Transcript Work and Energy

Work and Energy
WHY…?
• Curved paths (motion)
• Complicated motion is tough to
handle with just Newton’s Laws
Definitions and Units
• Contrary to what you might think, solving
word problems is no longer considered
“work” in this class, solving word problems
will hereafter be referred to as “play” or
“fun.”
• Work, physical work, is an energy
exchange, we will add it to a “system”…
Work and Energy
• Yes, we have equations for it…
• Work = Force times distance
– Or more appropriately the “dot” product of a
force vector and the displacement vector of
the object it acts on.
• What are the units?
Work and Energy
• Joules!
– You were probably thinking Newton’s times
meters, huh? You are correct, we just have a
special name for the units of work and energy.
• Since work is an energy exchange, they
both have the same units.
Work and Energy
• In the real world you can exchange dollars
for doughnuts, but in the physical world it’s
more like dollars for euros, yen, pounds(!)
etc.
– Work, kinetic, potential, heat, sound, light…
• Let’s look at the dot product a little more…
Work
 
Work  F d
F
q
d
Were interested in the component of force that actually moves the object
in the direction it goes. The other component, perpendicular to the
displacement, is “wasted.”
Work
 
Work  F d
Fcosq
Fsinq
F
q
d
Work
 
Work  F d
F
q Fcosq
d
Work
Workin  F d cos q
Yeah,
memorize this
one.
F
q Fcosq
d
Let’s Apply this puppy.
Tleash
angle
displacement
Puppy Pull
• Ok, 1 – 2- 3 go
• Tension in leash = 30 N
• Angle with ground = 30 degrees
• Displacement along the ground = 30
meters (this puppy is stubborn)
So what’s the work?
Work  F d cos q
W= 30 N x 30 m x cos(30) = 779 Joules
We did 780 joules of work on the puppy.
Energy
• So what is energy?
• The physical state of an object that gives it
the capacity to do work.
• Ok, brass tacks time…
Energy
• You can probably mention two types, maybe
more…
• Kinetic
– translational, rotational
• Potential
– gravitational, electrical, internal (temp)
• Let’s just do Translational Kinetic and
Gravitational Potential for now and save the
others for later in this course.
Kinetic Energy
1 2
KE  mv
2
Work and KE
Wnet  KE f  KEi
Work Kinetic energy theorem
Where’s this come from?
• Think back to
kinematics
v f  v0  2ad
2
2
mv f  mv0  2mad
2
2
1
1
2
2
mv f  mv0  mad
2
2
1
1
2
2
mv f  mv0  Fd
2
2
Apply!
• My truck is broken down, so you help me
push it. We give it a push of 300 Newtons,
parallel to the road, and quit after 20
meters. How much work did we do, on the
system (my truck)?
How fast is it going?
• Let’s ignore friction
right now. The mass
of the Miata is 750kg.
vf
Wnet
1
1
2
 mv f  mv0 2
2
2
2Wnet
2

 v0
m
Start from rest
Video Break!
•Big Truck
Energy
1 2
Kinetic Energy, KE  mv
2
Potential Energy, PE  mgh
Potential Energy
• Gravitational energy.
• Let’s think this one through. If I lift 100 N
one meter what work did I do?
• Yeah, 100 Joules
• How fast is it moving now? Yeah, nothin’
• What’s up? (besides the 100 N weight)
PE
• The energy went
somewhere, where?
• We say the weight
gained Potential
energy equal to the
change in vertical
position, altitude, or
height, times its
weight (the force it
took to get it there).
PE  mgh
Yep.
Work raising a weight
• How much work is done
raising a bucket from a
well?
– Bucket 10 kg
– Well 20 meters deep
• What work did the bucket
raiser person do?
• What work did gravity do?
W  PE f  PEi
W  ( PE f  PEi )
Conservative vs. Nonconservative forces
Conservative – we can get it back
So I lifted the 100N one meter, what happens
when I drop it?
It speeds up until it hits the ground.
The work transforms into KE of the weight, so
gravity is a conservative force.
Conservative vs. Nonconservative forces
Non-conservative
Think back to the puppy pull. Let’s make it a
box now, even though I did work on the box,
friction also did work on the box. Due to
Newton’s IIId law, friction did negative work on
the box!
What happens when we let go of the leash?
Will the box spontaneously spring back to where
it was? NO! Friction is non-conservative.
Con vs non
• Conservative forces store the energy
when you work against them. You can get
it back later.
– Gravity, electrical force, springs.
• Non-conservative Forces dissipate the
energy of work done against them. You
can’t get it back. It turns into; sound, heat
etc.
– Friction, airplane drag…
Enough!
• Let’s “play”
• Conservation of
mechanical energy
KE f  PE f  KE0  PE0
Yeah, this one too.
Block on a ramp
•
•
•
•
No friction
10 kg block is 10 meters up on an incline.
It starts from rest and slides to the bottom
How fast is it going at the bottom?
10 kg
10 meters
Fin.
• Questions??
Review
2
1
KE 
mv
2
Workin  Fd cos q
PE  mgh
Worknet  KE0  PE0  KE f  PE f
Power  work / time
P  Fv cos q
e  U / Workin