HOMEWORK
     set 1A

DUE WEDNESDAY, SEPTEMBER 17, 1997

SKY AND GALILEO, LECTURES 1-5
WORTH 5 POINTS, 5 PERCENT OF YOUR GRADE

Come to discussion sections or use FirstClass for homework help or call me at 262-3827 or email me at bdurand@theory2.physics.wisc.edu

• MANY THINK THIS IS THE HARDEST OF ALL THE HOMEWORK SETS BECAUSE PARTS OF IT ARE VERY TIME-CONSUMING.
• NUMBERS 2 AND 5 REQUIRE DISCUSSING AND COMPOSING AN ANSWER AS A GROUP (TO BE ASSIGNED BY ME IN DISCUSSIONS OR ON FIRSTCLASS), WITH ONLY ONE PAPER TURNED IN FOR THE WHOLE GROUP. IF DISCUSSION SECTIONS GO RIGHT, YOU CAN GET WELL INTO THOSE ANSWERS IN CLASS.
• DON'T FORGET TO SAVE YOUR FILE AND MAKE A PHOTOCOPY OF YOUR COMPLETED PAPER IN CASE THE ORIGINAL GETS LOST.

1. one point, from Lecture 1, involves finding information, observations, sketches, descriptions, not necessary to type. NOTE: DO NOT DELAY IN STARTING THIS PROBLEM!

(a) .4 Change of Season. Hint: use the Lecture 1 Supplements. Other useful sources are newspapers or TV weather, a calendar, and a telephone directory map.
Find out when the fall equinox is this year. (.1)
Find out the times of sunrise and sunset for three days between now and September 17 and calculate the average change in the length of the day. (.1)
Find a convenient street which runs due east-west and observe where the sun rises or sets on two different days relative to east-west. Is it north or south? (.1)
How is it changing this month? (.1)
In you answer, you must cite all of your sources, give the dates and locations of your observations, make a sketch of where the sun was relative to due east or west, and show your calculations. I suggest a sketch with a vertical line as if it were a post at the end of the street you are looking down, labeled east or west. Draw where the sun was relative to that post, and label whether it is north or south of due east or west.

(b) .3 Phases of the Moon. Find out what the phases of the moon are between September 1 and September 17. (.1)
Observe the moon on two clear evenings or mornings. You'll have to figure out when to look if it isn't obvious. Sketch, label and describe what you see. (.2)
Include the date, time, a picture of the moon with white for visible and black for invisible, and where in the sky (angle and direction) it was. Use the same way to depict this as I used in lecture: an arc with east on the left and west on the right, so that the peak of the arc is the highest position of the moon in the southern sky. Start soon, so the weather won't foil you!

(c) .3 Sideview Orbit Picture. Draw a side view of the earth's position relative to the sun on June 21 and December 22. Label the sun, earth, date, and distance from sun to earth; (.2)
and draw the earth's axis of rotation carefully, with the northern hemisphere and the angle of the axis relative to the orbital plane labeled. (.1)

2. one point, from Lecture 2, a group question, involves short answers

(a) .4 from Lectures 1 and 2, The essence of the lectures. In the future, I will ask your group to characterize a lecture in one phrase -- not just repeating the title of the lecture -- then discuss why you chose that phrase. As a warmup, I will characterize lectures 1 and 2 as "understanding how orbits determine what we see." What do I mean? (.2)
In discussing this, come up with a different characterization. State it. (.1)
Briefly justify it. (.1)

(b) .6 from Lecture 2, Changing Worldviews. Choose three specific featureS of Aristotle's worldview of the heavens which were challenged by Copernicus, Tycho, Kepler, and Galileo. Discuss how the later astronomers reached their conclusions. (.2 for each feature)

3. one point, from Lectures 2-4, involves calculation, not necessary to type.

(a) .4 from Lecture 2, Kepler's Third Law. A new comet is discovered with a period of 125 years. Use Kepler's Third Law to find the size of the comet's orbit relative to Earth's orbit. You must show your work to get credit for your answer.

(b) .6 from Lectures 3 and 4, Falling Down the Stairwell of Sterling Hall. This problem will not have a ``nice '' whole-number answer. First estimate how tall Sterling Hall is in meters from the floor of the basement to the roof. You don't have to see the building to do this. I will tell you that there is a basement and then four stories, and the ceilings are higher than in an average house. Call the estimated height of the building h. You must explain your reasoning to get credit for your estimate. (.3)
Next calculate how long a time t it takes for an object dropped down the stairwell from the ceiling of the top floor to hit the floor of the basement. Use h=½gt², g=10m/s², and whatever you estimated for h. (.3)

4. one point, from Lectures 4 and 5, involves time-consuming graphs, not necessary to type.

Ten Tedious but Necessary Spacetime Diagrams. Draw spacetime diagrams (graphs) for the five kinds of motion given below, on axes with the axis x for position in meters and the axis t for time in seconds.

• Plot each one first with the x axis vertical and the t axis horizontal,
• then with the x axis horizontal and the t axis vertical, to get ten graphs, worth .1 point apiece.

1 to 2 inches is a good size to allow for each graph. If you want to get partial credit in case of a careless math error, show your calculations in a table .

• Label the axes with the seconds and meters.
• Use a ruler, and draw the lines carefully and accurately.
• Ask for help if this gives you trouble.

Here are the conditions of motion. Don't forget to do 2 graphs for each. Draw all these graphs accurately!

• (1) Standing still at x=3m from time t=0 to time t=5s.
• (2) Starting at x=0 and moving forward with constant velocity v=9m/s from time t=0 to time t=5s.
• (3) Use the same scale as in the second graph. Starting at x=0 and moving forward with constant velocity v=3m/s from time t=0 to time t=5s. Notice the different looks of (2) and (3) (fast and slow).
• (4) Starting at rest (v=0) at x=0 and accelerating uniformly with x=3t² (acceleration equals 6 meters per second squared) from time t=0 to time t=5s.
• (5) Starting with speed v=30m/s at x=0 and decelerating uniformly so that x=30t-3t² (acceleration equals minus 6 meters per second squared) from time t=0 to time t=5s. This one is the hardest. To be safe, tabulate the motion one second at a time. Notice the different looks of (4) and (5) (speeding up and slowing down).

5. one point, from Lectures 3 and 5, a group question, involves short answers

(a) .6 from Lecture 3, Terrestrial Motion. Aristotle and Galileo found different rules for motion at or near the surface of the earth. Contrast three features of their theories (.3),
incorporating into your answers how Galileo reached his conclusions. (.3)

(b) .4 from Lecture 5, Principles. Characterize in a phrase the subject of this lecture on Galileo's three great principles. (.1)
Illustrate what you mean in your characterization with a clear example pertaining to each principle. (.3)

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