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Physics 1010:The Physics of Everyday Life

TODAY• Conservation Laws (Energy, Momentum)• Collisions• Work, Energy (Kinetic, Potential, Heat)

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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)

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Conservation Laws

• Momentum: p = mv• Different kinds of energy (kinetic,

potential, heat)• Energy converted from one kind to another,

but TOTAL energy is unchanged

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Newton’s second law revisited: Forcegives 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

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Newton’s second law revisited: Forcegives 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

m=0.1kg, v=10m/s Δt=0.1s F=?

F=D(mv)/Dt=-2mv/.1 N = -2/.1 N= -20N

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Momentum conserved in collisions becauseof Newton’s third law

• Force = ma is rate at whichmomentum changes

• Force on red object = negativeof force on green object

• Momentum change of firstobject = negative of momentumchange on second

• Momentum (sum of momenta ofboth balls) is conserved!

(m1v1 + m2v2)before = (m1v1 + m2v2)after

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Momentum conservation allows us topredict results of collisions

• A mass of 1 kg is movingto the right at 1 m/s

• It hits a stationary massof 0.5 kg and sends it tothe right at 1.33 m/s

• After the collision, howfast is the first massgoing?

(m1v1 + m2v2)before =(m1v1 + m2v2)after

a)0.21 m/sb)0.33 m/sc)1 m/sd)2 m/s

(m1v1 + m2v2)before= m1v1b

m1v1a + m2v2a = m1v1bv1a = v1b - (m2/m1)v2a = 1m/s- 0.5*1.33m/s = 0.33 m/s

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Conservation Laws

• Momentum: p = mv• Different kinds of energy (kinetic,

potential, heat)• Energy converted from one kind to another,

but TOTAL energy is unchanged

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Work transfers energy like impulsetransfers 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

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Work

Work = Force x Length

W = F x L

h = heightF

Constant Speed Up

L

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• Move straight up• Move cart up ramp (assuming friction is

negligible) - same “accomplishment” = samework

• Work = Framp x Lramp = Fvert x height

h = heightF hand Constant Speed Up

The work we have to do to move things up againstgravity is independent of how we get thereGRAVITY IS A CONSERVATIVE FIELD

mg

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Push frictionless cart up 1 meter ramp at constant velocity.

If want to push up ramp at constant velocity, force applied by hand must be: a. greater than the weight (=mg) of the cartb. less than the weight of the cartc. the same as the weight of the cart

h = heightF hand

Constant Speed Up

Work = Framp x Lramp = Fvert x heightmg

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Push frictionless cart up 1 meter ramp at constant velocity.

If want to push up ramp at constant velocity, force applied by hand must be: a. greater than the weight (=mg) of the cartb. less than the weight of the cartc. the same as the weight of the cart

h = heightF hand

Constant Speed Up

Work = Framp x Lramp = Fvert x heightmg

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How much “work” (force applied x distance) did I have to do to push cart along theramp a distance of 10 meters?

h = 1mF hand

Constant Speed Up

10 m

M=100kg

pick which one is closest

a. 980 Joule b. 9800 Joule d. 98 Joulee. impossible to tell from this data

1 Joule = 1N x 1m (unit of energy)Work = Framp x Lramp = Fvert x height

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How much “work” (force applied x distance) did I have to do to push cart along theramp a distance of 10 meters?

h = 1mF hand

Constant Speed Up

10 m

M=100kg

Work = Framp x Lramp = Fvert x height =100kg*9.8m/s2*1 m = 980 N

pick which one is closest

a. 980 Joule b. 9800 Joule d. 98 Joulee. impossible to tell from this data

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How big a force did I have to exert to push the cart along the ramp a distance of 10meters?

h = 1mF hand

Constant Speed Up

10 m

M=100kg

Work = Framp x Lramp = Fvert x height

pick which one is closest

a. 980 N b. 9800 N d. 98 Ne. impossible to tell from this data

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How big a force did I have to exert to push the cart along the ramp a distance of 10meters?

h = 1mF hand

Constant Speed Up

10 m

M=100kg

Work = Framp x Lramp = Fvert x height = 980 JSo Framp = 980J/10m = 98 N

pick which one is closest

a. 980 N b. 9800 N d. 98 Ne. impossible to tell from this data

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If no conservation law, have to do trig (ohmy!)

Part of the weight (Fg) is countered by the ramp (Framp)

The force down the ramp is proportional to the sine of theangle of the ramp

Fg

Framp

f = Fg sin(theta)

theta

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Different Kinds of Energy

• Kinetic Energy: the energy in a movingmass; Ek=(1/2)mv2

• Potential Energy: the energy stored in amass pushed up against a force (gravity,mgh; spring, (1/2)kx2)

• Heat: The energy stored in a mass byvirtue of its temperature (kinetic)

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Kinetic energy: conversion of work tomotion (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(vf

2 - vi2)=Fnet Δx

• Change of “kinetic energy” = work done• Speed one gets falling down a ramp depends

on the height (loss of potential energy)

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Energy of a spring can be calculated insame way

• Push from equilibrium• Work on spring = FΔx = Fx• Work = (1/2) (Finit + Ffinal) x• Finit = 0• Ffinal = kx• Work = (1/2) kx2

x

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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 anyother!

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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 anyother!

What about Friction?

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With friction, where does energy go?

ABCD

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With friction, where does energy go?

• Count Rumford (Benjamin Thompson)demonstrated the heating of water by boringcannon for the elector of Munich

• Joule (1818 - 1889) measure increase intemperature due to friction

• Able to equate loss of mechanical energy byfriction to heat

• Famous experiment with weights moving fins inwater (he measured the change in temperatureof the water)

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A note about friction

• Friction force varies with lots of things …roughness of material, little things sticking upon surface, etc.

• But we can find an average friction force for aparticular type of surface. Many fairly smoothsurfaces near friction force of 0.3 x weight(this is called the coefficient of friction, µ).

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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. = 5.8 N X 0.5 m = 2.9 J

0. 5 m

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.25 m0. 5 m

Now push it (weight = 19.5 N) up a hill so it goes up 0.25 m inmoving 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 Jans. 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

So now, how muchforce is required topush it up the board?a. 9.75 N, b. 15.6 N, c. 19.5 N, d. 5.8 N, e. impossible to tellans. 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.

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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

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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.

power= energy/second. 1 watt = 1J/s. 100 watt lightbulbmeans 100 Joules electrical energy/sec. Human burns 2500 calories per daymeans 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!

1 food calorie = 4184 J.

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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

1 food calorie = 4184 J.

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%)

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Where does the energy in the foodcome from?

• A sun• B• C• D

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Where does the energy our society usescome 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.

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How much food did Egypt have to growto build the great pyramid of Cheops

• A• B• C• D• E• F

Need to know:

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Summary

• Conservation Laws let us write equations(before)=(after) without knowing details

• Conservation of momentum isgeneralization of Newton’s Laws

• Many types of energy: Kinetic,gravitational potential, spring potential,heat, …

• Energy can be transformed from type totype but total energy is constant