Fri.,
6.5-.7 (.22) Rest Mass,Work by Changing Forces RE 6.b
Wed. 6.8-.9(.18, .19) Introducing Potential Energy
Lab The Things Physicists & Engineers Do
Fri. 6.10-.13 (.20) Gravitational P.E. & Visualizing
Mon. 6.14-.17 Electric and Rest Energy
Tues.
(last day to drop)
RE 6.c
RE 6.d
RE 6.e
EP6, HW6: Ch 6 Pr’s 58, 59, 91,
99(a-c), 105(a-c)
motion is neither created nor destroyed, but transferred via interactions.
f
Energy
f mc
i mc
2
all
1
1
2
v
c
2
E W
i

F
sys

drsys
Work
Work Example: Work with Angle
A kid pulls a sled at a constant speed by a rope at a 45 angle across ice for 10 m. If
she pulls with an 11.5 N force, How much work does she do on the sled?
System: Sled
| Fsled


Fsled rope drsled
i

Fsled rope rsled
f
rope | 11.5 N
initial
Wsled
rope
Wsled
rope
final

rsled
10m xˆ
Recall
W
or

F

r
Fx x Fy y Fz z

F

r

F

r cos
Wsled
rope

| Fsled
Wsled
rope
11.5 N 10m cos 45
Wsled
rope
rope
F
r
|| rsled | cos
81.3 Nm 81.3 J
Particle Energy: Kinetic and Rest
E
mc
2
1
where
1
When at rest, v = 0, so
Erest
2
v
c
= 1.
mc 2
Kinetic Energy = energy associated with motion: total - rest
K
E Erest
1 mc 2
K
1
for, v<<c,
so,
Or, rephrased, Total = Kinetic + Rest
E
K
Erest
K
1
2
mv 2
1
2
v
c
2
Consider an electron (mass 9e-31 kg)
moving with speed v = 0.9c. Its rest
energy is 0.81e-13 J, and its (total)
particle energy is 1.86e-13 J. What is
its kinetic energy?
1) 7.3e-31 J
2) 3.28e-14 J
3) 8.1e-14 J
4) 1.05`e-13 J
5) 1.86e-13 J
Rest Energy and Identity
Example: A stationary nucleus whose mass is 3.499612 10-25 kg undergoes
spontaneous “alpha” decay. The original nucleus spits out a He-4 nucleus (2
neutrons & 2 protons) of mass 6.640678 10-27kg and the remaining nucleus has
a mass of 3.433132 10-25kg. When the particles are far apart (so the electric
repulsion is negligible) what is the combined kinetic energy?
initial
final
parent nucleus
daughter nucleus
System: these particles
Active surroundings: none
E W
0
K
0
Erest
or
Kf
K
Erest
Ki
Erest . f
Kf
mpc2
Kf
349.9612
Kf
7.322 10
particle
Erest .i
md
m c2
343.3132 6.640678
30
kg c 2 6.59 10
13
J
10
27
kg c 2
Energy Units of Chemical / Nuclear Reactions
initial
final
parent nucleus
Kf
7.322 10
daughter nucleus
30
kg c
2
particle
6.59 10
13
J
All chemical interactions are fundamentally electric interactions, so involve
electric force and scale with electron charge.
1Joul 1Joul
1e
1.6 10 19 Coulombs
6.25 1018 e
J
C
6.25 1018 eV
Volt
Joul
Coulombs
Chemical reactions typically involve around 1eV of energy per molecule
Kf
6.59 10
13
J
6.25 1018 eV
1J
4.12 106 eV
4.12MeV
A nuclear reaction involves millions of times more energy than does Chemical reaction!
Work – Energy Relation
You drop a metal ball from 1 m up. How fast is it going just before it hits the
ground?
E W
W
System= ball
Active members of
environment = Earth
(neglecting air’s resistance)

FBall
Earth
final

vf
?
mgyˆ
f
Earth

FBall
Earth

drBall
i
WBall
y yˆ
y 1m
Earth
Constant force, so
initial

rball
WBall
WBall
Not
changing
Erest
K
Kf
Ki
WBall
WBall
E
E
1
2
mv 2f
E
1
2
mv 2f
mg y
vf
Earth
Earth
Earth

FBall
Earth
mg yˆ
mg y
Pretty sure v<<c, so K
WBall
2g y
Earth

rBall
y yˆ
1
2
mv 2
mg y
2 9.8 m s 2 1m
4.4 m s
If we throw the ball up at 5m/s, will
1) greater
have greater, less, or the same speed 2) less
when it lands?
3) The same
Work – Energy Relation
Slight variation: You throw a metal ball straight up at 5m/s from 1 m up. How
fast is it going just before it hits the ground? What changes in our solution?

vi
5 m s yˆ
E W
W
System= ball
Active members of
environment = Earth
(neglecting air’s resistance)

