Physics 1010:
The Physics of Everyday Life
TODAY
• Conservation Laws (Energy, Momentum)
• Collisions
• Work, Energy (Kinetic, Potential, Heat)
1
Admin Matters
• Cummulative grades are on the course
website, listed by clicker number
• Some clicker #s have no names: 137097,
202054, 241566
• Some names have no clicker number
• Please make sure Yu has your name and
clicker number
2
Conservation Laws
•
•
•
•
•
The real power behind Physics
Allow us to write equations:
(whatever before) = (whatever after)
We don’t need to know details of how
Newton’s Laws are conservation of momentum
No other science has conservation laws
(well…, Chemistry borrowed mass concerv)
3
Conservation Laws
•
•
•
Momentum: p = mv
Different kinds of energy (kinetic,
potential, heat)
Energy converted from one kind to another,
but TOTAL energy is unchanged
4
Newton’s second law revisited: Force
gives change of momentum
• Momentum (p) = mv
• Acceleration is rate at which velocity
changes: Δv = a Δt
• Force = rate at which momentum
changes: Δ(mv) = Fnet Δt (F=dp/dt)
• Impulse defined to be Fnet Δt
• Impulse is the transfer of momentum
mv
Impulse of wall on ball is -mv
5
Newton’s second law revisited: Force
gives change of momentum
• Momentum (p) = mv
• Acceleration is rate at which velocity
changes: Δv = a Δt
• Force = rate at which momentum
changes: Δ(mv) = Fnet Δt (F=dp/dt)
• Impulse defined to be Fnet Δt
• Impulse is the transfer of momentum
mv
m=0.1kg, v=10m/s Δt=0.1s F=?
F=D(mv)/Dt=-2mv/.1 N = -2/.1 N= -20N
Impulse of wall on ball is -mv
6
Momentum conserved in collisions because
of Newton’s third law
• Force = ma is rate at which
momentum changes
• Force on red object = negative
of force on green object
• Momentum change of first
object = negative of momentum
change on second
• Momentum (sum of momenta of
both balls) is conserved!
(m1v1 + m2v2)before = (m1v1 + m2v2)after
7
Momentum conservation allows us to
predict results of collisions
• A mass of 1 kg is moving
a)0.21 m/s
to the right at 1 m/s
b)0.33 m/s
• It hits a stationary mass
c)1 m/s
of 0.5 kg and sends it to
d)2 m/s
the right at 1.33 m/s
(m1v1 + m2v2)before= m1v1b
• After the collision, how
fast is the first mass
going?
m1v1a + m2v2a = m1v1b
(m1v1 + m2v2)before =
v1a = v1b - (m2/m1)v2a = 1m/s
(m1v1 + m2v2)after
- 0.5*1.33m/s = 0.33 m/s
8
Conservation Laws
•
•
•
Momentum: p = mv
Different kinds of energy (kinetic,
potential, heat)
Energy converted from one kind to another,
but TOTAL energy is unchanged
9
Work transfers energy like impulse
transfers momentum
• Impulse = F Δt = Δ momentum
• Work = F Δx = Δ energy
• Lift object: human chemical energy to
gravitational energy
• Falling object: gravitational potential
energy to kinetic energy
10
Work
Work = Force x Length
L
F
h = height
Constant Speed Up
W=FxL
11
The work we have to do to move things up against
gravity is independent of how we get there
GRAVITY IS A CONSERVATIVE FIELD
F hand
Con
S
t
n
a
st
p
U
d
e
e
p
h = height
mg
• Move straight up
• Move cart up ramp (assuming friction is
negligible) - same “accomplishment” = same
work
• Work = Framp x Lramp = Fvert x height
12
Push frictionless cart up 1 meter ramp at constant velocity.
Constant Speed Up
F hand
h = height
mg
Work = Framp x Lramp = Fvert x height
If want to push up ramp at constant velocity, force applied by hand must be:
a. greater than the weight (=mg) of the cart
b. less than the weight of the cart
c. the same as the weight of the cart
13
Push frictionless cart up 1 meter ramp at constant velocity.
