Download Physics 106P: Lecture 1 Notes

Physics 101: Chapter 6
Work and Kinetic Energy
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New stuff: Chapter 6, sections 6.1 - 6.7
UB, Phy101: Chapter 6, Pg 1
Work & Energy
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One of the most important concepts 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
UB, Phy101: Chapter 6, Pg 2
UB, Phy101: Chapter 6, Pg 3
UB, Phy101: Chapter 6, Pg 4
UB, Phy101: Chapter 6, Pg 5
Work/Kinetic Energy Theorem:
{Net Work done on object}
=
{change in kinetic energy of object}
Wnet  K
KE Demo
 K 2  K1

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1
1
2
2
mv 2  mv1
2
2
Also works for a variable force
UB, Phy101: Chapter 6, Pg 6
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Work and Kinetic Energy:
• WF = |F| |S| cos

• KE = 1/2 mv2
• Work-Kinetic Energy Theorem:
KE = Wnet
UB, Phy101: Chapter 6, Pg 7
Chapter 6, Preflight
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
UB, Phy101: Chapter 6, Pg 8
Chapter 6, Preflight
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.
UB, Phy101: Chapter 6, Pg 9
Chapter 6, Preflight
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 of the displacement
UB, Phy101: Chapter 6, Pg 10
Chapter 6, Preflight
You are towing a car up a hill with constant velocity.
The total work done on the car by all forces is:
1. positive
2. negative
3. zero
FN
V
T
correct
W
The car is not accelerating, so it has a net force of
zero and since work=Fcos0(s), work too will equal zero.
the initial KE equils the final KE and so the
difference is zero
UB, Phy101: Chapter 6, Pg 11
UB, Phy101: Chapter 6, Pg 12
UB, Phy101: Chapter 6, Pg 13
UB, Phy101: Chapter 6, Pg 14
Work Done by Gravity
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Example 1: Drop ball
Wg = (mg)(S)cos
Yi = h
S=h
Wg = mghcos(00) = mgh
mg
S
y
y = yf-yi = -h
Wg = -mgy
Yf = 0
x
UB, Phy101: Chapter 6, Pg 15
Work Done by Gravity
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Example 2: Toss ball up
Wg = (mg)(S)cos
S=h
Wg = mghcos(1800) = -mgh
y = yf-yi = +h
Wg = -mgy
Yi = h
mg
S
y
Yf = 0
x
UB, Phy101: Chapter 6, Pg 16
Work Done by Gravity
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Example 3: Slide block down incline
Wg = (mg)(S)cos
S = h/cos

h
mg
S
Wg = mg(h/cos)cos
Wg = mgh
y = yf-yi = -h
Wg = -mgy
UB, Phy101: Chapter 6, Pg 17
Summary: Work Done by Gravity
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Wg = -mg(yf - yi) = -mgy
Independent of path
If you end up where you began, Wg = 0
We call this a “Conservative Force” because we can
define a “Potential Energy” to go with it.
UB, Phy101: Chapter 6, Pg 18
Chapter 6, Preflight
(who read section 6.4 in the book ?)
Which of the following statements correctly define a Conservative
Force:
1. A force is conservative when the work it does on a moving object is
independent of the path of the motion between the object's initial and
final positions.
2. A force is conservative when it does no net work on an object moving
around a closed path, starting and finishing at the same point.
3. Both of the above statements are correct.
correct
4. Neither of the above statements is correct.
UB, Phy101: Chapter 6, Pg 19
Chapter 6, Preflight
Imagine that you are comparing three different ways of having a ball
move down through the same height. In which case does the ball get to
the bottom first?
1.
2.
3.
4.
correct
Dropping
Slide on ramp (no friction)
Swinging down
All the same
1
2
3
It seems logical because A has the shortest
distance to go, although the answer is probably all
3, for some crazy physics reason.
UB, Phy101: Chapter 6, Pg 20
Chapter 6, Preflight
Imagine that you are comparing three different ways of having a ball
move down through the same height. In which case does the ball reach
the bottom with the highest speed?
1.
2.
3.
4.
Dropping
Slide on ramp (no friction)
Swinging down
All the same
correct
1
2
3
In all three experiments, the balls fall from the same
height and therefore the same amount of their
gravitational potential energy is converted to kinetic
energy. If their kinetic energies are all the same, and their
masses are the same, the balls must all have the same
speed at the end.
UB, Phy101: Chapter 6, Pg 21
Friction Demo
UB, Phy101: Chapter 6, Pg 22
Modified Work-Kinetic Energy Theorem
• Work-Kinetic Energy Theorem:
•WNC = KE + PEg = KE + mgy
•
Friction Demo 2
E = total energy = KE + PEg
• WNC = E = Ef - Eih
• Conservation of Energy:
•If WNC = 0, then Ef = Ei
(KE+PEg)initial = (KE+PEg)final
NC: all forces except gravity
UB, Phy101: Chapter 6, Pg 23
Chapter 6, Preflight
Suppose the initial kinetic and potential energies of a system are 75J
and 250J respectively, and that the final kinetic and potential energies
of the same system are 300J and -25J respectively. How much work
was done on the system by non-conservative forces?
1. 0J
2. 50J
correct
3. -50J
4. 225J
5. -225J
Work done by non-conservative forces equals the
difference between final and initial kinetic energies
plus the difference between the final and initial
gravitational potential energies.
W = (300-75) + ((-25) - 250) = 225 - 275 = -50J.
UB, Phy101: Chapter 6, Pg 24
Conservation of Energy Demo
UB, Phy101: Chapter 6, Pg 25
UB, Phy101: Chapter 6, Pg 26
UB, Phy101: Chapter 6, Pg 27
UB, Phy101: Chapter 6, Pg 28
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UB, Phy101: Chapter 6, Pg 31