FBall
y yˆ
y 1m
Earth
1
2
?
Erest
K
Kf
Ki
m v 2f12 mv
vi22f
11
22
mv
mv2f2f
vf

FBall
Earth

drBall
i
Not
changing
mgyˆ
f
Earth
WBall
final

vf
Earth
Constant force, so
initial

rball
WBall
WBall
Earth
WBall
WBall
E
E
Earth
Earth

FBall
Earth
mg yˆ
mg y
Pretty sure v<<c, so K
E
WBall
mg
mg yy
1
2
Earth
mg y
mvi2
2 g y vi2
6.7 m s

rBall
y yˆ
1
2
mv 2
If we throw the ball down at 5m/s,
will have greater, less, or the same
speed when it lands compared with
what it had in when thrown 5m/s up?
1) greater
2) less
3) The same
Work – Energy Relation
Another Slight variation: You throw a metal ball straight down at 5m/s from 1 m
up. How fast is it going just before it hits the ground? What changes now?

vi
E W
W
5 m s yˆ
System= ball
Active members of
environment = Earth
(neglecting air’s resistance)

rball

FBall
y yˆ
y 1m
Earth
1
2

vf
?
Earth
f
Earth

FBall
Earth

drBall
i
Constant force, so
WBall
Not
changing
mgyˆ
WBall
WBall
Erest
K
Kf
Ki
m v 2f
vi2
1
2
mv 2f
vf
WBall
WBall
E
E
Earth
Earth
Earth

FBall
Earth
mg yˆ
mg y
y yˆ
Pretty sure v<<c, so K
E
WBall Earth
mg y 12 mvi2
2
i
2g y v

rBall
1
2
mv 2
mg y
6.7 m s
Nothing
Changes!
Systematic Approach to Energy Problems
1)
2)
3)
4)
5)
6)
7)
8)
Specify a system (the object or object’s you’re interested in)
Specify members of the surrounding that interact with the system
Specify the initial state
Specify the final state
Write out the Energy Principle for this system
Use the given information to evaluate all terms you can
Solve for the target unknown quantity
Check units and consistency of sign.
Work – Energy Relation
Example: An electron (mass 9e-31 kg) is traveling at a speed of 0.95c in an electron
accelerator. Over what distance would an electric force of 1.6e-13 N have to be applied to
accelerate it to 0.99c?

vi
0.95c yˆ System= electron
E W
Active members of
environment = Accelerator
f
mc
2
i
mc
2
initial
i
f

Fe

re
1.6 10
13
1
y
0.99c yˆ
f
N yˆ
1
y

vf
i
? yˆ
accelerator
final
 
F dr
f
37 m
0.99
i
mc 2
mc 2
F
1
2
1
0.95
F y
2
1
1
y
9 10
where
31
8
v 2
c
kg 3 10 m / s
1.6 10 13 N
2
Work by Changing Force
W

F1

r1

F2

r2

F3

r3

.... F20

r20
20
i 1
final
W
lim

r
0
initial

F

r
fin
init
 
F dr

F

r
Work by Changing Force
Spring
final
W
lim

r
0
initial

F

r
fin
 
F dr
init
f
W
k s x dx
i
2 f
W
1
2
ks x
W
1
2
k s x 2f
i
xi2
In an up-coming lab, you’ll use a spring-loaded gun to fire a metal ball. If we
know the ball’s mass, the stiffness of the spring and how much it’s been
stretched, then we should be able to predict where the ball will hit the ground.
Say the spring is initially compressed by 0.04m, and when it launches the ball it
stretches to a compression of 0.01m; if the ball is 0.05kg and the gun is
mounted 0.8m above the ground, then how far over will the ball hit the ground?
va=0
(a)
vb
(b)
(c)
Let’s say the Wizard of Oz’s balloon has a total mass of 1000 kg (including the
Wizard in the basket) and has most of its volume in the balloon which has a radiu
of 10 m. If the Scarecrow, whose mass is 50 kg (he is only made of straw after al
grabs a hold, when it starts lifting off, how fast will it be going when it gets 3 m up
at which point the Scarecrow lets go and drops?
Recall that air has a density of 1.3 10-3 g / cm3.
Fri.,
6.5-.7 (.22) Rest Mass,Work by Changing Forces RE 6.b
Wed. 6.8-.9(.18, .19) Introducing Potential Energy
Lab The Things Physicists & Engineers Do
Fri. 6.10-.13 (.20) Gravitational P.E. & Visualizing
Mon. 6.14-.17 Electric and Rest Energy
Tues.
(last day to drop)
RE 6.c
RE 6.d
RE 6.e
EP6, HW6: Ch 6 Pr’s 58, 59, 91,
99(a-c), 105(a-c)
motion is neither created nor destroyed, but transferred via interactions.
f
Energy
f mc
i mc
2
all
1
1
2
v
c
2
E W
i

F
sys

drsys
Work