PRETEST:
1.
MEASUREMENT
A straight runway is 100 m long. A small explosion occurs at the east end of the runway; 10 seconds later, an
explosion occurs at the west end of the runway. An airplane moves from west to east with speed 25 m/s relative
to the runway.
How far apart in space are the locations of the explosions:
2.
•
in the frame of the runway? Explain.
•
in the frame of the airplane? Explain.
Two spaceships, A and B, pass very close to each other. Alan is in the front of ship A, and Beth is in the front of
ship B. Andy and Becky are at rest at the backs of ships A and B respectively. In Alan’s frame, ship B moves
with speed v = 3 m/s and ships A and B each have length l2 m.
Define events 1,2, and 3 as follows:
Beth
Event 1: Alan and Beth are adjacent
Event 2: Andy and Beth are adjacent
Event 3: Alan and Becky are adjacent
The diagram at right represents the ships at the
instant of event 1 in Alan’s frame.
Becky
Ship B
Ship A
Andy
Alan
Determine numerical values for the following
( Alan)
ratios, in which the subscripts refer to the events defined above. Use the notation ! x12
= x2(Alan) " x1( Alan) = the
( Alan)
(signed) distance between the locations of events 1 and 2 in Alan’s frame. Signed means ! x12
can be either
positive or negative. Explain your reasoning.
! x12(Beth)
! x12(Alan)
! x13(Alan)
! x13(Beth)
Adapted from Scherr Thesis, U. Wash. Tutorials p.1
MEASUREMENT
A.
A train moves with constant nonrelativistic speed along a straight
track. The train is 12 meters long.
Becky
Beth
Alan and Andy stand 12 meters apart at rest on the track (see
figure). Beth and Becky stand at rest at the front and rear of the
train, respectively.
Define events 1, 2, and 3 as follows:
Event 1: Alan and Beth pass each other.
Event 2: Andy and Beth pass each other.
Event 3: Alan and Becky pass each other,
1.
Andy
On a large sheet of paper, sketch an event diagram showing Alan, Andy, Beth, and Becky at the instants of
events 1, 2, and 3 in Alan’s frame. (That is, sketch a separate picture for each different instant; sketch pictures
for successive instants one above the other; and indicate the location of each event on the appropriate picture.)
a.
What feature(s) of your event diagram can be used to indicate that it is a diagram for Alan’s frame?
b.
How would an event diagram for Andy’s reference frame compare to the one you drew above? Explain.
c.
What procedure could Alan (or Andy) follow to measure the distance between the locations of events 1
and 2?
d.
How far apart in space are the locations of the following pairs of events in Alan’s frame?
•
•
•
2.
Alan
Events l and 2
Events 2 and 3
Events 1 and 3
Sketch an event diagram showing events 1, 2, and 3 in Beth’s frame. Be sure your diagram correctly represents
the motion of the train in this frame.
How far apart in space are the locations of the following pairs of events in Beth’s reference frame?
•
•
•
Events 1 and 2
Events 2 and 3
Events 1 and 3
Adapted from Scherr Thesis, U. Wash. Tutorials p.2
3.
How does Beth’s procedure for measuring the distance between the positions of two events compare to Alan’s
procedure?
4.
On the basis of your answers above, develop a general rule that uses an event diagram to determine how far
apart the locations of two events are in a given reference frame.
( Alan)
Remember that the symbol ! x12
indicates the spatial separation between events 1 and 2 as measured in Alan’s
( Alan)
reference flame. So ! x12
= x2(Alan) " x1( Alan) where x1( Alan) and x2(Alan) are the positions of events 1 and 2 in Alan’s
reference frame. Note that the spatial separation between events is a signed quantity (it may be positive or negative).
B.
Give interpretations for the magnitude of each of the following quantities; that is, tell the meaning of the
number in this physical context. One has been provided as an example. Some quantities may have more than
one interpretation.
! x12(Alan) The displacement of Beth (or the displacement of
the train) as measured by Alan (or Andy)
! x12(Beth)
! x13(Alan)
! x13(Beth)
( Alan)
! x23
( Beth)
! x23
Adapted from Scherr Thesis, U. Wash. Tutorials p.3
C.
A train of unknown length moves with constant nonrelativistic speed on the same track. Alan and his
assistants stand shoulder-to-shoulder on the track.
1.
Describe a method by which Alan can determine the length of the train in his frame if he knows the speed of
the train in his frame. Specify two events associated with this measurement procedure.
Event a:
Event b:
2.
Describe a method by which Alan can determine the length of the train in his frame without knowing or
measuring its speed first. Specify two events associated with this measurement procedure.
Event c
Event d:
D.
Suppose event 4 occurs at the front of a long ship, and event 5 occurs at the rear of the same ship. Describe
(??)
the circumstances in which the absolute value of ! x45
is equal to the length of the ship:
• in the frame S in which the ship is at rest
• in frame F, in which the ship is moving
Draw event diagrams to support your answers.
Adapted from Scherr Thesis, U. Wash. Tutorials p.4