Download 4.1 The Concepts of Force and Mass

Chapter 6
Work and Energy
6.1 Work Done by a Constant Force
W  Fs
1 N  m  1 joule J 
6.1 Work Done by a Constant Force
W  F cos s
cos 0  1
cos 90  0
cos 180  1
6.2 The Work-Energy Theorem and Kinetic Energy
DEFINITION OF KINETIC ENERGY
The kinetic energy KE of an object with mass m
and speed v is given by
KE  mv
1
2
2
6.2 The Work-Energy Theorem and Kinetic Energy
THE WORK-ENERGY THEOREM
When a net external force does work on an object, the kinetic
energy of the object changes from its initial value of KE0 to a
final value of KEf , the difference between the two values
being equal to the work:
W  KEf  KEo  mv  mv
1
2
2
f
1
2
2
o
6.3 Gravitational Potential Energy
DEFINITION OF GRAVITATIONAL POTENTIAL ENERGY
The gravitational potential energy PE is the energy that an
object of mass m has by virtue of its position relative to the
surface of the earth. That position is measured by the height
h of the object relative to an arbitrary zero level:
PE  mgh
1 N  m  1 joule J 
6.4 Conservative Versus Nonconservative Forces
A force is conservative when the work it does on a moving
object is independent of the path between the object’s initial
and final positions.
Wgravity  mg ho  h f 
6.4 Conservative Versus Nonconservative Forces
Non-conservative force – a force is non-conservative if the
work it does on an object moving between two points
depends on the path of motion between the points.
The work done by the kinetic frictional force is always negative.
6.4 Conservative Versus Nonconservative Forces
In normal situations both conservative and nonconservative
forces act simultaneously on an object, so the work done by
the net external force can be written as
W  Wc  Wnc
W  KEf  KEo  KE
Wc  Wgravity  mgho  mgh f  PE o  PE f  PE
6.4 Conservative Versus Nonconservative Forces
W  Wc  Wnc
KE  PE  Wnc
THE WORK-ENERGY THEOREM
Wnc  KE  PE
6.5 The Conservation of Mechanical Energy
Wnc  KE  PE  KEf  KEo   PE f  PE o 
Wnc  KEf  PE f   KEo  PEo 
Wnc  Ef  Eo
If the net work on an object by nonconservative forces
is zero, then its energy does not change:
Ef  Eo
6.5 The Conservation of Mechanical Energy
THE PRINCIPLE OF CONSERVATION OF
MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an object
remains constant as the object moves, provided that the net
work done by external nononservative forces is zero.
6.5 The Conservation of Mechanical Energy
6.5 The Conservation of Mechanical Energy
Example 8 A Daredevil Motorcyclist
A motorcyclist is trying to leap across the canyon by driving
horizontally off a cliff 38.0 m/s. Ignoring air resistance, find
the speed with which the cycle strikes the ground on the other
side.
6.5 The Conservation of Mechanical Energy
Ef  Eo
mghf  mv  mgho  mv
1
2
2
f
1
2
gh f  12 v 2f  gho  12 vo2
2
o
6.5 The Conservation of Mechanical Energy
gh f  12 v 2f  gho  12 vo2
vf 


2 g h
o
 hf
 v
2
o
v f  2 9.8 m s 35.0m  38.0 m s   46.2 m s
2
2
6.7 Power
DEFINITION OF AVERAGE POWER
Average power is the rate at which work is done, and it
is obtained by dividing the work by the time required to
perform the work.
Work W
P

Time
t
joule s  watt (W)
6.7 Power
Change in energy
P
Time
1 horsepower  550 foot  pounds second  745.7 watts
P  Fv
6.8 Other Forms of Energy and the Conservation of Energy
THE PRINCIPLE OF CONSERVATION OF ENERGY
Energy can neither be created nor destroyed, but can
only be converted from one form to another.
Problems To Be Solved
• 6.12, 6.23, 6.39, 6.60, 6.63, 6.65
• B6.1 The heart may be regarded as an
intermittent pump that forces about 70cm3
of blood into the 1.0cm radius aorta about
75 times a minute. Measurements show
that the average force with which the
blood is pushed into the aorta is about
5.0N. What is the approximate power
used in moving the blood to the aorta?
Ans: 1.39W
• B6.2 A dieter lifts a 10kg mass a distance
of 0.5m 1000 times. (a) How much work
does he do against gravitational force? (b)
Fat supplies 3.8×107J of energy per
kilogram, which is converted to
mechanical energy with a 20% efficiency
rate. How much fat will the dieter use up?
Ans: (a) 49000J; (b) 6.4×10-3kg
• B6.3 A beer can is dropped from a window
30m above the ground. How fast will it be
moving just before it lands?(Neglect air
resistance) Ans: 24.25m/s
• B6.4 A 55kg carton of bananas with an
initial speed of 0.45m/s slides down a
ramp inclined at an angle of 23⁰ with the
horizontal. If the coefficient of friction
between the carton and the ramp is 0.24,
how fast will the carton be moving after it
has travelled a distance of 2.1m down the
ramp? Ans: 2.68m/s