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Physics 211: Lecture 9, Pg 1
Physics 111: Lecture 9
Today’s Agenda
Work & Energy
Discussion
Definition
Work of a constant force
Work/kinetic energy theorem
Work of multiple constant forces
Comments
Physics 211: Lecture 9, Pg 2
Work & Energy
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
Physics 211: Lecture 9, Pg 3
Forms of Energy
Kinetic: Energy of motion.
A car on the highway has kinetic energy.
We have to remove this energy to stop it.
The brakes of a car get HOT!
This is an example of turning one form of energy into another (thermal energy).
Physics 211: Lecture 9, Pg 5
Energy Conservation
Energy cannot be destroyed or created.
Just changed from one form to another.
We say energy is conserved!
True for any closed system.
i.e. when we put on the brakes, the kinetic energy of the car is turned into heat using friction in the brakes. The total energy of the “car-brakes-road-atmosphere” system is the same.
The energy of the car “alone” is not conserved...
» It is reduced by the braking.
Doing “work” on an isolated system will change its “energy”...
Returning
Can
Physics 211: Lecture 9, Pg 6
Definition of Work:
Ingredients: Force (F), displacement (r)
Work, W, of a constant force F
acting through a displacement r
is:
W = F r = F r cos = Fr r
F
r Fr
“Dot Product”
Physics 211: Lecture 9, Pg 7
Definition of Work...
Only the component of F along the displacement is doing work.
Example: Train on a track.
F
r
F cos
Hairdryer
Physics 211: Lecture 9, Pg 12
Back to the definition of Work:
Work, W, of a force F acting
through a displacement r is:
W = F r F
r
Inclined Plane
Physics 211: Lecture 9, Pg 13
Lecture 9, Act 1 Work & Energy
A box is pulled up a rough (m > 0) incline by a rope-pulley-weight arrangement as shown below.
How many forces are doing work on the box?
(a) 2
(b) 3
(c) 4
Physics 211: Lecture 9, Pg 14
Lecture 9, Act 1 Solution
Physics 211: Lecture 9, Pg 15
Work: 1-D Example (constant force)
A force F = 10 N pushes a box across a frictionless floor for a distance x = 5 m.
x
F
Work done by F on box :
Physics 211: Lecture 9, Pg 16
Units:
N-m (Joule) Dyne-cm (erg)
= 10-7 J
BTU = 1054 J
calorie = 4.184 J
foot-lb = 1.356 J
eV = 1.6x10-19 J
cgs other mks
Force x Distance = Work
Newton x
[M][L] / [T]2
Meter = Joule
[L] [M][L]2 / [T]2
Physics 211: Lecture 9, Pg 17
Work & Kinetic Energy:
A force F pushes a box across a frictionless floor for a distance x. The speed of the box is v1 before the push and v2 after the push.
x
F
v1 v2
i
m
Physics 211: Lecture 9, Pg 18
Work & Kinetic Energy...
Since the force F is constant, acceleration a will be constant. We have shown that for constant a:
v22 - v1
2 = 2a(x2-x1) = 2ax.
multiply by 1/2m: 1/2mv22 - 1/2mv1
2 = max
But F = ma 1/2mv22 - 1/2mv1
2 = Fx
x
F
v1 v2
a
i
m
Physics 211: Lecture 9, Pg 19
Work & Kinetic Energy...
So we find that
1/2mv2
2 - 1/2mv12 = Fx = WF
Define Kinetic Energy K: K = 1/2mv2
K2 - K1 = WF
WF = K (Work/kinetic energy theorem)
x
F a
i
m
v2 v1
Physics 211: Lecture 9, Pg 20
Work/Kinetic Energy Theorem:
{Net Work done on object}
=
{change in kinetic energy of object}
KWnet
12 KK
2
1
2
2 mv2
1mv
2
1
We’ll prove this for a variable force later.
Physics 211: Lecture 9, Pg 21
Lecture 9, Act 2 Work & Energy
Two blocks have masses m1 and m2, where m1 > m2. They are sliding on a frictionless floor and have the same kinetic energy when they encounter a long rough stretch (i.e. m > 0) which slows them down to a stop. Which one will go farther before stopping?
(a) m1 (b) m2 (c) they will go the same distance
m1
m2
Physics 211: Lecture 9, Pg 22
Lecture 9, Act 2 Solution
m
Physics 211: Lecture 9, Pg 23
Lecture 9, Act 2 Solution
m
Physics 211: Lecture 9, Pg 24
Lecture 9, Act 2 Solution
m
Physics 211: Lecture 9, Pg 25
A simple application: Work done by gravity on a falling object
What is the speed of an object after falling a distance H, assuming it starts at rest?
H
v0 = 0
Physics 211: Lecture 9, Pg 26
What about multiple forces?
Suppose FNET = F1 + F2 and the
displacement is r.
The work done by each force is:
W1 = F1 r W2 = F2 r
WTOT = W1 + W2
= F1 r + F2 r
= (F1 + F2 ) r
WTOT = FTOT r It’s the total force that matters!!
FNET
r F1
F2
Physics 211: Lecture 9, Pg 27
Comments:
Time interval not relevant
Run up the stairs quickly or slowly...same W
Since W = F r
No work is done if:
F = 0 or
r = 0 or
= 90o
Physics 211: Lecture 9, Pg 28
Comments...
W = F r
No work done if = 90o.
No work done by T.
No work done by N.
T
v
v
N
Physics 211: Lecture 9, Pg 29
Lecture 9, Act 3 Work & Energy
An inclined plane is accelerating with constant acceleration a. A box resting on the plane is held in place by static friction. How many forces are doing work on the block?
a
(a) 1 (b) 2 (c) 3
Physics 211: Lecture 9, Pg 30
Lecture 9, Act 3 Solution
a
Physics 211: Lecture 9, Pg 31
Lecture 9, Act 3 Solution
a
Physics 211: Lecture 9, Pg 32
EXTRA EXAMPLE 1
Return to ACT 2:
m
Physics 211: Lecture 9, Pg 33
EXTRA EXAMPLE 2a
Consider an inclined plane with no friction:
Physics 211: Lecture 9, Pg 34
EXTRA EXAMPLE 2a
Consider an inclined plane with no friction:
Physics 211: Lecture 9, Pg 35
EXTRA EXAMPLE 2b
Consider an inclined plane with friction:
Physics 211: Lecture 9, Pg 36
EXTRA EXAMPLE 2b
Consider an inclined plane with friction:
Physics 211: Lecture 9, Pg 37
EXTRA EXAMPLE 2c
Consider an inclined plane with friction:
Physics 211: Lecture 9, Pg 38
EXTRA EXAMPLE 2c
Consider an inclined plane with friction:
Physics 211: Lecture 9, Pg 39
Recap of today’s lecture
Work & Energy (Text: 6-1 and 7-4)
Discussion
Definition (Text: 6-1)
Work of a constant force (Text: 7-1 and 7-2)
Work/kinetic energy theorem (Text: 6-1)
Properties (units, time independence, etc.)
Work of a multiple forces
Comments