Chapter 39Serway & Jewett 6th Ed.

Fig 39-1a, p.1246

Fig 39-1b, p.1246

Fig 39-3, p.1248

Comparing Stationary and Moving Mirrors

Latticework of Clocks

Send out light pulse from reference clock at t = 12 noon

Nearest neighbors will see the pulse at ns 33103.3m 1 9 .sc

t

Set time to noon + 3.3 ns …

The Pole-Barn Paradox

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

The pole-barn paradox is a famous one which must be addressed with the ideas of simultaneity in relativity. The fact that two events are simultaneous in one frame of reference does not imply that they are simultaneous as seen

by an observer moving at a relativistic speed with respect to that frame.

The Pole-Barn Paradox

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

For

bidd

en R

egio

n Forbidden R

egion

O

ct

z

ct =

zct = z

AllowedPast

AllowedFuture

World LineLight Cone

For

bidd

en R

egio

n Forbidden R

egion

O

ct

z

ct =

zct = zLight Cone

World Line

Muon Experiment: Nonrelativistic

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

Muon Experiment: Relativistic Earth Frame

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

Muon Experiment: Relativistic, Muon Frame

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

Muon Experiment: Comparison

In the muon experiment, the relativistic approach yields agreement with experiment and is greatly different from the non-relativistic result. Note that the muon and ground frames do not agree on the distance and time, but they agree on the final result. One observer sees time dilation, the other sees length contraction, but neither sees both.

Time in terms of

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

Twin Paradox

The story is that one of a pair of twins leaves on a high speed space journey during which he travels at a large fraction of the speed of light while the other remains on the Earth. Because of time dilation, each will see the others clock running more slowly. Which twin will be older when the traveling twin returns to Earth?

From Hyperphysics: http://hyperphysics.phy-astr.gsu.edu

Is this real? Would one twin really be younger?

Before Photon Emitted   

Center of Mass for a discrete distribution:

For a continuous distribution:

where = mb/l.

 

0

b

ii

i

iicm m

xm

m

xmX

02

12

2

22

22

2

2

2

l

l

l

ll

l

l

lcm l

xxdx

ldx

xdxX

l

Before Photon Emitted

 

x

cm

Ec

Em

b

b

v

v

c

l

mc

E

tx v

After Photon Absrobed

mlxmb The center of mass doesnot move if !

Photon transfers mass m from one side of car to the other!

2mcE