Physics 101: Lecture 9, Pg 1

Physics 101: Physics 101: Lecture 9Lecture 9Work and Kinetic EnergyWork and Kinetic Energy

Today’s lecture will be on Textbook Sections 6.1 - 6.4

Hour Exam 1, Monday 7:00 pm!Conflict Monday 5:15 signup in grade bookReview Session: Sunday 8 pm (Lincoln Hall Theatre)

Exam II

Physics 101: Lecture 9, Pg 2

Energy is ConservedEnergy is ConservedEnergy is “Conserved” meaning it

can not be created nor destroyed Can change formCan be transferred

Total Energy does not change with time.

This is a BIG deal!10

Physics 101: Lecture 9, Pg 3

EnergyEnergyForms

Kinetic Energy Motion (Today)Potential Energy Stored (Monday)Heat laterMass (E=mc2) p102

Units Joules = kg m2 / s2

12

Physics 101: Lecture 9, Pg 4

Work: Energy Transfer due to ForceWork: Energy Transfer due to ForceForce to lift trunk at constant speed

Case a Ta – mg = 0 T = mgCase b 2Tb - mg =0 or T = ½ mg

But in case b, trunk only moves ½ distance you pull rope.

F * distance is same in both!Ta

mg

Tb

mg

Tb

15

W = F dcos()

Physics 101: Lecture 9, Pg 5

Work by Constant ForceWork by Constant ForceOnly component of force parallel to

direction of motion does work!W = F r cos

F

r

F

WF > 0: 90< < 180 : cos() > 0

r

FWF = 0: =90 : cos() =0

r

FWF < 0: 90< < 270 : cos() < 0

rF WF > 0: 0< < 90 : cos() > 0

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A) W>0 B) W=0 C) W<0

1)

2)

3)

4)

Note Change in r!

r

F

r F

Physics 101: Lecture 9, Pg 7

Work by Constant ForceWork by Constant ForceExample: You pull a 30 N chest 5

meters across the floor at a constant speed by applying a force of 50 N at an angle of 30 degrees. How much work is done by the 50 N force?

30

50 N

W = F x cos

m) cos (30)

= 217 Joules

T

mg

N

f

21

Physics 101: Lecture 9, Pg 8

Where did the energy go?Where did the energy go?Example: You pull a 30 N chest 5

meters across the floor at a constant speed, by applying a force of 50 N at an angle of 30 degrees.

How much work did gravity do?

How much work did friction do?

mg90r

W = F r cos 30 x 5 cos(90)

T

mg

N

fX-Direction: F = ma T cos(30) – f = 0 f = T cos(30)

f r

180W = F r cos 50 cos(30) x 5 cos(180)Joules

25

Physics 101: Lecture 9, Pg 9

Preflight 1 Preflight 1 You are towing a car up a hill with constant velocity. The work done on the car by the normal force is:1. positive2. negative3. zero

63%

5%

32%

0% 20% 40% 60% 80%

T

W

FN V

“The work done on the car by the normal force is 0 because it is perpendicular”

correct

28

Physics 101: Lecture 9, Pg 10

Preflight 2 Preflight 2 You are towing a car up a hill with constant velocity. The work done on the car by the gravitational force is:1. positive2. negative3. zero

The work done on the car by the gravitational force is negative because it hinders motion up the hill

25%

68%

7%

0% 20% 40% 60% 80%

W

T

FN V

correct

30

Physics 101: Lecture 9, Pg 11

Preflight 3 Preflight 3 You are towing a car up a hill with constant velocity. The work done on the car by the tension force is:1. positive2. negative3. zero

the work done on the car by the tow rope is positive because the car is moving up

6%

6%

89%

0% 20% 40% 60% 80% 100%

W

T

FN V

correct

32

Physics 101: Lecture 9, Pg 12

Kinetic Energy: MotionKinetic Energy: Motion Apply constant force along x-direction to a

point particle m.W = Fx x = m ax x = ½ m (vf

2 – v02)

Work changes ½ m v2

Define Kinetic Energy K = ½ m v2

W = K For Point Particles

)(21 :recall 2

02

xxx vvxa

35

Physics 101: Lecture 9, Pg 13

Preflight 4 Preflight 4 You are towing a car up a hill with constant velocity. The total work done on the car by all forces is:1. positive2. negative3. zero

The total work done is positive because the car is moving up the hill. (Not quite!)

Total work done on the car is zero because the forces cancel each other out.

26%

4%

70%

0% 20% 40% 60% 80%

W

T

FN V

correct

37

Physics 101: Lecture 9, Pg 14

Example: Block w/ frictionExample: Block w/ friction A block is sliding on a surface with an initial speed of 5

m/s. If the coefficent of kinetic friction between the block and table is 0.4, how far does the block travel before stopping?

5 m/s

mg

Nf x

y

Y direction: F=ma N-mg = 0 N = mg

Work WN = 0 Wmg = 0 Wf = f x cos(180) = -mg x

W = K -mg x = ½ m (vf

2 – v02)

-g x = ½ (0 – v02)

g x = ½ v02

x = ½ v02 / g

= 3.1 meters

44

Physics 101: Lecture 9, Pg 15

Falling Ball ExampleFalling Ball ExampleBall falls a distance 5 meters, What

is final speed?

Only force/work done by gravity

W = KEWg = ½ m(vf

2 – vi2)

Fg h cos(0) = ½m vf2

mgh = ½m vf2

Vf = sqrt( 2 g h ) = 10 m/s

mg

47

Physics 101: Lecture 9, Pg 16

Work by Variable ForceWork by Variable ForceW = Fx x

Work is area under F vs x plot

Spring F = k x» Area = ½ k x2 =Wspring

Force

Distance

Work

Force

Distance

F=kx

Work

49

Physics 101: Lecture 9, Pg 17

SummarySummaryEnergy is ConservedWork = transfer of energy using

force Can be positive, negative or zeroW = F d cos()

Kinetic Energy (Motion)K = ½ m v2

Work = Change in Kinetic EnergyW = K

50