Example Problems for Ch. 37 Part 1

1
Example Problems for Ch. 37 Part 1
2
Problem 37.7

• A spacecraft flies away from the earth with a
  speed of 4.80 x 106 m/s relative to the earth and
  then returns to the earth at the same speed. The
  space craft returns to the earth 365 days later
  as measured by an atomic clock on the earth. If
  there is an atomic clock on the spaceship which
  was previously synchronized to the clock on the
  earth, what is the difference in elapsed times as
  measured by the two clocks? Which clock shows the
  smallest elapsed time?

3
Convert to fraction of c

• This is the easiest way to deal with the radical
  sign.
• 4.80 x 106 m/s / 3 x 108 m/s is 0.016 so
• v1.6c

4
This is a time dilation problem

• In our case, we must determine which clock
  measures proper time
• The clock is at rest on the moving spaceship
• So Dt365 days
• So now solve for Dt0 using u1.6c

5
Substituting

• So Dt365 days
• So now solve for Dt0 using u1.6c

6
Problem 37.13

• A space craft of the Trade Federation flies past
  the planet Coruscant at a speed of 0.600c. A
  scientist on Coruscant measures the length of the
  moving space craft to be 74 m. The spacecraft
  later lands on Coruscant and the scientist now
  measures the length of the now stationary
  spacecraft. What value does she get?

7
This is a length contraction problem

• L0 is the proper length
• L74 m
• u0.6c

8
Problem 37.23

• An imperial spaceship moving at high speed
  relative to planet Arrakis, fires a rocket toward
  the planet with a speed of 0.920c relative to the
  spaceship. An observer on Arrakis measures that
  the rocket is approaching with a speed of 0.36c.
• What is the speed of the spaceship relative to
  Arrakis?
• Is the spaceship moving towards or away from
  Arrakis?

9
Draw It!
vx0.36c
u
vx0.92c
Arrakis
10
Must solve for velocity, u
Since u