Work%20

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Work Energy
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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 (Today)
• Potential Energy Stored (Wednesday)
• Heat later
• Mass (Emc2) 1161
• Units Joules kg m2 / s2

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Work
The definition of work, when the force is
parallel to the displacement
(7-1)
SI work unit newton-meter (Nm) joule, J
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Typical Work
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Positive Negative Work
Work done may be positive, zero, or negative,
depending on the angle between the force and the
displacement
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Force at an Angle Work
If the force is at an angle to the displacement
(7-3)
Only the horizontal component of the force
does any work (horizontal displacement).
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Work by Constant Force at Angle

• 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?

W T cos q Dx (50 N) cos (30) (5 m)
217 Joules
Ty
Tx
50 N
30
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Where did the energy go?

• 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 30o.
• How much work did gravity do?
• How much work did friction do?

W Fcos q Dx 30 cos(90) x 5 0
X-Direction SF ma T cos(30) f 0 f
T cos(30) 43.3 N
W f cos(180) Dx (43.3 N) cos(180) x 5
-217 Joules
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Perpendicular Force and Work
A car is traveling on a curved highway. The
force due to friction fs points toward the center
of the circular path. How much work does the
frictional force do on the car? Zero!
General Result A force that is everywhere
perpendicular to the motion does no work.
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Work Done by Gravity
In lifting an object of weight mg by a height h,
the person doing the lifting does an amount of
work W mgh. If the object is subsequently
allowed to fall a distance h, gravity does work W
mgh on the object.
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ACTS Ball Toss

• You toss a ball in the air.
• What is the work done by gravity as the ball goes
  up?
• A) Positive B) Negative C) Zero
• What is the work done by gravity as the ball goes
  down?
• A) Positive B) Negative C) Zero

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Work By Gravity
When positive work is done on an object, its
speed increases when negative work is done, its
speed decreases.
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Kinetic Energy Motion

• Apply constant net force along x-direction to an
  object m.
• W Fx Dx
• m a Dx
• ½ m (v2 v02)
• Work changes ½ m v2
• Voila new concept
• Define Kinetic Energy K ½ m v2
• W D K

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Work-Energy Theorem
Work-Energy Theorem The total work done on an
object is equal to its change in kinetic energy.
(7-7)
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Falling Ball Example

• A ball falls a distance 5 meters, what is
  final speed?

Only force/work done by gravity SW DKE Wg ½
m(vf2 vi2) Fg h ½m vf2 mgh ½m vf2 Vf
sqrt( 2 g h ) 10 m/s
mg
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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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Loading with a Crane
A 3,000 kg truck is to be loaded onto a ship by a
crane that exerts an upward force of 31 kN on the
truck. This force, which is large enough to
overcome the gravitational force and keep the
truck moving upward, is applied over a distance
of 2.0 m. (a) Find the work done on the truck by
the crane. (b) Find the work done on the truck
by gravity. (c) Find the net work done on the
truck.
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Preflight 1
V

• You are towing a car up a hill with constant
  velocity. The work done on the car by the normal
  force is
• 1. positive 2. negative 3. zero

T
38 13 50
work done by normal force is 0 because q is 90
and cos 90 0
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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. positive 2. negative 3. zero

0 63 37
The work done on the car by the gravitational
force is negative because it hinders motion up
the hill
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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. positive 2. negative 3. zero

63 25 12
work done by tension is positive because the
angle of the force is between 0 and 90
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KE ACTS
Car 1 has twice the mass of Car 2, but they both
have the same kinetic energy. If the speed of
Car 1 is v, approximately what is the speed of
Car 2?
b) 0.707 v
a) 0.50 v
e) 2.00 v
d) 1.414 v
c) v
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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. positive 2. negative 3. zero

63 12 25
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.
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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 SFma 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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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