Transcript Chapter 7 Energy

Chapter 7 Energy
• Work
• Power
• Mechanical Energy
– Potential Energy
– Kinetic Energy
– Work-Energy Theorem
• Conservation of Energy
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PHY 1071
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Work
• When we lift a load against Earth’s gravity, work
is done.
– The heavier the load or the higher we lift the load, the
more work is done.
– Two things enter the picture whenever work is done:
• (1) application of a force, and
• (2) the movement of something by that force.
Work is done in lifting the
barbell. If the weight lifter
were taller, he would have
to expend proportionally
more energy to press the
barbell over his head.
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• Thus, in the simplest case, where the force is
constant and the motion takes place in a straight
line in the direction of the force, we define the
work done on an object as:
Work = force  distance
Unit of work = N m = joule (J)
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Definition of work involves both
a force and a distance.
He may expend energy
when he pushes on the
wall, but if it doesn’t move,
no work is performed on
the wall.
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Power
• Why are we more tired after running upstairs
in a few seconds than after walking upstairs
in a few minutes?
The three main engines of a space
shuttle can develop 33,000 MW of
power when fuel is burned at the
enormous rate of 3400 kg/s. This is
like emptying an average-size
swimming pool in 20 s.
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• To understand this difference, we need to
talk about a measure of how fast the work is
done - power:
Power = work done / time interval, or how fast
the work is done
Unit of power = J / s = watt
Other units commonly used: horsepower,
kilowatts, etc.
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Power of an automobile engine
Power = work done / time interval
• An engine of great power can do work rapidly.
• What does it mean that one engine is twice as
powerful as another?
– It means that it can do the same amount of work in half
the time or twice the work in the same amount of time.
• For example, a more powerful engine can get an
automobile up to a given speed in less time than a
less powerful engine can.
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Energy
• When work is done by an archer in drawing a
bow, the bent bow has the ability to do work on
the arrow; When work is done to wind a spring
mechanism, the spring acquires the ability to do
work on various gears to run a clock, ring a bell,
etc.
• In each case, something has been acquired. This
“something” given to the object enables the
object to do work. What is this “something”?
• This “something” that enables an object to do
work is energy!
Unit of energy = joule (J)
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Energy appears in many forms
• For now, we focus on mechanical energy
– (I) Potential energy: the form of energy due to the
relative position of interacting bodies
– (II) Kinetic energy: the form of energy due to their
motion.
• Mechanical energy may be in the form of either
potential energy or kinetic energy, or both.
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Potential energy
m = 3 kg • An object may store energy because of its
position relative to some other object. This
energy is called potential energy because in
the stored state, it has the potential to do work.
h=4m
• The potential energy of a body due to elevated
positions is called gravitational potential
energy.
Gravitational potential energy = weight  height
Potential energy of the
= mgh
ball = mgh = (3 kg  10
m/s2) 4 m = 120 J
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Gravitational potential energy =
weight  height
• Weight of the ball = 10 N
• Height of all three shapes = 3 m.
• What is the potential energy of the ball in each of the three cases?
The potential energy of the ball at the top of the ledge depends on the
height but does not depend on the path taken to get there!
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• One of the kinds of energy into which
potential energy can change is energy
of motion, or kinetic energy.
• The potential energy of the elevated
ram is converted to kinetic energy
when released.
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Kinetic energy
• If an object is moving, then by virtue of that
motion it is capable of doing work. We call
energy of motion kinetic energy.
• The kinetic energy of an object depends on
mass and speed:
The downhill “fall” of the
Kinetic energy = (1/2)  mass  speed 2
roller coaster results in its
roaring speed in the dip, • So, if the speed of an object is doubled, its
and this kinetic energy
kinetic energy is quadrupled.
sends it up the steep track
to the next summit.
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Energy transition between potential
energy and kinetic energy
• Energy transition in a pendulum. Potential energy is relative to
the lowest point of the pendulum, when it is vertical.
• At the lowest point, its potential energy is 0, but its kinetic energy
is the largest.
• At its initial position, its potential energy is the largest, but its
kinetic energy is 0.
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Work-energy theorem
• Work equals change in kinetic energy. This is the
work-energy theorem.
Work = Change in kinetic energy
– Consider the long-range cannon example discussed in the
previous chapter.
• The work in this equation is the net work.
– For example, if you push something when there is friction
present, then part of the work goes into generating heat,
and the rest of the work goes to changing the object’s
kinetic energy.
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Conservation of energy
• The law of conservation of energy, one of the
greatest generalizations in physics:
Energy cannot be created or destroyed; it may be
transformed from one form into another, but the
total amount of energy never changes.
• A circus diver at the top of a pole has a potential
energy of 10,000 J. As he dives, his potential
energy converts to kinetic energy. Note that the
total energy is constant.
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Homework
• Chapter 7, P. 127, Exercises: 11, 28, 51, 52.
• The above problems are from the 10th
edition of the textbook by Hewitt.
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