoe mcvc boy mbvb Total 0
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Momentum is a vector mvcollision in 2 dimensions
10
Finding nemo
eating
11
Billiard balls
2
before
after
ptot
2
ptot
1
1
12
Conservation of momentumon a sub-atomic level
before
p
p
ptot
proton
after
p
ptot
p
p- meson
p- meson
13
Rocket travel
before
P0
after
P0 p
exhaust
p
14
Rifle recoil
mV
mV
15
Machine-gun granny
16
Work and Energy
17
Physicists definition of work
dist?
A scalar (not a vector)
dist
Work F x dist?
18
Atlas holds up the Earth
But he doesnt move, dist? 0
Work Fx dist? 0
He doesnt do any work!
19
Garcon does work whenhe picks up the tray
but not while he carries it around the room
dist is not zero, but dist? is 0
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Why this definition?
A vector equation
Newtons 2nd law Fm a
Definition of work a little calculus
A scalar equation
Work change in ½mv2
This scalar quantity is given a special name
kinetic energy
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Concept of Kinetic Energy
Emilie du Châtelet (1706-1749) Brilliant
mathematician One of Voltaires lovers
22
Work change in KE
This is called the Work-Energy Theorem
23
Units again
Kinetic Energy ½mv2
m2 s2
kg
work F x dist?
same!
1Joule
m s2
N
m
kg
m
24
Work done by gravity
end
start
dist
dist?
change in vertical height
Wmg
Work F x dist?
-mg x change in height
-change in mg h
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Gravitational Potential Energy
Workgrav -change in mgh
This is called Gravitational Potential Energy
(or PEgrav)
Workgrav -change in PEgrav
change in PEgrav -Workgrav
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If gravity is the only force doing work.
Work-energy theorem
-change in mgh change in ½ mv2
0 change in mgh change in ½ mv2
change in (mgh ½ mv2) 0
mgh ½ mv2 constant
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Conservation of energy
mgh ½ mv2 constant
Gravitational Potential energy
Kinetic energy
If gravity is the only force that does work
PE KE constant
Energy is conserved
28
Free fall (reminder)
height
t 0s
80m
V0 0
75m
t 1s
V1 10m/s
60m
t 2s
V2 20m/s
t 3s
35m
V3 30m/s
t 4s
0m
V4 40m/s
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m1kg free falls from 80m
mgh ½ mv2 sum
t 0s
V0 0 h080m
800J 0
800J
t 1s
750J 50J
V1 10m/s h175m
800J
t 2s
V2 20m/s h260m 600J 200J
800J
t 3s
V3 30m/s h335m 350J 450J
800J
t 4s
V4 40m/s h40 0 800J
800J
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pendulum
T
Wmg
Two forces T and W T is always - to the
motion ( does no work)
31
Pendulum conserves energy
Etotmghmax
Etotmghmax
hmax
Etot1/2 m(vmax)2
32
Roller coaster
33
Work done by a spring
Relaxed Position F0
x
F
I compress the spring (I do work spring does
-work)
Work done by spring - change in ½ kx2
34
If spring is the only force doing work.
Work-energy theorem
-change in ½ kx2 change in ½ mv2
0 change in ½ kx2 change in ½ mv2
change in ( ½ kx2 ½ mv2) 0
½ kx2 ½ mv2 constant
potential energy in the spring
35
Conservation of energysprings gravity
mgh ½ kx2 ½ mv2 constant
Gravitational potential energy
spring potential energy
Kinetic energy
If elastic force gravity are the only forces
doing work PEgrav PEspring KE constant
Energy is conserved
36
example
grav PE
KineticE
Spring PE
37
Two types of forces

• Conservative forces
• forces that do work
• Gravity
• Elastic (springs, etc)
• Electrical forces

• Dissipative forces
• forces that only do work
• Friction
• Viscosity
• .

-work ? heat (no potential energy.)
-work ? change in PE
38
(-)Work done by friction?heat
39
Thermal atomic motion
Air
solid
Heat energy KE and PE associated with
the random thermal motion of atoms
40
Work-energy theorem(all forces)
Workfric change in (PEKE)
Work done dissipative Forces (always -)
potential energy From all Conservative forces
Kinetic energy
-Workfric change in heat energy
Workfric -change in heat energy
-change in Heat Energy change in
(PEKE)
41
Work Energy Theorem(all forces)
0 change in Heat Energy change
in (PEKE)
0 change in (Heat EnergyPEKE)
Heat Energy PE KE constant
Law of Conservation of Energy
42
Energy conversion while skiing
Potential energy
Potential energy?kinetic energy
Friction energy gets converted to heat
43
Units again
Heat units 1 calorie heat energy required to
raise the temp of 1 gram of
H2O by 1o C
Kg m2/s2
1 calorie 4.18 Joules
44
Food Calories
1 Calorie 1000 calories 1Kcalorie
The Calories you read on food labels
1 Calorie 4.18x103 Joules
7 x 106 J
8 x 105 J
2 x 106 J
45
Power
amout of energy elapsed time
Rate of using energy
Power
Joule second
Units
1
1 Watt
A 100 W light bulb consumes 100 J of electrical
energy each second to produce light
46
Other units
Over a full day, a work-horse can have an
average work output of more than 750 Joules each
second
1 Horsepower 750 Watts
47
Kilowatt hours
energy time
Power
? energy power x time
? power unit x time unit energy unit
Kilowatts (103 W)
hours (3600 s)
Elec companies use
x
1 kilowatt-hour 1kW-hr
103 W x 3.6x103 s 3.6x106 Ws
J
48
about 300 won
In Hawaii electrical energy costs about 25cents
/kW-hr
What is the cost in Seoul?