Work, Energy, and Power

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Work, Energy, and Power

• Samar Hathout
• KDTH 101

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Work
Work is the transfer of energy through motion.
In order for work to take place, a force must be
exerted through a distance. The amount of work
done depends on two things the amount of force
exerted and the distance over which the force is
applied. There are two factors to keep in mind
when deciding when work is being done something
has to move and the motion must be in the
direction of the applied force. Work can be
calculated by using the following formula
Workforce x distance
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Work
Work is done on the books when they are being
lifted, but no work is done on them when they are
being held or carried horizontally.
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Work can be positive or negative

• Man does positive work lifting box
• Man does negative work lowering box
• Gravity does positive work when box lowers
• Gravity does negative work when box is raised

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Work done by a constant Force

• W F s F s cos ? Fs s
• F magnitude of force
• s s magnitude of displacement
• Fs magnitude of force in
• direction of displacement
• Fs F cos ?
• angle between displacement and force
• vectors
• Kinetic energy Ekin 1/2 m v2
• Work-Kinetic Energy Theorem

F
s
?Ekin Wnet
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Work Done by Gravity

• Example 1 Drop ball

Wg (mg)(S) S h0-hf Wg mg(h0-hf)
mg(h0-hf) Epot,initial Epot,final
S
S
mg
mg
y
y
x
x
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Work Done by Gravity

• Example 2 Toss ball up

Wg (mg)(S) S h0-hf Wg -mg(h0-hf)
Epot,initial Epot,final
S
mg
y
x
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Work Done by Gravity

• Example 3 Slide block down incline

h0
Wg (mg)(S)cos? S h/cos? Wg
mg(h/cos?)cos? Wg mgh with h h0-hf
?
h
S
mg
hf

• Work done by gravity is independent of path
• taken between h0 and hf
• The gravitational force is a conservative
  force.

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Work done by a Variable Force

• The magnitude of the force now depends on the
• displacement Fs(s)
• Then the work done by this force is equal to the
• area under the graph of Fs versus s, which can be
  
• approximated as follows
• W S DWi S Fs(si) Ds
  (Fs(s1)Fs(s2)) Ds

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Concept Question

• Imagine that you are comparing three different
  ways of having a ball move down through the same
  height. In which case does the ball reach the
  bottom with the highest speed?
• 1. Dropping2. Slide on ramp (no friction)3.
  Swinging down4. All the same

In all three experiments, the balls fall from the
same height and therefore the same amount of
their gravitational potential energy is converted
to kinetic energy. If their kinetic energies are
all the same, and their masses are the same, the
balls must all have the same speed at the end.
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Types of Energy
Kinetic Energy
Potential Energy
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Forms of Energy
Chemical
Sound
Radiant
Electrical
Mechanical
Magnetic
Thermal
Nuclear
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Mechanical Energy
Mechanical energy is the movement of machine
parts. Mechanical energy is also the total
amount of kinetic and potential energy in a
system. Wind-up toys, grandfather clocks, and
pogo sticks are examples of mechanical energy.
Wind power uses mechanical energy to help create
electricity.
Potential energy Kinetic energy Mechanical
energy
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Mechanical Energy
Potential energy Kinetic energy Mechanical
energy
Example of energy changes in a swing or pendulum.
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Conservation of Mechanical Energy

• Total mechanical energy of an object remains
  constant
• provided the net work done by
  non-conservative forces
• is zero
• Etot Ekin Epot constant
• or
• Ekin,fEpot,f Ekin,0Epot,0
• Otherwise, in the presence of net work done by
• non-conservative forces (e.g. friction)
• Wnc Ekin,f Ekin,0 Epot,f-Epot,i

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Example Problem

• Suppose the initial kinetic and potential
  energies of a system are 75J and 250J
  respectively, and that the final kinetic and
  potential energies of the same system are 300J
  and -25J respectively. How much work was done on
  the system by non-conservative forces?
• 1. 0J 2. 50J 3. -50J 4. 225J 5.
  -225J

Work done by non-conservative forces equals the
difference between final and initial kinetic
energies plus the difference between the final
and initial gravitational potential energies. W
(300-75) ((-25) - 250) 225 - 275 -50J.
Samar Hathout
Samar Hathout
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Kinetic Energy
Same units as work
Remember the Eq. of motion
Multiply both sides by m,
Samar Hathout
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Example
Samar Hathout
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Potential Energy

• Potential energy exists whenever an object which
  has mass has a position within a force field
  (gravitational, magnetic, electrical).
• We will focus primarily on gravitational
  potential energy (energy an object has because of
  its height above the Earth)

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Potential Energy
If force depends on distance,
For gravity (near Earths surface)
Samar Hathout
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Conservation of Energy

• Conservative forces
• Gravity, electrical, QCD
• Non-conservative forces
• Friction, air resistance
• Non-conservative forces still conserve
  energy!Energy just transfers to thermal energy

Samar Hathout
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Example
A diver of mass m drops from a board 10.0 m above
the water surface, as in the Figure. Find his
speed 5.00 m above the water surface. Neglect air
resistance.
9.9 m/s
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Example
A skier slides down the frictionless slope as
shown. What is the skiers speed at the bottom?
start
H40 m
finish
L250 m
28.0 m/s
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Example
Three identical balls are thrown from the top of
a building with the same initial speed.
Initially, Ball 1 moves horizontally. Ball 2
moves upward. Ball 3 moves downward.Neglecting
air resistance, which ball has the fastest speed
when it hits the ground?
A) Ball 1 B) Ball 2 C) Ball 3 D) All have the
same speed.
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Springs (Hookes Law)
Proportional to displacement from equilibrium
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Potential Energy of Spring
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Example
A 0.50-kg block rests on a horizontal,
frictionless surface as in the figure it is
pressed against a light spring having a spring
constant of k 800 N/m, with an initial
compression of 2.0 cm.
b) To what height h does the block rise when
moving up the incline?
3.2 cm
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Power

• Average power is the average rate at which a net
  force
• does work
• Pav Wnet / t
• SI unit P J/s watt (W)
• Or Pav Fnet s /t Fnet vav

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Example
A 1967 Corvette has a weight of 3020 lbs. The 427
cu-in engine was rated at 435 hp at 5400 rpm.
a) If the engine used all 435 hp at 100
efficiency during acceleration, what speed would
the car attain after 6 seconds? b) What is the
average acceleration? (in gs)
a) 120 mph b) 0.91g
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Example
Consider the Corvette (w3020 lbs) having
constantacceleration of a0.91g
a) What is the power when v10 mph? b) What is
the power output when v100 mph?
a) 73.1 hp b) 732 hp (in real world a is
larger at low v)