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Physics 101: Lecture 12
Work and Energy
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Chapter 6: Work and Energy
Reminders:
Exam I, Tuesday September 30th at 5 PM
See PHY101 Web page for room assignments
Do not forgot to bring your UB ID card !
Physics 101: Lecture 12, Pg 1
Work & Energy
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An important concept in physics
Alternative approach to mechanics
Many applications beyond mechanics
Thermodynamics (movement of heat)
Quantum mechanics...
Very useful tools
You will learn new (sometimes much easier) ways to
solve problems
Physics 101: Lecture 12, Pg 2
Work done by a Constant Force
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The work done on an object by a constant (i.e.
displacement independent) force F is given by
W = Fs s
Unit : [W] = N m = J (Joule)
s : magnitude of displacement
Fs : magnitude of the force in the direction of the
displacement (Fs=F cosΘ)
W can be positive or negative:
W = + Fs s if Fs points in the same direction as s
W = - Fs s if Fs is opposite of s
Physics 101: Lecture 12, Pg 3
Lecture 9, Preflight 1 & 2
You are towing a car up a hill with constant velocity.
The work done on the car by the normal force is:
1. positive
2. negative
3. zero
FN
V
T
correct
W
The normal force is perpendicular to the
displacement, hence, does no work.
Physics 101: Lecture 12, Pg 4
Concept Question
You are towing a car up a hill with constant velocity.
The work done on the car by the gravitational force is:
1. positive
2. negative
3. zero
FN
V
T
correct
W
With the surface defined as the x-axis, the x component
of gravity is in the opposite direction of the
displacement, therefore work is negative.
Physics 101: Lecture 12, Pg 5
Concept Question
You are towing a car up a hill with constant velocity.
The work done on the car by the tension force is:
1. positive
2. negative
3. zero
FN
correct
V
T
W
Tension is in the same direction as the displacement.
Physics 101: Lecture 12, Pg 6
Work/Kinetic Energy Theorem:
Work done by a constant net force:
Wnet = Fnet s = m a s = m (vf2 –v02)/2
KE = m v2/2 is called the kinetic energy of an object.
{Net Work done on an object}
=
{change in kinetic energy of object}
Wnet=ΔKE
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= KEf - KE0 = ½ m vf2 – ½ m v02
Also works for a variable force !
Physics 101: Lecture 12, Pg 7
Work done by Gravity
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Object falling vertically upward or downward :
Wgravity = Fgravity s = m g (h0-hf)
PE = m g h is called gravitational potential energy
Object falling downward: Wgravity > 0
Object moving upward: Wgravity < 0
Gravity is an example for a conservative force:
work done is independent of path or
force does no net work on object moving around a closed path.
Physics 101: Lecture 12, Pg 8
Conservation of Mechanical Energy
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or
Total mechanical energy of an object remains constant
provided the net work done by non-conservative forces
is zero:
Etot = KE + PE = constant
KEf + PEf = KE0 + PE0
=> ΔKE + ΔPE = 0
Otherwise, in the presence of a net work done by
non-conservative forces (e.g. friction):
Wnc = ΔKE + ΔPE = KEf – KE0 + PEf-PEo
Physics 101: Lecture 12, Pg 9