Download Hour Exam #1 Kinetic energy Work-Energy relation Energy content

Hour Exam #1
Kinetic energy
• The kinetic energy of an object is
•
•
•
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•
Hour Exam I, Wed. Feb. 14, in-class (50 minutes)
Material Covered: Chap 1, 3-6
One page of notes (8.5” x 11”) allowed
20 multiple choice questions
Scantron sheets will be used bring #2 HB pencils and calculator
• In-class review, Monday Feb. 12
1 2
mv
2
• Positive work done on isolated object
– object speeds up, kinetic energy increases
• Negative work
! done on isolated object
– object slows down, kinetic energy decreases
On-line review questions, previous exams, at course web site
uw.physics.wisc.edu/~rzchowski/phy107
Fri, Feb. 9
Phy107, Spring 2007 Lecture 9
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Fri, Feb. 9
Work-Energy relation
1 gallon gasoline has energy content of 125,000 BTU
1 BTU ~ 1,000 J (actually 1,055.056 J)
Suppose the energy in gasoline was converted completely
into kinetic energy of a 1000 kg car. How fast would the
car be going after burning 1 gallon of gas?
A. 5 m/s
B. 10 m/s
1
125,000,000 J = (1000 kg)v 2
C. 50 m/s
2
D. 100 m/s
v 2 = 250,000 m 2 /s2
E. 500 m/s
v = 500 m /s = 1,118 miles /hour!
• As the result of a net work W net, the velocity
increases to vfinal,
1 2
!
and the Kinetic Energy increases to 2 mv final
1
1 2
W net = mv 2final " mv initial
2
!2
The change in kinetic energy of an isolated
object is equal to the net work done on it.
!
Phy107, Spring 2007 Lecture 9
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Energy content
• Suppose object initially moving at vinitial
2
It has kinetic energy 1 mv initial
2
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!
Friction and resistance
Storing energy
1N
Move ball up at constant speed
-> I exert force exactly canceling gravity
• Means some of the energy went elsewhere
– Air resistance
– Friction of tires on road
– Heat losses in engine
I exert force mg on ball.
Over a distance h, I have done mgh of work
• Total energy is always conserved
1N
Energy is stored
– Some of it just left gas-car system
h
Lifting
force
mg
Can be released at any time
Called ‘potential energy’
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Fri, Feb. 9
Phy107, Spring 2007 Lecture 9
Gravitational
force
-mg
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1
Potential energy
Releasing potential energy
• Let go of the ball
• The potential energy of a system is the work
required to get the system into that configuration.
– i.e. turn off the upward force I apply
• Gravity force accelerates ball downward
• Examples
– For a pendulum, it is the work required to move the bob to
the top of its swing.
– For a falling apple, it is the work required to lift the apple.
– For a spring, it is the work required to compress the spring
• Gravity does work on the ball
– Force = mg directed downward
– Work done by gravity
= Force x Distance
= mg x h = mgh
1
mgh = mv 2final
2
Work turned into kinetic energy
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!
Gravity and work
Question
A ball is dropped from 5 meters.
How fast is it going when it hits the ground?
• Work done to move object vertically up work done is the same for both paths
• The work done is ‘independent of path’
• Change in gravitational energy,
A. 1 m/s
B. 2 m/s
Change in energy = mgh
C. 5 m/s
D. 10 m/s
true for any path :
h is the height difference, yfinal - yinitial
• A falling object converts
gravitational potential energy
to kinetic energy
2
1
mgh = mv 2final v final = 2gh " v final = 2gh
2
= 2 #10m /s2 # 5m
= 100m 2 /s2 = 10m /s
!
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!
Question
Potential E independent of path
• Gravitational force pointed directly downward
– only the vertical distance determines the potential energy.
If balls are released from the same height on these
two different tracks, which will have greater speed
at the bottom?
A. Both same
B. Track A
C. Track B
• We say it is ‘independent of the path’
(also called ‘conservative’)
• True for most ‘non-contact’ (field) forces.
