1. A spaceship A (at rest in inertial frame A) of proper length L, =75.0m is moving in the +x direction at a speed v= 0.650 c as measured in the Earth frame. Another spaceship B (at rest in inertial frame B) is moving on a parallel path in the opposite direction (-x) with u, =-0.720c as measured in the Earth frame. The two spaceships pass each other. a. What is the velocity and speed parameter of spaceship B in inertial frame A, u,,B' ? b. In inertial frame A, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? c. In inertial frame B, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? d. In the Earth frame, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?
1. A spaceship A (at rest in inertial frame A) of proper length L, =75.0m is moving in the +x direction at a speed v= 0.650 c as measured in the Earth frame. Another spaceship B (at rest in inertial frame B) is moving on a parallel path in the opposite direction (-x) with u, =-0.720c as measured in the Earth frame. The two spaceships pass each other. a. What is the velocity and speed parameter of spaceship B in inertial frame A, u,,B' ? b. In inertial frame A, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? c. In inertial frame B, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? d. In the Earth frame, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?
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![Special Relativity:
Reminder: if all the variables are measured in one consistent, properly synchronized inertial frame,
then the usual rules of kinematics apply:
Ax
V =
Δι
Ax'
Δxν Δ , Δ'v' Δ' etc .
At'
1
=; speed parameter: B=- y =
v?
Lorentz gamma factor: y =
Lorenz contraction: L=-L,;
Time dilation: At = yAt,
x' = r(x-vt)
x = 7(x' + vt')
y' = y
y = y'
Lorentz Transform:
z' = z
z = z'
Inverse Lorentz:
vx'
t = y| t'+
Vx
u +v
uy
u',
u'
Velocities: u̟ =
u. =
7[1+ (w; /e*)]'
1+(vu', / c²)'
1+(v/c)
1-(v/c)
r[1+(vď, I c°)]
1
Relativistic Doppler: f' =
f (approaching)
r(1-(v/c))
1-(v/c)
V1+(v/c)
1
Relativistic Doppler: f"
f (receding)
=
r(1+(v/c))
mū
и
pc
Momentum: p=
m is rest mass of particle;
u?
E
mc?
-mc?
v²
Kinetic energy: K =
Rest energy: E = mc?
mc²
Total energy: E = K+E, =
E² = p°c² +(mc²)?
ymc²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F84d0f3d8-91eb-4c63-9951-4d4796754d53%2Fbbbc6581-f581-4a56-b490-a4ed5bc5d227%2Fqsob3qs_processed.png&w=3840&q=75)
Transcribed Image Text:Special Relativity:
Reminder: if all the variables are measured in one consistent, properly synchronized inertial frame,
then the usual rules of kinematics apply:
Ax
V =
Δι
Ax'
Δxν Δ , Δ'v' Δ' etc .
At'
1
=; speed parameter: B=- y =
v?
Lorentz gamma factor: y =
Lorenz contraction: L=-L,;
Time dilation: At = yAt,
x' = r(x-vt)
x = 7(x' + vt')
y' = y
y = y'
Lorentz Transform:
z' = z
z = z'
Inverse Lorentz:
vx'
t = y| t'+
Vx
u +v
uy
u',
u'
Velocities: u̟ =
u. =
7[1+ (w; /e*)]'
1+(vu', / c²)'
1+(v/c)
1-(v/c)
r[1+(vď, I c°)]
1
Relativistic Doppler: f' =
f (approaching)
r(1-(v/c))
1-(v/c)
V1+(v/c)
1
Relativistic Doppler: f"
f (receding)
=
r(1+(v/c))
mū
и
pc
Momentum: p=
m is rest mass of particle;
u?
E
mc?
-mc?
v²
Kinetic energy: K =
Rest energy: E = mc?
mc²
Total energy: E = K+E, =
E² = p°c² +(mc²)?
ymc²
Transcribed Image Text:1. A spaceship A (at rest in inertial frame A) of proper length L, =75.0m is moving in the
+x direction at a speed v= 0.650c as measured in the Earth frame. Another spaceship
B (at rest in inertial frame B) is moving on a parallel path in the opposite direction (-x)
with u, =-0.720c as measured in the Earth frame. The two spaceships pass each
other.
a. What is the velocity and speed parameter of spaceship B in inertial frame A, u,,B' ?
b. In inertial frame A, how long does it take for the tip of spaceship B to move from the
tip of spaceship A to the tail of spaceship A?
c. In inertial frame B, how long does it take for the tip of spaceship B to move from the
tip of spaceship A to the tail of spaceship A?
d. In the Earth frame, how long does it take for the tip of spaceship B to move from the
tip of spaceship A to the tail of spaceship A?
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