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Work and Energy
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Work…
…is the product of the magnitude of displacement times the component of force parallel to the displacement.
W = F‖ dUnits: N·m or Joules (J)
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Work = Fd cos
Consider a crate pulled across a surface. Where… F is the applied force d is the displacement θ is the angle between the force
and the direction
F
d
F‖ = Fcosθ
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θ = ZERO in this situation!!! The force and the displacement are in the same directionF
d
Work = Fd cos
Consider the same crate being pulled up an incline…
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Work
Net work in moving an object is independent of the path to get there.
More force neededShorter distance traveled
Less force neededGreater distance traveled
Same amount of work done
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Energy – What is it?
The ability to do work
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KineticGravitational PotentialElastic Potential
HeatLightSoundElectricalChemicalNuclear
Types of Energy
Mechanical Energy – energy associated with an object’s position or
motion
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Consider a cart with an initial velocity vi and a net force acting on it through a distance d…
viFnet Fnet
vf
d
Wnet = Fnet d
Remember F = ma = m(vf2 – vi
2/2d)So…
Wnet = m(vf2 – vi
2/2d)d
Wnet = m(vf2 – vi
2/2)
Wnet = ½ mvf2 – ½ mvi
2
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Energy - Kinetic
Kinetic Energy is the energy that an object possesses due to its motion
If the mass of a body is m and its speed is v then its kinetic energy is given by
KE = ½ mv2
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Work-Energy Theorem
W = ½ mvf2 – ½ mvi
2
W = ΔKE
The net work done on an object (by a net force) is equal to a change in kinetic energy of the object
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Example problem
-A 10.0 kg sled is initially moving across a frozen pond at a speed of 4.2 m/s. How far will it travel if the coefficient of friction between the sled and ice is 0.10?
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Energy - Potential
• Potential Energy – the energy of an object due to its position, shape, or condition
• An system acquires potential energy when work is done against another force
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Energy - PotentialGravitational Potential Energy
This is the energy of an object associated with its position in a gravitational field (work done against the force of gravity to put it there)
GPE = mgh m = mass of the object h = height of object above some fixed
position (the position is arbitrary) g = the acceleration due to gravity
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Energy - Potential
Elastic Potential Energy This is the energy that an object possesses
due to its position of being stretched or deformed (work done against the elastic restoring force)
FOR A SPRING (or similar)…EPE= ½ k x2
x = amount of stretch k = the spring constant (a characteristic of
the object being stretched)
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The Principle of Conservation of Energy
Energy can be transformed from one form to another, but it cannot be created nor destroyed, i.e. the total energy of a system is constant
Energy transformations occur when work is done
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Conservation of Energy
Since energy is conserved for a system, when we compare the total at two different points…
Total E1 = Total E2
KE1 + GPE1 + EPE1 = KE2 + GPE2 + EPE2
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Power
Power is the rate of doing work or the rate at which energy is transferred.
P = W/tUnits: J/s = Watt
Alternate: P = W/t = Fd/t = Fv