Download Lecture 11 - School of Physics

Energy and Work
EDUH 1017
Sports Mechanics
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Lecture 11
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Energy and Work
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Work
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Say you lift with a constant velocity (i.e. acceleration = 0), then
the upward force F = weight FW = mg
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The work done by your hand to raise an object a height h
“against gravity” is
W = Fd
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Energy
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What is the work done on the 1.0 kg object by the hand in
raising it by 2.0 m?
The SI unit of work (and energy) is the newton-meter, known
as the Joule (J)
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kinetic energy
Energy is needed to do useful work.
Energy can move things, heat things up, cool them down, join
things, break things, cut things, make noise, make light, and
power our electronics, etc.
Energy can be changed from one form to another.
gravitational potential energy
elastic potential energy
chemical energy
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= ( mg)h
In lifting an object, your hand is doing
work to lift the object “against gravity”
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EDUH 1017 Sports Mechanics L11
Work
At the heart of the concept of work is
the idea of movement with some force
or against some “resistance”
In jumping, it is gravity that is
resisting the attempt to jump up
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There is another way to think about jumping – as a change in
Energy
Energy derives from the Greek words en (meaning in) and
ergon (meaning work). Energy is the capacity to do work.
But what does work mean?
In mechanics, work is the change in energy resulting from the
application of a force to an object as the object moves through a
distance in space.
W = Fd or more generally
W = Fd cos θ where θ is the angle
between the direction of the force F and the displacement d
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Kinetic Energy
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Under the influence of a net force, a body accelerates as
(positive) work is done on it. It increases its speed and gains
energy
Energy associated with motion is called Kinetic Energy (KE)
KE =
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Kinetic Energy
1 2
mv
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Example:
• A Boeing 747 weighing 2.2 x 106 N at take-off cruises at
960 km/h. Calculate its KE.
Note that the units are Joules
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How much KE?
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Shoaib Akhtar hold the world record for the fastest bowl in
cricket, with a speed of 161.3 km/h.
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How much more energy does Akhtar’s ball have than a ball
bowled by the school kid?
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This retrievable stored energy is called Gravitational
Potential Energy (PE)
The change in PE of an object in moving from one point to
another equals the work done in overcoming the interaction
that stores the energy.
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Energy values
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We have already calculated the work done in lifting an object a
height h “against gravity”
W = Fd
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= ( mg)h
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An object lifted against gravity still experiences the downward
force of gravity when it is held up, but at rest. When no longer
held up, it will obviously fall.
Energy will appear as KE as it falls, but what’s happening
while the object is held motionless, high in the gravitational
field?
Apparently it is possible to do work on a system when lifting it
and not have it appear as KE.
Energy is stored, waiting to be let loose.
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Gravitational Potential Energy
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EDUH 1017 Sports Mechanics L11
Gravitational Potential Energy
A primary school child can throw a cricket ball (m=0.156
kg) at a speed of 40 km/h
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A force acting over a distance results in a change in KE
Your arm can do work on a cricket ball and increase the ball’s
KE. It travels some distance and then crashes into the stumps,
doing work on them and losing a corresponding amount of KE.
The ball transports energy in the form of KE from one place to
another
PE is a relative quantity since the h is relative – from where are
we measuring height?
Thus the zero level of PE is arbitrary and chosen for
convenience in any situation.
Usually we are only concerned with changes in PE so where
the zero value is doesn’t really matter.
KE is also relative – any measured velocity depends on our
velocity
So Gravitational PE (sometimes GPE) is PE = mgh
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Mechanical Energy
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A Pendulum
Mechanical Energy of a system is defined as the sum of KE and
gravitational PE of all its parts.
If no additional forces (except
gravity) are applied to a system, no
energy is transferred into or out of
the system, and mechanical energy
is conserved. This is a limited case
of the more general concept of
conservation of all forms of energy
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Again, if we
ignore air
resistance, no
forces other than
gravity are acting
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Roller coaster
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Example
The zero point of PE
can be located
anywhere convenient
The change is PE is
the same
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Summary
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Energy and Work and very closely related concepts in Mechanics
Work is a change in energy resulting from the application of a
force
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Kinetic Energy (KE)
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Gravitational Potential Energy (PE)
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If no additional forces are applied to a system, no energy is
transferred into or out of the system, and mechanical energy
(KE + PE) is conserved.
NEXT: Jumping
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KE =
EDUH 1017 Sports Mechanics L11
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mv
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PE = mgh
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Hecht Example 6.11
A 60 kg skier starts from rest at the top of a 60 m high slope.
She descends without using her poles.
• What is her initial gravitational PE?
• Assuming friction is negligible, what is her speed at the
bottom of the slope?
• If her speed at the bottom of the run is 25 m/s, what is the
net energy transferred via friction (i.e. “lost” to warming
her, the skis, the slope and the air)?
Energy is conserved – in what other forms?
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