Last Thoughts on Work
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Transcript of Last Thoughts on Work
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Last Thoughts on Work Work can be done by friction
Friction always opposes motion so the work it does is usually negative. (exceptions are like conveyor belt.)
Friction is a “dissipative force.” Turns Mech. Energy into another form:
often useless heat.Sometimes called non-conservative force, since it doesn't conserve mechanical energy.
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Kinetic EnergyEnergy associated with the motion of an object
Scalar quantity with the same units as work
Work is related to kinetic energy
2mv2
1KE
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K.E. Is not momentum p = momentum
p = mv p is a vector p is always conserved in a closed system. Always. Always. Always.
K.E. = 1/2mv2
K.E. Is a scalar
K.E. Is not always conserved. It can turn into any other form of energy.
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Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy
Speed will increase if work is positive
Speed will decrease if work is negative
net fiW KE KE KE
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Work and Kinetic Energy An object’s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest The moving hammer has kinetic energy.
The hammer will be doing work on the nail.
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Types of Forces
There are two general kinds of forcesConservative
Work and energy associated with the force can be recovered.
(Usually means all the energy stays as some form of mechanical energy. Put ME in to the system and get ALL the ME out.)
NonconservativeThe forces are generally dissipative and work done against it cannot easily be recovered
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More About Conservative ForcesExamples of conservative forces include:Gravity (Roller Coaster, lift a brick)
Spring force (Pull a spring)Electromagnetic forces (Magnetic crane at junk yard lifting a car)
Potential energy is another way of looking at the work done by conservative forces
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Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the pointsThe work depends only upon the initial and final positions of the object
Any conservative force can have a specific potential energy for each point in space.
(move brick straight up 2 feet. 2nd. Spin around in circles and move brick up 2 feet.)
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Nonconservative ForcesA force is nonconservative if:
The work it does is path dependent.
Examples of nonconservative forcesKinetic friction, air drag.
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Friction Depends on the Path
Which path loses more energy to friction?
Red or Blue?
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Friction Depends on the Path
Which path loses more energy to friction?
Red or Blue?
Red, because the path is longer.
Pushing the book backwards across the table won't give you the energy back.
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Potential EnergyPotential energy is associated with the position of the object within some systemPotential energy is a property of the system, not the object.
Assuming no friction, ME of the system is constant. It can transfer from one object to another in the system.
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Work and Potential EnergyFor every conservative force, a potential energy is associated with each position.
Think about a projectile. When the object falls, it “gets the energy back” that went into elevating it.
(Royals hitting a foul ball up into top deck vs ball falling back down to 1st row.)
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Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen for each problemThe choice is arbitrary since the change in the potential energy is the important quantity
Choose a convenient location for the zero reference heightOften the Earth’s surfaceMay be some other point suggested by the problem
Once the position is chosen, it must remain fixed for the entire problem.
(Go back to Royals picture. Where does problem suggest as Frame of Ref? 3 good choices, bat height, top of flight, ground, but could do anything such as center of the earth.)
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Reference Levels At location A, the desk may be the convenient reference level
At location B, the floor could be used
At location C, the ground would be the most logical reference level
The choice is arbitrary, though,
it must remain fixed for the entire problem.
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Conservation of Energy, cont.
Total mechanical energy is the sum of the kinetic and potential energies in the system.
ME = KE + PE of any point in the system.
Equation: ME = KE + PE = constantThis is only valid in the absence of friction!
ffii
fi
PEKEPEKE
EE
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Additional Questions: 1.) Above KE everywhere, add v =2.) Above v = everywhere, add ME=3.) What is mass?
Below the Line write:1.) Equation for ME.2.) Equation for KE.3.) Equation for PE.MEMORIZE these for the test.
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Problem solving strategy:
1)“Where did the energy start out?”
2)“How much of it was changed?”--(work)
3)“Where did the energy end up?”4)Did the path matter?
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Discuss:Where is work positive and negative and relate it to velocity of skier.
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The Work-Energy Theorem and Kinetic Energy
Example 4 Deep Space 1
The mass of the space probe is 474-kg and its initial velocityis 275 m/s. If the 56.0-mN force acts on the probe through adisplacement of 2.42×109m, what is its final speed?
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The Work-Energy Theorem and Kinetic Energy
2212
f21W omvmv
sF cosW
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6.2 The Work-Energy Theorem and Kinetic Energy
2
212
f2192- sm275kg 474kg 474m1042.20cosN105.60 v
2212
f21cosF omvmvs
sm805fv
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The gymnast leaves the trampoline at an initial height of 1.20 mand reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?
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Gravitational Potential Energy
2212
f21W omvmv
fo hhmgW gravity
221
ofo mvhhmg
foo hhgv 2
sm40.8m 80.4m 20.1sm80.92 2 ov
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Example 11 Fireworks
A bottle rocket is set off. It flies upwards 29 m from it’s original height, and the propellant supplies 425 J, what is the final speedof the rocket. Ignore air resistance. Mass = .2kg
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Nonconservative Forces and the Work-Energy Theorem
2212
21
ofofnc mvmvmghmghW
2
21
2
kg 20.0
m 0.29sm80.9kg 20.0J 425
fv
221
fofnc mvhhmgW
sm61fv