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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
18
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