Constant Speed Up
F hand
h = height
mg
Work = Framp x Lramp = Fvert x height
If want to push up ramp at constant velocity, force applied by hand must be:
a. greater than the weight (=mg) of the cart
b. less than the weight of the cart
c. the same as the weight of the cart
14
How much “work” (force applied x distance) did I have to do to push cart along the
ramp a distance of 10 meters?
F hand
M=100kg
Constant Speed Up
10 m
h = 1m
pick which one is closest
a. 980 Joule b. 9800 Joule d. 98 Joule
e. impossible to tell from this data
1 Joule = 1N x 1m (unit of energy)
Work = Framp x Lramp = Fvert x height
15
How much “work” (force applied x distance) did I have to do to push cart along the
ramp a distance of 10 meters?
F hand
M=100kg
Constant Speed Up
10 m
h = 1m
pick which one is closest
a. 980 Joule b. 9800 Joule d. 98 Joule
e. impossible to tell from this data
Work = Framp x Lramp = Fvert x height =
100kg*9.8m/s2*1 m = 980 N
16
How big a force did I have to exert to push the cart along the ramp a distance of 10
meters?
F hand
M=100kg
Constant Speed Up
10 m
h = 1m
pick which one is closest
a. 980 N b. 9800 N d. 98 N
e. impossible to tell from this data
Work = Framp x Lramp = Fvert x height
17
How big a force did I have to exert to push the cart along the ramp a distance of 10
meters?
F hand
M=100kg
Constant Speed Up
10 m
h = 1m
pick which one is closest
a. 980 N b. 9800 N d. 98 N
e. impossible to tell from this data
Work = Framp x Lramp = Fvert x height = 980 J
So Framp = 980J/10m = 98 N
18
If no conservation law, have to do trig (oh
my!)
Framp
f = Fg sin(theta)
theta
Fg
Part of the weight (Fg) is countered by the ramp (Framp)
The force down the ramp is proportional to the sine of the
angle of the ramp
19
Different Kinds of Energy
•
•
•
Kinetic Energy: the energy in a moving
mass; Ek=(1/2)mv2
Potential Energy: the energy stored in a
mass pushed up against a force (gravity,
mgh; spring, (1/2)kx2)
Heat: The energy stored in a mass by
virtue of its temperature (kinetic)
20
Kinetic energy: conversion of work to
motion (velocity no longer constant)
•
•
•
•
•
•
•
Suppose only force along motion is net force
Fnet = ma
vf - vi = Δv = a x Δt = (Fnet/m) Δt
(1/2)(vf + vi)(vf - vi)=(Fnet/m) (1/2)(vf + vi) Δt
(1/2)m(vf2 - vi2)=Fnet Δx
Change of “kinetic energy” = work done
Speed one gets falling down a ramp depends
on the height (loss of potential energy)
21
Energy of a spring can be calculated in
same way
x
•
•
•
•
•
•
Push from equilibrium
Work on spring = FΔx = Fx
Work = (1/2) (Finit + Ffinal) x
Finit = 0
Ffinal = kx
Work = (1/2) kx2
22
Now have three forms of energy
• Kinetic energy = (1/2)mv2
• Gravitational potential energy = mgh
• Spring energy = (1/2)kx2
Through work we can convert any one to any
other!
23
Now have three forms of energy
• Kinetic energy = (1/2)mv2
• Gravitational potential energy = mgh
• Spring energy = (1/2)kx2
Through work we can convert any one to any
other!
What about Friction?
24
With friction, where does energy go?
A
B
C
D
25
With friction, where does energy go?
• Count Rumford (Benjamin Thompson)
demonstrated the heating of water by boring
cannon for the elector of Munich
• Joule (1818 - 1889) measure increase in
temperature due to friction
• Able to equate loss of mechanical energy by
friction to heat
• Famous experiment with weights moving fins in
water (he measured the change in temperature
of the water)
26
A note about friction
• Friction force varies with lots of things …
roughness of material, little things sticking up
on surface, etc.
