In-class Assignment for Chapter 1 Name: _______Key_________
Chuck and Dean agree to do three more runs with
the 100 foot bus so that Anne and Bev can collect more data. On these three runs, the pigeon flies from
the back, where Chuck is located, to the front and immediately turns around and
flies back to Chuck. The pigeon flies at
its usual 20 ft/s but the speed of the bus is 10 ft/s for the first run and
then is increased to 20 ft/s and 30 ft/s for the next two runs.
Bev is positioned at just the right spot to be
next to Dean just as the pigeon arrives and turns around. (For our purposes, the pigeon can change its
velocity from +20 ft/s to -20 ft/s “instantaneously.”)
Your mission is to draw three space and time
diagrams, one for each of the experiments.
All the experiments begin when Chuck is adjacent to Anne and the pigeon
begins its trip. The experiments end
when the pigeon gets back to Chuck.
The space and time diagrams are to be drawn from
the perspective of Anne and Bev.
1.
How long does experiment 1 last? 10
seconds_____
How long does experiment 2
last? 10 seconds_____
How long does experiment 3
last? 10 seconds
____
2.
At the end of the exp 1, how far to the
right of Anne is Dean? _200 ft___
At the end of the exp 2, how far
to the right of Anne is Dean? _300 ft___
At the end of the exp 3, how far
to the right of Anne is Dean? _400 ft___
3.
In the 1st exp, how far to
the right of Anne does Bev need to be? _100
ft
In the 2nd exp, how
far to the right of Anne does Bev need to be?
_150 ft
In the 3rd exp, how
far to the right of Anne does Bev need to be?
_200 ft
4.
As the pigeon flies from Chuck to Dean,
what is VPE in exp 1? __30
ft/s_
As the pigeon flies from Chuck to
Dean, what is VPE in exp 2?
__40 ft/s_
As the pigeon flies from Chuck to
Dean, what is VPE in exp 3?
__50 ft/s_
5.
As the pigeon flies from Dean to Chuck,
what is VPE in exp 1? __-10
ft/s_
As the pigeon flies from Dean to Chuck,
what is VPE in exp 2? ___0
ft/s__
As the pigeon flies from Dean to Chuck,
what is VPE in exp 3? __10
ft/s__
Now it is time to draw the space and time
diagrams. Your answers to questions 1
and 2 tell you the amount of time and space that the diagram needs to encompass
to capture the experiment from beginning to end. Notice that it is different for the three
experiments. To help you get started, I
have attached scaled graph paper, one for each experiment.
The steps for drawing the space and time diagrams
are not etched in stone but I will suggest a sequence that worked for me. The same sequence can be used for the three
different experiments.
1.
Draw the worldlines for Anne and
Bev. (We start with those because they
are not moving in the earth frame.)
2.
Label the spacetime point where the
pigeon reaches Bev as point A. Use that
point to draw the worldline of the pigeon as it flies from Chuck to Dean.
3.
Use point A to draw the worldline of Dean. (Remember we know his worldline passes
through A and we also know where he was at T = 0, the start of the experiment.
4.
Draw Chuck’s worldline.
5.
Label the point where the pigeon
returns to Chuck as point B. Use that
point to draw the worldline of the pigeon as it flies back to Chuck from Dean.
6.
Before going on to the next
experiment, use points A and B to find the velocity of the pigeon with respect
to earth as it flies from Dean to Chuck,
.
_________________
Make sure your answer to 6 agrees with the VPE
from the question 5 on the previous page.
If the answers differ, figure out where the error occurred. If the answers agree, go on to the next
experiment. Of course all the
answers to the questions on the first page have to be consistent with the space
and time diagram!
