Transcript Relativity III - Momentum

Relativity III
Momentum:
Prior to 1905 (Newton’s momentum)…
p = mv
or
x
p = m
t
Relativity III - Momentum
After 1905 (with relativity)…
p = m
x
to
Where to (proper time) is the time to travel
x as measured by someone traveling with
the object.
Relativity III - Momentum
Remember (from yesterday)…
Δt =
Δto
v
1c
Δto = Δt
2
v
1c
substituting into momentum equation…
p = m
x
v
Δt 1 c
2
2
Relativity III - Momentum
x
p = m
t
p =
1
v
1c
mv
v
1c
2
2
This is the momentum
for objects moving at
high speeds.
* Note that if the speeds are very slow (v << c),
the equation becomes old fashion momentum.
Relativity III - Momentum
p =
mv
v
1c
2
● As the speed of an object approaches the speed of
light, the momentum approaches infinity.
● An object with mass has infinite momentum at the speed
of light.
● Therefore, the force required to get an object with mass
from rest to the speed of light…
p
pf - pi
F = t = t
=
∞-0
t
=
∞
t
=
∞
Relativity III
Mass-Energy:
Prior to 1905…
There are two separate conservation laws that
deal with mass and energy.
a) Law of Conservation of Mass
b) Law of Conservation of Energy
Relativity III - Mass-Energy
After 1905 (with relativity)…
There is now one conservation law that deals
with mass and energy.
Law of Conservation of Mass-Energy
In the sun \ stars and in nuclear reactions,
energy is given off because mass is converted
into energy.
Relativity III - Mass-Energy
The amount of energy in an object that is not
moving is called its mass energy of rest energy.
This is the energy that an object has simply
because it has mass.
rest energy → Eo = m c2
Object
Mass
Rest Energy
Electron
9.11 x 10-31 kg
8.19 x 10-14 Joules
Uranium atom
3.95 x 10-25 kg
3.55 x 10-8 Joules
U.S. Penny
3.1 x 10-3 kg
2.8 x 1014 Joules
(~78,000,000 kW∙h)
Relativity III - Mass-Energy
Assuming* no potential energy, the Total Energy
of an object really is…
E = Eo + K
*
E = m c2 + K
●
●
●
E =
m c2
v
1c
2
This is a valid assumption
since the magnitudes of
potential energy are so
very small compared to
the rest energy or the
kinetic energy.
Relativity III - Mass-Energy
Assuming no potential energy, the Kinetic
Energy of an object really is…
K = E - Eo
K =
m c2
v
1c
K = m
c2
- m c2
2
1
v
1c
-1
2
Relativity III - Mass-Energy
relativistic
K
classical
0
0
0.2
0.4
0.6
v/c
0.8
1.0
Relativity III
Mr. O’s final thought
for the class:
This is why everyone
should know the
basics of physics…
Relativity III