• But we can find an average friction force for a
particular type of surface. Many fairly smooth
surfaces near friction force of 0.3 x weight
(this is called the coefficient of friction, µ).
27
Push weight (file cabinet, stone block) across board.
Weight of “file cabinet” = 19.5 N, µ =0.3
Ffriction = 0.3 x weight = 5.8 N
Slide it 0.5 m.
Work done (Force x distance) = ?
a. 5.8 J, b. 19.5 J, C. 2.9 J., d. 11.6 J
answer: C.
0. 5 m
= 5.8 N X 0.5 m
= 2.9 J
28
Now push it (weight = 19.5 N) up a hill so it goes up 0.25 m in
moving 0.5 m. How much work will it take to push it up (µ=0.3)?
a. 2.9 J. b. 4.9 J, c. 9.8 J, d. 19.5 J, e. 7.8 J
ans. is e: 7.8 J. Total work =
work against friction (= 2.9 J)
+ work to lift it up against gravity
(= mg*change in height = 19.5 N x 0.25 m = 4.9 J
= 7.8 J
.25 m
So now, how much
m
5
0.
force is required to
push it up the board?
a. 9.75 N, b. 15.6 N, c. 19.5 N, d. 5.8 N, e. impossible to tell
ans. is b: 15.6 N.
work=force x distance = 7.8 J from above = F x 0.5 m.
so F= 7.8 J/0.5 m = 15.6 N.
29
Power: the rate of doing work
• Work / elapsed time = power
• Joule / sec = Watt
• 1 horsepower = 550 ft-lbs/sec
= 550 ft-lbs/sec x 0.3 m/ft x 4.45 lbs/N
= 734 Watts
• 200 HP car produces 147 kW, enough to
light 1470 100W light bulbs
30
Human energy.
1. What the heck is a Joule??
= force(N) x distance(m) = 0.75 foot pounds (lift 1 pound up 1ft)
lift 20 pound barbell up 7 feet = 140 foot pounds = 187 Joules.
1 food calorie = 4184 J.
power= energy/second. 1 watt = 1J/s. 100 watt lightbulb
means 100 Joules electrical energy/sec.
Human burns 2500 calories per day
means 2500/(24x 60 x 60 s) = 0.29 cal/sec =
0.29 cal/s x 4184 cal/J = 121watts.
100 watts of heat just sitting here!
31
1 food calorie = 4184 J.
How much of food goes into work?
How much force x distance can person do?
easy to measure with stationary bicycle.
elite women bicyclist can produce 300 W power,
typical tour de France rider 400 W of power, [~1/2 horsepower]
and Lance Armstrong can hit 500 W of power.
Athletic man sustain ~150 watts (nonheat!) for 10 hour day
= 150 J/s x 10 x 60 x 60 s = 5,400,000 J of work/day.
How many calories is this?
a. 2140 cal, b. 1290 cal, c. 150 cal d. 12000 cal
a. 5.4E6 J/4184J/cal =1291 cal.
eats ~ 5800 cal/day
where does the rest of the energy (5800-1291=4500 cal) go?
a. chemical, b. sweating, c. light, d. heat, e. odor
d. heat.(80%)
32
Where does the energy in the food
come from?
•
•
•
•
A sun
B
C
D
33
Where does the energy our society uses
come from?
•
•
•
•
•
•
A oil: sun
B coal: sun
C wind: sun
D hydro: sun
E geothermal: supernovae
F nuclear: supernovae
Ultimately, all energy comes from the Big Bang. No physical process
in the universe can create or destroy energy.
34
How much food did Egypt have to grow
to build the great pyramid of Cheops
Need to know:
•
•
•
•
•
•
A
B
C
D
E
F
35
Summary
•
•
•
•
Conservation Laws let us write equations
(before)=(after) without knowing details
Conservation of momentum is
generalization of Newton’s Laws
Many types of energy: Kinetic,
gravitational potential, spring potential,
heat, …
Energy can be transformed from type to
type but total energy is constant
36