AP Physics Chp 28

• Event – physical occurance

• Reference Frame – x,y,z axes and time

• Inertial reference frame a=0 and Fnet =0

• Postulates of Special Relativity• 1) Laws of Physics are constant in every

inertial reference frame

• 2) Speed of light in a vacuum is c regardless of how fast the source and/or observer are moving relative to each other

• Absolute velocity?

• Luminiferous Ether

• Time Dilation

• ∆to is the observers time that is at “rest”• ∆t is the time for observers that are in motion

compared to the “event”• v is the relative velocity between the two

observers• c is 3.00 x 108 m/s

2

21o

vt t

c

• Length contraction

• Lo is the proper length – distance at rest with object

• Only in direction of motion

• Proper doesn’t mean “correct” or “absolute”

2

21o

vL L

c

• If you fly to Mars at 0.8 c and it takes 182 seconds to get there for those on the spaceship, how long does it seem for us left on earth? And if the ship is 1500 m long what length would it appear while moving?

2

21o

vt t

c

2

2

(0.8 )182 1

cs t

c 303t s

2

21o

vL L

c

2

2

(.8 )1500 1

cL m

c

900L m

• Relativistic Momentum

• p= mv for low velocity situations

2

21

mvp

vc

• Energy

• Eo=mc2 this is the rest energy

2

2

21

mcE

vc

• E = KE + Eo

• KE = E - Eo

22 2

2 2

2 2

11

1 1

mcKE mc mc

v vc c

• A change in energy causes a change in mass.

• Often it is too small to notice.

• Total Energy and Momentum

• E2 = p2c2 + m2c4

• Why is c the maximum? KE vs work

• Relative and Relativistic Velocities

• Tossing a ball from a moving vehicle

• Vab = Vac + Vbc Ex. 22 m/s + 5 m/s = 27m/s

• Velocity addition formula

21

ac cbab

ac cb

v vv

v vc

• If the large haldron collider can get a proton up to 0.9999c what is the classical momentum and what is the relativistic momentum for the proton?

• Classical• p = mv = 1.67x10-27Kg (0.9999) 3x108m/s• p = 5.01 x 10-19 Kgm/s

• Relativistic

• p= 3.5x10-17 Kgm/s so momentum is greater

27

2 2

2 2

(1.67 10 )(0.9999 )

(0.9999 )1 1

mv x cp

v cc c

• What are the rest energy, total energy, and kinetic energy for the accelerated proton?

• E0 = mc2 = (1.67x10-27Kg)(3x108m/s)2

• E0 = 1.44x10-10 J

27 28

2 2

2

1.67 101.06 10

0.99991

x cE x J

cc

• KE = E-E

• KE = 1.06x10-8 J - 1.44x10-10 J = 1.05 x 10-8 J