9/26/2012PHY 113 A Fall 2012 -- Lecture 121 PHY 113 A General Physics I 9-9:50 AM MWF Olin 101 Plan for Lecture 12: Chapter 7 -- The notion of work 1.Kinetic

PHY 113 A Fall 2012 -- Lecture 12 19/26/2012

PHY 113 A General Physics I9-9:50 AM MWF Olin 101

Plan for Lecture 12:

Chapter 7 -- The notion of work

1. Kinetic energy and the Work-Kinetic energy theorem

2. Potential energy and work; conservative forces






Note: Because of the special lecture, the tutorial this evening will be moved to Olin 104 after 6:30 PM.


Back to work:

F

dr

ri rj

rFr

rdW

f

i

fi


A man must lift a refrigerator of weight mg to a height h to get it to the truck.

iclicker exercise:For which method does the man do more work:

A. Vertically lifting the refrigerator at constant speed to height h?

B. Moving the refrigerator up the ramp of length L at constant speed with h=L sin .q


FP

q

mg

n

fk

xi xf

Assume FP sin q <<mg

Work of gravity? 0

Work of FP? FP cos q (xf-xi)

Work of fk?-mkn (xf-xi)=-mk(mg- FP sin ) q (xf-xi)

Multiple forces on block moving from xi to xf


iclicker exercise:Which of the following statements about friction forces are true.

A. Friction forces always do positive work.B. Friction forces always do negative work.C. Friction forces can do either positive or

negative work.


Why is work a useful concept?

Consider Newton’s second law:

Ftotal = m a Ftotal · dr= m a · dr

dtdtd

mdtdtd

dtd

mddtd

mdmdf

i

f

i

f

i

f

i

f

i

total vvrv

rv

rarFr

r

r

r

r

r

r

r

r

r

Wtotal = ½ m vf2 - ½ m vi

2

Kinetic energy (joules)


Introduction of the notion of Kinetic energy

Some more details:

Consider Newton’s second law:

Ftotal = m a Ftotal · dr= m a · dr

dtdtd

mdtdtd

dtd

mddtd

mdmdf

i

f

i

f

i

f

i

f

i

t

t

t

ttotal v

vrvr

vrarF

r

r

r

r

r

r

Wtotal = ½ m vf2 - ½ m vi

2

Kinetic energy (joules)

22

21

21

21

if

f

i

t

tmvmvmddmdt

dtd

mf

i

f

i

vvvvv

v v

v


Kinetic energy: K = ½ m v2

units: (kg) (m/s)2 = (kg m/s2) m

N m = joules

Work – kinetic energy relation:

Wtotal = Kf – Ki


Kinetic Energy-Work theorem

22

2

1

2

1if

f

i

totalfi mvmvdW rF

Example: A ball of mass 10 kg, initially at rest falls a height of 5m. What is its final velocity?

i

f

h

??fv

0iv

22

2

1

2

1iffi mvmvmghW

0

smmghv f /899.9)5)(8.9)(2(2


ExampleA block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity?

hh=0.5m

22

2

1

2

1iffi mvmvmghW

0

smmghv f /13.3)5.0)(8.9)(2(2


Example A mass m initially at rest and attached to a spring compressed a distance x=-|xi|, slides on a frictionless surface. What is the velocity of the mass when x=0 ?

k

smv

mxmNkkgm

xm

kv

mvmvkxW

f

i

if

ififi

/63.02.05.0

5

2.0 /5 5.0For

2

1

2

1

2

1 222

0


Special case of “conservative” forces conservative non-dissipative

if

f

i

fi UUdW rrrF

F

write topossible isit , forces edissipativ-nonFor

iiff

ifif

f

i

fi

mgyUmgyU

mgymgyyymgdW

)( and )(

:Earth of surfacenear gravity of Example

rr

rF


2

212

21

2212

21

)( and )(

:force spring of Example

iiff

if

x

x

f

i

fi

kxUkxU

kxkxdxxkdWf

i

rr

rF

k


iclicker exercise:Why would you want to write the work as the difference between two “potential” energies?

A. Normal people wouldn’t.B. It shows a lack of imagination.C. It shows that the work depends only on the

initial and final displacements, not on the details of the path.

dx

dUF

dU

x

ref

that Note

:functionenergy potential Define

rFrr

r


(constant) 2

1

2

1

:Or2

1

2

1

22

22

EUmvUmv

mvmvUUW

iiff

ififfi

rr

rr

Work-Kinetic Energy Theorem for conservative forces:


Energy diagrams 22

2

1

2

1kxmvE

2max2

1221

2max2

1

max

,0(0)

:0 when :Note

,0

: when :Note

kxmvU

x

kxEv

xx


Example: Model potential energy function U(x) representing the attraction of two atoms

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9/26/2012PHY 113 A Fall 2012 -- Lecture 121 PHY 113 A General Physics I 9-9:50 AM MWF Olin 101 Plan for Lecture 12: Chapter 7 -- The notion of work 1.Kinetic