CPI: Lecture 9 Work and Kinetic Energy

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CPI Lecture 9Work and Kinetic Energy
Exam II

• Todays lecture will be on Textbook Sections 6.1
  - 6.4

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Most Difficult Concepts

• all...try starting from the beginning...ease
  into it...this is gonna be a bumpy ride
• The concept of comprehending the fact that I
  will have a Physics exam in a week.
• Understanding how can a car move up hill and no
  work is being done
• I do not quite understand what is making it
  positive, negative, or zero work. The book didn't
  explain it very well or I just didn't understand
  what the book was trying to tell me. Also, are
  the quizes in discussion always trying to throw
  you off?

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Energy is Conserved

• Energy is Conserved meaning it can not be
  created nor destroyed
• Can change form
• Can be transferred
• Total Energy does not change with time.
• This is a BIG deal!

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Energy

• Forms
• Kinetic Energy Motion
• Potential Energy Stored
• Heat later
• Mass (Emc2)
• Units Joules kg m2 / s2

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Work Energy Transfer due to Force

• Force to lift trunk at constant speed
• Case a Ta mg 0 T mg
• Case 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!

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Work by Constant Force

• Only component of force parallel to direction of
  motion does work!
• W F Dr cos q

WF gt 0 0lt q lt 90 cos(q) gt 0
WF 0 q 90 cos(q) 0
WF lt 0 90lt q lt 270 cos(q) lt 0
WF gt 0 0lt q lt 90 cos(q) gt 0
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Work by Constant Force

• 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
  have you (Tension) done?

W F Dr cos q (50 N) (5 m) cos (30)
217 Joules
50 N
30
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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?

W F Dr cos q 50 x 5 cos(90) 0
X-Direction F ma T cos(30) f 0 f
T cos(30)
W F Dr cos q 50 cos(30) x 5 cos(180)
-217 Joules
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Preflight 1 2
V

• 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

T
Since the direction of the force is positive the
value of work will be positive.
it's negative because it's trying to slow down
the car.
The normal force does no work because it acts in
a direction perpendicular to the displacement of
the car.
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Preflight 3 4

• 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 gravitational force has a component parallel
to the velocity, so gravity does positive work.
The gravitational force is pulling the car
downward, which is in the opposite direction of
movement. Therefore, work is negative.
Since the velocity is constant, the normal and
gravitational force cancel out and the work is
then zero.
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Preflight 5 6

• 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 force of tension is in the same direction as
the motion of the car, making the work positive.
Its negative because while you exert a force on
the rope the tension from the rope is exerted
back on you and then exerted in the opposite
direction on the car.
Zero because if you use the equation Fma,
acceleration is zero, and to figure the work done
by the tow rope, you use the equation WFchange
in rcos(angle), so the force is zero, therefore
work is zero.
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Kinetic Energy Motion

• Apply constant force along x-direction to a point
  particle m.
• W Fx Dx
• m ax Dx
• ½ m (v2 v02)
• Work changes ½ m v2
• Define Kinetic Energy K ½ m v2
• W D K For Point Particles

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Preflight 7 8

• 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 car is being towed up the hill, not down
The net forces are pointing away from the
direction of displacement.
WKEf-KEi(0.5mvf2) - (0.5mvi2). Because the
final and initial velocities are the same, there
is no change in kinetic energy, and therefore no
total work is done.
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Example 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?

Y direction Fma N-mg 0 N mg
Work WN 0 Wmg 0 Wf f Dx
cos(180) -mmg Dx
W D K -mmg Dx ½ m (vf2 v02) -mg
Dx ½ (0 v02) mg Dx ½ v02
Dx ½ v02 / mg 3.1 meters
5 m/s
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Work by Variable Force

• W Fx Dx
• Work is area under F vs x plot
• Spring F k x
• Area ½ k x2 Wspring

Force
Work
Distance
Work
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Summary

• Energy is Conserved
• Work transfer of energy using force
• Can be positive, negative or zero
• W F d cos(q)
• Kinetic Energy (Motion)
• K ½ m v2
• Work Change in Kinetic Energy
• S W DK

Chapter 6, problems 1, 3, 5, 7, 15
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Suggested Problems

• Chapter 6, problems 1, 3, 5, 7, 15