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Work and Energy
Chapter 6 Griffith
Simple Machines
1.
2.
3.
4.
5.
6.
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Simple Machines
1.
2.
3.
4.
5.
6.
Lever
Pulley
Inclined Plane
Wedge
Screw
Wheel and Axle
Mechanical Advantage
Reduction of Friction
Pulley System
T
T
d1
T = W/2
d2 = 2d1
F=T
d2
W
Mechanical Advantage
Less force is advantageous, even though the
smaller force must act over a larger distance in
order to transfer the same amount of work.
Concept of Work
• Work = Force × Displacement = Fd
– F must be constant.
– F and d must be collinear.
• Work = 200 Nm = 200 Joules
F = 50 N
d = 4.0 meters
If F and d are not collinear,
F = 50 N
Fy = 30 N
Work = Fxd = 160 J
Fx = 40 N
d = 4.0 meters
Work is the product of displacement and the component
of force in the direction of the displacement.
Work = Fd = Fd
Vector or Scalar?
• Note that even though force and displacement
are both vectors and have direction, work has
no direction.
• All forms of energy have no directions either.
Work and energy are scalar quantities.
Work and Uniform Circular Motion
v
Tension
F = mv2/r
What is the work done on the
mass by the tension in the string?
Work and Uniform Circular Motion
v
Tension
F = mv2/r
The work done by tension in the string is
zero!! The mass does not move toward
or away from the center of the circle.
Units of Work
• 1.0 Joule = 1.0 Newton × meter
= 1.0 kg m2/s2
• 1.0 erg = 1.0 dyne x cm
= 1.0 g cm2/s2
How many dynes in 1.0 Newton?
How many ergs in 1.0 Joule?
Units of Work
• 1.0 Joule = 1.0 Newton × meter
= 1.0 kg m2/s2
• 1.0 erg = 1.0 dyne x cm
= 1.0 g cm2/s2
How many dynes in 1.0 Newton?
How many ergs in 1.0 Joule?
105
107
Power
• In General Physics we describe average power.
Pavg
work done
 average power 
time taken
• Units of power = J/s = Watt = kg m2/s3
– 1.0 horsepower = 746 Watts
Kinetic Energy
• Energy of motion
• Formulated by Gottfried Wilhelm Leibniz
– also developed calculus independent of Newton
KE  E K  K  mv
1
2
2
Work-Energy Theorem
• The work done on a body changes the kinetic
energy of the body.
E Kf  E Ki  W
• Notice that work can be positive or negative.
– Positive work adds kinetic energy to the body.
– Negative work takes kinetic energy away from the
body.
Positive and Negative Work
W>0
v
F
W<0
v
F
Force does positive work on
the car. The acceleration is in
the direction of the velocity,
and the car speeds up.
Force does negative work on
the car. The acceleration is
opposite the direction of the
velocity, and the car slows
down.
Work-Energy Example
vi = 2.0 m/s
10 kg
vf = ?
F = 50 N
10 kg
d = 4.0 meters
A 10-kg block moving at 2.0 m/s to the right is
pushed to the right by a 50-N force. The force
continues as the block moves 4.0 m in a straight
line. What is the final speed of the block?
Work-Energy Example
vi = 2.0 m/s
10 kg
vf = ?
F = 50 N
10 kg
d = 4.0 meters
E Ki  W  E Kf
1
2
102.02  50 4.0  12 10v 2
vf  6.6 m/s
f
Is the Work-Energy Theorem mysterious?
E Ki  W  E Kf
1
2
1
2
mvi2
mv
2
vf
 Fd 
2
f
2
 vi
2
 vi
1
2
mv 2f
special case of
constant force
  Fd  mad
 2ad
third “Big 3”
equation!
No, the work-energy theorem is not mysterious!
Potential Energy
• Applies only to Conservative Forces
– Gravity, Elastic forces
– Friction, Applied forces
• Work done against a conservative force can be
later completely converted to kinetic energy.
– The work is thus “stored.”
Potential Energy
100 kg
d = 2.0 m
100 kg
Fapplied = mg = 980 N
ag = 9.8 m/s2
v = constant
Despite work applied to
the box against gravity,
the kinetic energy does
not change.
This means that potential
energy is increasing.
Fapplied
Potential Energy
100 kg
d = 2.0 m
100 kg
W = Fappliedd = 1960 J
ag = 9.8 m/s2
v = constant
PEi + W = PEf
PEf – PEi = 1960 J
This 1960 J will be turned
into kinetic energy if the
box is dropped.
Fapplied
Potential Energy
• Notice that only the change in potential
energy (PEf – PEi = DPE) tells us about forces,
displacements, and velocities.
• The value of potential energy at any one
location is completely arbitrary.
Mechanical Energy
• Both potential and kinetic energy are created
by work, so both are types of mechanical
energy.
PE + KE = Emech