A spaceship of proper length Lo = 54.0 m is moving relative to the Earth in the +x direction at a constant velocity with a speed parameter ß=0.9750. (Hint: The proper length of an object is measured in the rest frame of that object.) The tip of the spaceship crosses the origin (x = 0) at t = 0 in the Earth frame and at t', =0 in the frame of the moving spaceship. A A What is the length of the moving spaceship, L , in the Earth frame? b. At what time in the Earth frame does the tail of the spaceship pass the Earth frame origin, tR а.
A spaceship of proper length Lo = 54.0 m is moving relative to the Earth in the +x direction at a constant velocity with a speed parameter ß=0.9750. (Hint: The proper length of an object is measured in the rest frame of that object.) The tip of the spaceship crosses the origin (x = 0) at t = 0 in the Earth frame and at t', =0 in the frame of the moving spaceship. A A What is the length of the moving spaceship, L , in the Earth frame? b. At what time in the Earth frame does the tail of the spaceship pass the Earth frame origin, tR а.
Related questions
Question
Please answer parts d, e, and f
Transcribed Image Text:6.
A spaceship of proper length L, = 54.0 m is moving relative to the Earth in the +x
direction at a constant velocity with a speed parameter ß= 0.9750. (Hint: The proper length
of an object is measured in the rest frame of that object.) The tip of the spaceship crosses the
origin (x = 0) at t = 0 in the Earth frame and at t, =0 in the frame of the moving spaceship.
What is the length of the moving spaceship, L , in the Earth frame?
a.
b.
At what time in the Earth frame does the tail of the spaceship pass the Earth frame origin, tR
с.
At what time in the frame of the moving spaceship does the tail of the spaceship pass the
Earth frame origin, t, ?
В
d. If, in the spaceship frame, a laser is fired from the tip of the spaceship at time t', = 0 (in the
spaceship frame), when in the spaceship frame, does the light from the laser reach the tail of
the spaceship, t. ?
е.
For the laser described in part d., when in the Earth frame does the laser light reach the tail
of the spaceship, t,?
f.
In the Earth frame, where is the tail of the spaceship, x, , when the laser beam reaches the
tail at time t. ?
Transcribed Image Text:Waves in general:
FORMULA PAGE 1
a y
1-dimensional wave equation:
1 a'y
; here v is the speed of the wave
v? ôt?
Solution: f(x- vt) or f(x+vt)
Harmonic or sinusoidal waves: y(x,t)= Asin(kx- ot)
2л
k
2n
= 27f; v=-
T
v = f2
General Constants:
-34
h = 6.626×10*J.s = 4.13567×10¬eV ·s ; (with recent revisions to the SI system of
units Planck's Constant is defined to have an exact value: h= 6.62607015×10¯“J·s)
–34
-19
hc = 1240 eV · nm; hc=1239.84eV · nm (for more accuracy); leV =1.6022×10-J
= 299,792, 458 m /s (exact);
-31
electron mass: m, =9.1094×10' kg
proton mass: m,
=1.6726×10-27 kg
Photons: E = hf
hc
; Protons: m,c² = 938.3MEV , Electrons: m.c² = 511.0keV
%3|
h
= 1.0546x10 34J•s = 6.5821×10-1eV ·s
Chapter 36. Diffraction
Single slit diffraction:
Minima:
a sin 0, = ma, m=1,2,3,...where a is the slit width, note: there is a maximum at
0 = 0
sin(a)
па
Intensity:
I(0) = ,,
a =
-sin(0)
m
a
Circular aperture: First minimum: sin 0 = 1.22-
Rayleigh's criterion ( 1 <d ): a =1.22-
d
Double slit experiment with slit separation d and slit width a:
sin a
Intensity: I(0) = I„(cos? B)|
where
B =
-sin 0 , a =
па
-sin O
Grating equation (normal incidence): d sin 0 = m
order in which the grating is being used, d is the line or groove spacing
m
= 0,1, 2,3,... (maxima), where m is the
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