Download Work and energy

Work
Power
Energy
Work Concepts
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Work (W) ~ product of the force exerted
on an object and distance the object
moves in the direction of the force.
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W is transfer of energy by mechanical means.
W is done on an object only if it moves in the
direction of the force.
Only the component of the force in the
direction of the motion does work.
Work Equations
Wnet = Fnet x displacement x (cos Q)
Wnet= Fnetd (cos Q)
Note: F = m x a so W = m x a x d
Or: work makes you “mad”
Unit: work = newton * meter or Nm
This is also known as a “joule” or j which is commonly used for energy
F
Here, the horizontal component

provides the forward force
d
Fx = FcosӨ
Here, the force is parallel to the
F
motion so cos 0o = 1
d
The Sign of Work
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Positive work is done when the motion is in the same
direction as the force of motion. For a moving object
(+) net work results in increased velocity.
Negative work results from a force applied in the
direction opposite the motion. For a moving object
(-) net work results in decreased velocity.
f does (-) work
f
F
d
F does (+) work
Energy
Energy
(the ability to do work)
Mechanical
Kinetic
K = ½ mv2
Potential
Gravitational
Ug = mgh
Non-mechanical
chemical
thermal
nuclear
Elastic
Us = ½ kx2
Mechanical Energy
Mechanical energy is the energy which is
possessed by an object due to its motion
or its stored energy of position, shape, or form
Etotal = Ktotal + Utotal
Kinetic Energy
K = ½ x mass x velocity²
Kinetic energy is the energy an object
has because of its motion
Work-Energy Theorem
According to the Work-Energy theorem,
the work done on an object, by the net
force acting on it, is equal to the change
in kinetic energy of the body
Work = D K
F d cosQ = Kf - Ki
Potential Energy
Potential energy (U) is the energy an object
has because of its position, shape, or form
There are two types of PE:
gravitational
spring (or elastic)
Gravitational P E
Ug = mgh
(mass x gravity x height)
Gravitational potential energy depends on
the weight of the body and
its position in a gravity field
Where is Ug measured from?
If A is your reference point then
points B and C have –U.
If C is your reference, then B
and A have +U.
Elastic PE
Us = ½ kx2
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Elastic potential energy is energy stored
within an elastic system. This energy is
based on two factors:
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The constant, k, (called the spring constant)
is based on the type of material and twist of
the spring
The distance, x, the spring is stretched or
compressed from its rest position
Conservation of
Energy
According to the law of conservation
of energy, the total energy of a closed,
isolated system is constant
Einitial = Efinal
Ki + Ugi + Usi = Kf + Ugf + Usf
Power

Power (P) ~ rate at which work is done or
rate at which energy is transferred.
Measured in watts.
 Power
= Work / time
1 watt = 1 joule / second (J/s
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Watt (W) ~ one joule of energy transferred in
one second.
Alternate: P = F x (d / t)
so P = F x v
Simple Machines
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A simple machine is one in which the work
(or transfer of energy) is done by one
motion.
Work is done ON the machine to operate it
– this is considered “workin”
so that the machine can do work ON the
object or load – this is considered
“workout”
Ideal Machines
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In the real world, energy is lost to friction
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So, Win = Wout + Wf
Ideal machines exist only in a frictionless,
air resistance-less world.
No energy or work is lost to the system
through outside forces
For ideal machines (Wf = 0) :
Work input = Work output
Findin = Fout dout
 Note: energy always conserved
Mechanical Advantage
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How much the machine multiplies the effort
IMA (ideal MA) : ratio of the dimensions of the
machine
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IMA = din / dout
AMA (actual MA) : ratio of the actual force
output (load) to force input
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AMA = Fout / Fin
Efficiency
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Efficiency : ratio of work output to work
input expressed in percent.
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Also: Ratio of mechanical advantage
efficiency = (Wout / Win) x 100
Or
efficiency = (AMA /IMA)x100