Homework Exercise for Chapter 1 Name: _____Key__________
Chuck and Dean once again agree to do three more
runs with the 100 foot bus so that Anne and Bev can collect even more
data. For these experiments, three
different pigeons are used. In the first
experiment the pigeon flies at a constant speed of 20 ft/s, the second pigeon
flies 30 ft/s while the third and last pigeon zips along at 40 ft/s.
The pigeons fly from the back, where Chuck is
located, to the front and immediately turn around and fly back to Chuck. The speed of the bus is 30 ft/s for each of
the three experiments. Bev is positioned
at just the right spot to be next to Dean just as each pigeon arrives and turns
around.
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. The
diagrams can be enhanced by using different colors of the worldlines of Anne
& Bev, Chuck & Dean, and the pigeon.
1.
How long does experiment 1 last? __10
seconds___
How long does experiment 2
last? __6 2/3 seconds__
How long does experiment 3 last? __5
seconds__
2.
At the end of the exp 1, how far to
the right of Anne is Dean? _400 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? _250 ft__
3.
In the 1st exp, how far to
the right of Anne does Bev need to be?
__250 ft_
In the 2nd exp, how
far to the right of Anne does Bev need to be?
_200 ft_
In the 3rd exp, how
far to the right of Anne does Bev need to be?
_175 ft_
4.
As the pigeon flies from Chuck to Dean,
what is VPE in exp 1? __50
ft/s_
As the pigeon flies from Chuck to
Dean, what is VPE in exp 2?
__60 ft/s_
As the pigeon flies from Chuck to
Dean, what is VPE in exp 3?
__70 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. Dean’s
position at the end of the experiment is irrelevant. So I made no effort to include enough x-axis
for Dean’s worldline to still be on the graph at the end of the 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 your
velocity for the pigeon from the question 5 on the previous page. If the answers do not agree, find your error. If the answers agree, go on to the next
experiment. Of course all the answers to
the questions on page one have to be consistent with the information on the
space and time diagram!
