Transcript HONORS PPTX Format

Work & Energy
AP1 Ch7
Or, “Why don’t Taylor count
HomeWORK as WORK?”
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Nitty Gritty?

Definitions?
Work
A
force acting through a
displacement
W  Fd cos
Work → a force acting through a displacement
W  Fd
W  Fd cos
F

Fcos
Figure 7.3
(a)
(b)
A graph of F cos θ vs. d , when F cos
θ is constant. The area under the
curve represents the work done by
the force.
A graph of F cos θ vs. d in which the
force varies. The work done for each
interval is the area of each strip; thus,
the total area under the curve equals
the total work done.
Nitty Gritty?

Definitions?
Energy
Work
PE
PE  mgh
Why?
W  Fd
W  (ma)d
W  mgh  PEg
Nitty Gritty?

Definitions?
Energy
KE
1 2
KE  mv
2
Why?
W  Fd
W  mad
W  m(ad )
v v
W  m
 2

2
f
2
i




v 0
W  m
 2

2
f
v
W  m
 2

2
f
2
i





  KE


Figure 7.8
PEi
PE + KE
KEBot

The speed of a roller coaster increases as gravity pulls it downhill and is greatest at
its lowest point. Viewed in terms of energy, the roller-coaster-Earth system’s
gravitational potential energy is converted to kinetic energy. If work done by friction
is negligible, all ΔPEg is converted to KE .
Figure 7.9
PETop
KEBot

A marble rolls down a ruler, and its speed on the level surface is measured.
Figure 7.10
(b)
An undeformed spring has no PEs stored in it.
The force needed to stretch (or compress) the spring a distance x has a magnitude F = kx , and the work done to stretch (or compress) it
1
is 𝑘𝑥2
(c)
Because the force is conservative, this work is stored as potential energy (PEs) in the spring, and it can be fully recovered.
(d)
A graph of F vs. x has a slope of k , and the area under the graph is 𝑘𝑥2 . Thus the work done or potential energy stored is 𝑘𝑥2.
(a)
2
1
2
1
2
Figure 7.12

A toy car is pushed by a compressed spring and coasts up a slope. Assuming negligible friction,
the potential energy in the spring is first completely converted to kinetic energy, and then to a
combination of kinetic and gravitational potential energy as the car rises. The details of the path
are unimportant because all forces are conservative—the car would have the same final speed
if it took the alternate path shown.
Figure 7.15

(a)
(b)
Comparison of the effects of conservative and nonconservative forces on the mechanical energy of a system.
system with only conservative forces. When a rock is dropped onto a spring, its mechanical energy remains constant (neglecting air
resistance) because the force in the spring is conservative. The spring can propel the rock back to its original height, where it once again
has only potential energy due to gravity.
A system with nonconservative forces. When the same rock is dropped onto the ground, it is stopped by nonconservative forces that
dissipate its mechanical energy as thermal energy, sound, and surface distortion. The rock has lost mechanical energy.
Figure 7.16

A person pushes a crate up a ramp, doing work on the crate. Friction and
gravitational force (not shown) also do work on the crate; both forces oppose the
person’s push. As the crate is pushed up the ramp, it gains mechanical energy,
implying that the work done by the person is greater than the work done by friction.
Figure 7.19
PETop
KEBot

Rolling a marble down a ruler into a foam cup.
Figure 7.19
MVTotal

MVBall
Rolling a marble down a ruler into a foam cup.
Figure 7.33
Figure 7.35

A man pushes a crate up a ramp.
Figure 7.36


The boy does work on the system of the wagon and the child when he
pulls them as shown.
Figure 7.37

A rescue sled and victim are lowered
down a steep slope.
Figure 7.40


The skier’s initial kinetic energy is partially used in coasting to the top of a
rise.
Nitty Gritty?

Definitions?
Energy
PE
in Spring
1 2
PE  kx
2
W
W  Fd
Fd
F f  Fi
W
d
2
1
1
W  Fd  kxx
2
2
Work & Energy
-Pt
2
Or, “Why don’t Taylor count
HomeWORK as WORK?”
PE = mgh
M
h
PE = mgh
M
h
PE = mgh
M
h
PE = mgh
PE + KE
M
h
PE = mgh
PE + KE
h
M
PE = mgh
PE + KE
h
M
PE = mgh
PE + KE
h
KE
M
PE = mgh
PE + KE
h
KE
M
PE = mgh
PE + KE
h
KE
M
h
P  K
1 2
mgh  mv
2
v  2 gh
M
PE
PE
KE

L
PE
PE
h
KE

L
PE
PE
h
h  L(1  cos  )
KE
t
t
d h  vh t
2d
g
2H
d h  2 gh
g
2H
g
4 ghH
dh 
g
vh
d h  2 hH
H
dh
t
t
E

