9/19/2013phy 113 c fall 2013-- lecture 81 phy 113 c general physics i 11 am-12:15 pm mwf olin 101...

PHY 113 C Fall 2013-- Lecture 8 19/19/2013

PHY 113 C General Physics I11 AM-12:15 PM MWF Olin 101

Plan for Lecture 8:

Chapter 8 -- Conservation of energy

1. Potential and kinetic energy for conservative forces

2. Energy and non-conservative forces

3. Power


Comments on preparation for next Thursday’s exam


Comments on preparation for next Thursday’s exam -- continued


Comments on preparation for next Thursday’s exam – continued

What you should bring to the exam (in addition to your well-rested brain): A pencil or pen Your calculator An 8.5”x11” sheet of paper with your favorite

equations (to be turned in together with the exam)

What you should NOT use during the exam Electronic devices (cell phone, laptop, etc.) Your textbook

PHY 113 A Fall 2013 -- Lecture 1 6

Advice:

1. Keep basic concepts and equations at the top of your head.

2. Practice problem solving and math skills

3. Develop an equation sheet that you can consult.

Equation Sheet

dt

ddt

d

m

rv

va

aF

Problem solving skills

Math skills

8/27/2013


iclicker questionWhich of the following best describes your opinion about the equation sheet:

A. I have not prepared my equation sheet yet but hope to do so soon

B. I have a preliminary equation sheet but have not used it for doing homework

C. I have a preliminary equation sheet and have used it for doing homework

D. I am dreaming about preparing the equation sheet, but have not done it yet

E. In my opinion, the equation sheet is not really necessary


rFr

r

dWf

i

fi : workof Definition

Review of energy concepts:

2

2

1 :energy kinetic of Definition mvK

22

2

1

2

1

:oremenergy the kinetic-Work

if

f

i

totaltotal

fi mvmvdW rF


Some questions from webassign Assignment #7

In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth.

(a) How much work was done on the object by Arfeuille in this lift, assuming the object was lifted at constant velocity?

T

mg

T

mg

yf

yi

if

iffifi

yymg

yyTWdW

mgTmgTf

i

0

rFr

r



In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth.

How much work was done on the object by gravity?

T

mg

T

mg

yf

yi

iffifi yymgWdWf

i

rFr

r



What is the work done as the particle moves from x=0 to x=3m?

N75.6m3N5.42

13

0

dxxFdW xfi

f

i

rFr

r


Some questions from webassign Assignment #7 -- continued

What is the work done as the particle moves from x=8 to x=10m?

N5.2m2N32

110

8

dxxFdW xfi

f

i

rFr

r



A 4.34-kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x = 0. What is its speed at x = 5.00 m?

02

1

2

1

2

1

25

0

22

fxtotal

fi

if

f

i

totaltotal

fi

mvdxxFW

mvmvdW rF


Work and potential energy

rFr

r

dWf

i

fi : workof Definition

rFrr

r

r dWUref

ref

:energy potential of Definition

Note: It is assumed that F is conservative


rFrr

r

r dWUref

ref :energy potential of Definition

Work and potential energy -- continued

mg

mg

y

yref

Example – gravity near the surface of the Earth:

ref

y

y

ref

yymg

dymgyU

dWU

ref

ref

' )(

rFrr

r

r


Work and potential energy for gravity (near Earth’s surface)

mg

mg

yf

yi

ref

y

y

ref

yymg

dymgyU

dWU

ref

ref

' )(

rFrr

r

r

yref

iffi

iffifi

UUddW

yymgWdW

i

ref

f

ref

f

i

rrrFrF

rF

r

r

r

r

r

r

:elyAlternativ


Work and potential energy continued

iffi UUddWi

ref

f

ref

rrrFrFr

r

r

r

rFrr

r

r dWUref

ref :energy Potential

iclicker questionWhy is there a strange “-” sign in the definition of potential energy?

A. Physicists like to be annoyingB. No reason at allC. There is a somewhat good reason


22

2

1

2

1


if

f

i

totaltotal

fi mvmvdW rF

Work and potential energy continued

iffi UUddWi

ref

f

ref

rrrFrFr

r

r

r

For the case that the total force acting on the system is conservative, we can use the definition of potential energy with the work-kinetic energy theorem

(contant) :gRearrangin

EUKUK

KKUUW

iiff

ififtotal

fi

rr


22

2

1

2

1


if

f

i

totaltotal

fi mvmvdW rF

Summary of work, potential energy, kinetic energy relationships

edissipativ

fiiiff

ifedissipativ

fiiftotal

fi

WUKUK

KKWUUW

:gRearrangin

rr

edissipativfiif

edissipativfi

veconservatifi

totalfi

WUU

WWW


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

hh=0.5m

i

f

2

2

1 ;0 ;0 :

; ;0 :

fff

ii

mvEUvf

mghEmghUvi

r

r

m/s 3.13

5.08.92

2

2

1 2

ghv

mghmv

f

f


Energy diagram

E

yiyf

K

U

U,

K,

E (

J)

m


2

212

21

2212

21

)( and )(

:force spring of Example

iiff

if

x

x

f

i

fi

kxUkxU

kxkxdxxkdWf

i

rr

rF

k


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


dx

dUxF

dxxFWxU

dWU

x

x

xref

ref

ref

ref

:tiveAntideriva

'')( :dimension oneIn

' :energy Potential rFrr

r

r

Comment on relationship between potential energy and (conservative) force:


Example: Mass sliding on frictionless looping track

i

iclicker exercise:In order for the ball completes the loop at A, what must the value of h?

A. h=RB. h=2RC. h>2RD. Not enough

information.


i

Example: Mass sliding on frictionless looping track

RmgmvE

mghmvE

A

i

22

12

1

2

2

mgRmv

R

vmmgn

A

A

2

1

2

1

:Aat on track stayingfor Condition

2

2

0

0

Rh

mgRmgRmgRRmgmvmghE A

2

52

52

2

12

2

1 2


Another example; first without friction

Mass m1 (=0.2kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)?

iclicker exercise:What is the relationship of the final velocity of m1 and m2?

A. They are equalB. m2 is faster than m1.C. m1 is faster than m2.


Another example; first without friction

Mass m1 (=0.2kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)?

T

T

m2 g

21

2

22122

22

212

2

2

12

1

mm

xgmv

vmmxgmyygm

gymvmmgym

UKUK

f

ffi

ffi

ffii

xgmm

mmxTW

gmm

mmT

amgmT

amT

21

21

21

21

22

1


Another example; now with friction

Mass m1 (=0.2kg) slides horizontally on a table with kinetic friction and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)?

T

T

m2 g

f


21

12

122

21

1222

21

2

2

12

1

mm

xgmgmv

xgmxgmvmm

xgmgymgymvmm

WUKUK

kf

kf

kiff

edissipativfiiiff


iclicker exercise:Assume a mass m starts at rest at A and moves on the frictionless surface as shown. At what position is the speed the largest?

A. AB. BC. CD. none of these.


Power

Watt(s)

(Joules) : Units

: thatNote

: workof change of rate timeas Defined

P

dt

d

dt

dW

ddWdt

dW P

vFr

F

rF


Watts106/3102

/3 ,102For

:motorby exertedPower

44

4

smNP

smvNT

Tvdt

dW P vF

9/19/2013phy 113 c fall 2013-- lecture 81 phy 113 c general physics i 11 am-12:15 pm mwf olin 101...

Documents

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