phys141 principles of physical science chapter 4 work and energy
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Phys141 Principles of Physical Science Chapter 4 Work and Energy. Instructor: Li Ma Office: NBC 126 Phone: (713) 313-7028 Email: [email protected] Webpage: http://itscience.tsu.edu/ma Department of Computer Science & Physics Texas Southern University, Houston. Sept. 20, 2004. - PowerPoint PPT PresentationTRANSCRIPT
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Phys141 Principles of Physical Science
Chapter 4 Work and Energy
Instructor: Li Ma
Office: NBC 126Phone: (713) 313-7028Email: [email protected]
Webpage: http://itscience.tsu.edu/ma
Department of Computer Science & PhysicsTexas Southern University, Houston
Sept. 20, 2004
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Topics To Be Discussed
WorkKinetic Energy and Potential EnergyConservation of EnergyPower
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About Work & Energy
Common meaning of Work– Work is done to accomplish some task or
job– When work is done, energy is expended
Mechanically, Work involves force & motion
Energy is a concept, is abstract, is stored work
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Work
The work done by a constant force F acting on an object is the product of the magnitude of the force (or component of force) and the parallel distance d through which the object moves while the force is applied
W = F·d
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Work (cont)
If only apply force but no motion, then there is technically no work
Only the component of force in the direction of motion has contribution to work
Example:
d
F
Fh
Fv
W = Fh·d
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Work (cont)
Unit of Work– In Metric system: N·m, or joule (J)– In British system: pound·foot (ft·lb)
Newton’s third law force pair– When the force is applied, work is done
against this force pair– Moving box forward: do work against
friction– Lifting the box: do work against gravity
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Energy
Common sense:– when work is done, some physical quantity
changes: work against gravity, height is changed; work against friction, heat is produced; etc.
With concept of energy:– When work is done, there is a change in
energy, and the amount of work done is equal to the change in energy
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Energy (cont)
Energy is described as a property possessed by an object or system
Energy is ability to do work:– An object or system that possess energy
has the ability or capability to do workUnit of Energy
– Same as work
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Work and Energy
Doing work is the process by which energy is transferred from one object to another:– When work is done by a system, the
amount of energy of the system decreases– When work is done on a system, the
system gains energyBoth work and energy are scalar
quantities
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Work and Energy (cont)
One scenario: when work is done on an object (at rest initially), the object’s velocity changes
d = ½a·t2, v = a·t, F = m·a, W = F·dW = m·a·d = m·a·(½a·t2) = ½ m·(a·t)2 = ½ m·v2
So W = ½ mv2
This amount of work is now energy of motion, or kinetic energy
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Work and Energy (cont)
Another scenario: when work is done on an object, the object’s position changes
There is also a change in energy, since the object has potential ability to leave that position and do work
This amount of work is energy of position, or potential energy
Kinetic & Potential energy: two forms of Mechanical energy
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Kinetic Energy
Kinetic energy is the energy an object possesses because of its motion, or simply stated, it is energy of motion:
kinetic energy = ½ x mass x (velocity)2
Ek = ½ mv2
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Kinetic Energy (cont)
If the work done goes into changing the kinetic energy, then
work = change in kinetic energy
W = ΔEk = Ek2 – Ek1
So W = ½ mv22 - ½ mv2
1
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Potential Energy
An object does not have to be in motion to have energy
Potential energy is the energy an object has because of its position or location, or simply, it is energy of position
Examples: lifted weight, compressed or stretched spring, drawn bowstring
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Potential Energy (cont)
One scenario: Lift an object at a (slow) constant velocity up to a height h from the ground (or saying sea level)
Work is done against gravity
Work = weight x height
W = m·g·h (W = F·d)
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Gravitational Potential Energy
The object has potential ability to do work, it has energy
Gravitational potential energy is equal to the work done against gravity
gravitational potential energy = weight x height
Ep = m·g·h
More generally, Ep = m·g·Δh
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Conservation of Energy
Understanding of conservation– Energy can be neither created nor
destroyed– Energy can change from one form to
another, but the amount remains constant– Energy is always conserved
The total energy of an isolated system remains constant
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Conservation of Mechanical Energy
Ideal systems– Energy is only in two forms: kinetic and
potentialConservation of mechanical energy
– The mechanical energy of the ideal system remains constant
Initial Energy = Final Energy
(Ek + Ep)1 = (Ek + Ep)2
(½ mv2 + mgh)1 = (½ mv2 + mgh)2
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Conservation of Mechanical Energy (cont)
Want the velocity of a freely falling object when fallen a height of Δh:– velocity and acceleration:
Vt = gt, Δh = ½ gt2 (Δh = d)
=> Vt = (2gΔh) ½
– Conservation of mechanical energy:
(½ mv2 + mgh)i = (½ mv2 + mgh)t
½ m(v2t - v2
i ) = mg(hi - ht)
=> Vt = (2gΔh) ½
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Power
Do same thing in different amount of time: the rate at which the work is done is different
Power is the time rate of doing work
power = work / time
P = W/t = F·d/tUnit: watt in the SI, 1 W = 1 J/s
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Power (cont)
The greater the power of an engine or motor, the faster it can do work
Power may be thought of as energy produced or consumed divided by the time taken
P = E/t
=> E = p·t