E
Top
Bottom
d h  vh t
2d
g K Top  PTop  K Bot  PBot
2H
d h  2 gh
2 H1 mv 2  mgh  1 mv 2  0 g
Top
Bot
2
g2
4 ghH
vh
dh 
g
d h  2 hH
H
dh
BATMAN!
Power!
Or “What
the heck does a
horsepower have to do with
a horse”?
W
W  E
P
t
E
P
t
E
P
t PE
P
t
mgh
P
t
I thought this was
PHYSICS, not
PhysEd!
D
h
mgh
P

t
 s (m)
m
(kg)
2
sec
What’s this unit?
N m J
P
 W
s
s
Advanced Shtuff?
b

W  F cos  dl
So,
a
b
W 

Fdx
a
x

1 2
W  kxdx  kx
2
0
Advanced Shtuff?
Conversely;
dW
F ( x)  
dx
r2
r2
M 1M 2
W   Fg dr   G
dr
2
r
r1
r1
Advanced Shtuff?
r2
1
W  GM1M 2  2 dr
r
r1
Advanced Shtuff?
GmM E
W
 PEg
r
Advanced Shtuff?
dE
dx
P
F
 Fv
dt
dt
Momentum
Ch8
Or, “How to make Newton’s Laws
even more complicated without
even trying…”
Daryl L Taylor
Greenwich HS, CT
©2004, 2006, 2007, 2009, 2012 (Just in case…)
Nitty Gritty?

Definitions?
‘member
FMA?
F  ma
F  ma
v
F m
t
Impulse
Latin impulsus, from past participle
of impellere, to impel
Impel: See impulse…
Ft  mv
Ft  mv
Momentum
Latin mōmentum, movement
Nitty Gritty?

Definitions?
P
Conservation
Pi  Pf
m1v1  m2 v2 
'
m1v1
Why?
'
 m2 v2
NL3
F1  F2
m1a1  m2 a2
m1v1
m2 v2

t
t
m1v1  m2 v2
POP
QUIZ;
#1
2-D Momentum

Momentum is a linear vector
1   2
m1v1  0  0  m2 v2
2-D Momentum

Angles?
m1v1i
2-D Momentumm v
2 2f

Angles?

m1v1i

m1v1f
2-D Momentumm v
2 2f

Angles?

m1v1i

m1v1f
POP
QUIZ;
#2
2.5 m/s
Figure 8.6

An elastic one-dimensional twoobject collision. Momentum and
internal kinetic energy are conserved.
Figure 8.8

(a)
(b)
An inelastic one-dimensional two-object collision. Momentum is conserved, but internal kinetic energy is not
conserved.
Two objects of equal mass initially head directly toward one another at the same speed.
The objects stick together (a perfectly inelastic collision), and so their final velocity is zero. The internal kinetic
energy of the system changes in any inelastic collision and is reduced to zero in this example.
Figure 8.10

An air track is nearly frictionless, so that momentum is conserved. Motion is onedimensional. In this collision, examined in Example 8.6, the potential energy of a
compressed spring is released during the collision and is converted to internal
kinetic energy.
Figure 8.11

A two-dimensional collision with the coordinate system chosen so that m2 is initially at rest and
v1 is parallel to the x -axis. This coordinate system is sometimes called the laboratory coordinate
system, because many scattering experiments have a target that is stationary in the laboratory,
while particles are scattered from it to determine the particles that make-up the target and how
they are bound together. The particles may not be observed directly, but their initial and final
velocities are.
Figure 8.12

A collision taking place in a dark
room is explored in Example 8.7. The
incoming object m1 is scattered by an
initially stationary object. Only the
stationary object’s mass m2 is known.
By measuring the angle and speed at
which m1 emerges from the room, it
is possible to calculate the magnitude
and direction of the initially stationary
object’s velocity after the collision.
Figure 8.16

A small object approaches a collision with a much more massive cube, after which
its velocity has the direction 𝜽1. The angles at which the small object can be
scattered are determined by the shape of the object it strikes and the impact
parameter 𝒃 .
Types of Collisions;
Elastic

AND KE are conserved
i   f
KEi  KE f
Types of Collisions;
Inelastic

ONLY are conserved
i   f
POP
QUIZ;
#3
MV & cm
 cm
 Center
 NOT
(cg)
of Mass
to be confused with Center of Gravity
vcm
mv

m
MV & cm
 cm
 Examples
MV & cm
 Cm
 Examples
MV & cm
 cm
MV & cm

Cm – Hume Beans
Bending over
 Sitting
 Standing
 Walking
 One-Leg Lift (Wall & Free-standing)
 Butt against wall – Touch toes
 Chair pick-up
 Babies vs Adults

 Head
size – ¼ vs 1/8
MV & cm
 Cm
– Hume Beans
 Wile
E. Coyote Video
 m-stick and hat
 Rolling UP HILL demo
mx
xcm 
m
mv
vcm 
m