– Gravity
– Electromagnetism
– Nuclear forces
Fri, Feb. 9
Phy107, Spring 2007 Lecture 9
B
A
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2
Energy conservation
Testing conservation of energy
• At top:
• Total energy ‘E’ is sum of
– Kinetic energy =0
1) K = kinetic energy (visible)
2) U = potential (invisible) energy
– Potential energy = mgh
• At bottom:
– Kinetic energy = 1/2 m v2
– Potential energy = 0
• E = K + U = constant
• On flat section, use
timer and distance
traveled to determine
speed.
• Many situations become much clearer from
an energy perspective.
Fri, Feb. 9
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Fri, Feb. 9
h
Phy107, Spring 2007 Lecture 9
A pendulum
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Work
At top of swing, velocity of ball is zero,
so it’s kinetic energy is zero.
I do mgh of work on the bowling ball.
Gravity did -mgh of work on the ball.
Net work = 0.
No change in kinetic energy.
At the bottom of the swing, it’s velocity
is very large, so it’s kinetic energy is
large.
How much work was done on the Earth?
None - the Earth did not move.
Work = Force x Distance
Final position
Where did this energy come from?
θ
θ
h
h
Initial position
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Now release the ball
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Questions about the pendulum
• Energy stored in the system as
potential energy.
• Releasing the ball lets it
accelerate and turn the potential
energy into kinetic energy.
top of swing
h
h
bottom of swing
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3
Question
Question
If the pendulum swing has 1.0 m vertical height, what
is the kinetic energy of the 1 kg pendulum bob at
the top of its swing?
A. 1 J
B. 10 J
C. 0.1 J
D. 1.4 J
The velocity is zero, so the
E. 0 J
If the pendulum swing has 1.0 m vertical height, what
is the kinetic energy of the 1 kg pendulum bob at
the bottom of its swing?
A. 1 J
B. 0.1 J
C. 1.4 J
D. 10 J
Conservation of energy. Kinetic =
E. 0 J
kinetic energy is zero.
Fri, Feb. 9
Phy107, Spring 2007 Lecture 9
potential, potential = mgh =
(1kg)x(10m/s2)x(1m)=10 J
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Fri, Feb. 9
Phy107, Spring 2007 Lecture 9
Conservation of energy
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What speed
You are jumping a 600 kg motorcycle between ramps.
The ramps are 10 meters high.
In order to jump successfully, the bike must leave the
ramp with a speed of 10 m/s. (Kinetic En.=30,000 J)
What kinetic energy must the motorcycle have entering
the jump?
What speed must the 600 kg motorcycle have at the
ramp entrance (needs 90,000 J)?
A.
B.
C.
D.
A. 30,000 J
B. 60,000 J
C. 90,000 J
10 m/s
17.3 m/s
13.2 m/s
5.0 m/s
= 39 mi/hr
(1/2)mv2 = 90,000 J
(300 kg)x(v)2 = 90,000 J
v = sqrt(300) m/s = 17.32 m/s
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Power
P=
Work Joules(J)
,
" Watts (W)
time second(s)
You run up the first flight of stairs, then walk up the
second flight. How do the work and power compare
on the two flights?
A.
B.
C.
D.
It is measured in Watts.
(also Horsepower, 1 horsepower = 750 Watts)
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Question
Power is the rate at which work is done
!
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Work
Work
Work
Work
Fri, Feb. 9
same, power same
different, power same
different,
` power different
same, power different
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4
Question
Question
You press a 500 N weight up to arms length (0.8m) in 2
seconds. Your power output while lifting was
You weigh 500 N and run up a stairs with a 4 m vertical
height. You do this in 5 seconds. Your power output is
A.
B.
C.
D.
A.
B.
C.
D.
400
400
100
200
Fri, Feb. 9
J
W
W
W
Power = work / time
= Force x Distance / time
= (500N)x(0.8m)/2 sec
= 400 J / 2 sec = 200 Watts
Phy107, Spring 2007 Lecture 9
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400 W
200 W
100 W
50 W
Weight = 500 N = mg
Energy change = (mg)h = 2,000 J
Power = energy / time = 400 W
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