General
1. Estimate the total number of hairs on your head.
2. Estimate the number of square inches of pizza consumed by all the students at the University of Maryland during one semester.
3. When it rains, water would accumulate on the roofs of flat-topped buildings if there were no drains. A heavy rain may deposit water to a depth of an inch or more. Given that water has a mass of about 1 gm/cm³, estimate the total force the roof of the physics lecture hall would have to support if we had an inch of rain and the roof drains were plugged.
4. One suggestion for putting satellites into orbit cheaply without using rockets is to build a tower 300 km high containing an elevator. One would put the payload in the elevator, lift it to the top, and just step out into orbit. Ignoring other problems (such as structural strain on the tower), estimate the weight of such a tower if its base were the size of Washington DC and it were made of steel. (Steel is about 5 times as dense as water, which has a density of 1 gm/cm³.)
5. Estimate the total amount of time 19-year-olds in the US spent during this past semester studying for exams in college. (Not counting finals.)
6. The deficit in the Federal Budget this past year was approximately $100 Billion ($1011). (a) Assuming this was divided equally to every man, woman, and child in the country, what is your share of the debt? (b) Supposing the deficit were paid in $1 bills and they were laid out on the ground without overlapping, estimate what fraction of the District of Columbia could be covered. (c) Suppose you put these $1 bills in packages of 100 each and gave them away at the rate of 1 package every 10 seconds. If you start now, when will you be finished giving them away? (d) Are any of these calculations relevant for a discussion which is trying to understand whether the deficit is ridiculously large or appropriate in scale? Explain your reasoning.
7. The Federal Budget Deficit is approximately $100 Billion this year. Compare this to what we spend on what we eat by estimating the total amount US consumers spend on food in grocery stores, markets, and restaurants in one year.
8. In the 1989 Loma Prieta earthquake in California, approximately 2 million books fell off the shelves at the Stanford University library. If you were the library administrator and wanted to hire enough part-time student labor to put the books back on the shelves in order in 2 weeks, how many students would you have to hire? (You may assume that the books just fell off the shelves and got a bit mixed up but books in different aisles did NOT get shuffled together.)
9. Estimate the total number of sheets of 8.5 x 11-inch paper used by all the students at the University of Maryland in one semester.
10. If the land area of the earth were divided up equally for each person on the planet, about how much would you get?
11. After the Gulf War, large areas of desert had to be cleared of mines using special bulldozers that simply sweep the sand in front of them like a snowplow, but whose blades are strong enough to withstand the explosion of a mine. Estimate how long it would take a single bulldozer to clear a patch of desert that is 10 km square.
12. This winter, the East coast has been hit by a number of snowstorms. Estimate the amount of work a person does shoveling the walk after a snowstorm. Among your estimates you may take the following:
- The length of a typical path from a house to the street is 10 meters.
- Assume the snow fell to a depth of 4 inches.
- Assume the snow was only moderately packed so that its density was equal to 0.2 g/cm³ -- about one fifth that of water.
13. A floppy disk for a computer stores information by magnetizing small regions of the disk. For a typical floppy disk, estimate the area of the disk that corresponds to a single bit of information. (Remember: the storage capacity of a disk is cited in bytes where 1 byte = 8 bits.)
14. Ali El-Ectrical is an Engineering student at your university taking a "normal" load (for Engineers!) and paying full tuition. Estimate how much he is paying for each hour of class time he spends with an instructor over one semester.
15. Estimate the number of blades of grass a typical suburban house's lawn has in the summer.
16. How many notes are played on a given radio station in a given year?
17. How many pencils would it take to draw a straight line along the entire Prime Meridian of the earth?
18. If all the string was removed from all of the tennis rackets in the US and laid out end-to-end, how many round trips from Detroit to Orlando could be made with the string?
19. How many drops of water are there in all of the Great Lakes?
20. How many piano tuners are there in New York?
21. How many atoms are there in the jurisdiction of the continental US?
22. How far can a crow fly without stopping?
23. How many golf balls can be fit in a typical suitcase?
24. How tall is this building?
25. Estimate the number of cars and planes entering the state at any given time.
26. How much air (mass) is there in the room you are in?
27. How long does it take a light bulb to turn off?
28. How much energy does it take to split a 2x4?
29. How much milk is produced in the US each year?
30. If you drop a pumpkin from the top of a ten-story building what is the farthest a single pumpkin seed can land from the point of impact?
31. How many flat tires are there in the US at any one time?
Mechanics
1. Estimate the angular momentum that your body has as a result of the earth's turning on its axis.
2. The mass of the earth is about 6x10^24 kg. Estimate the kinetic energy it has as a result of its orbiting the sun.
3. A professor of physics is going ice skating for the first time. He has gotten himself into the middle of an ice rink and cannot figure out how to make the skates work. Every motion he makes simply slips on the ice and leaves him in the same place he started. He decides that he can get off the ice by throwing his gloves in the opposite direction.
- (a) Suppose he has a mass M and his gloves have a mass m. If he throws them as hard as he can away from him, and they leave his hand with a velocity v. Explain whether or not he will move. If he does move, calculate his velocity, V.
- (b) Discuss his motion from the point of view of the forces acting on him.
- (c) If the ice rink is 10 m in diameter and the skater starts in the center, estimate how long it will take him to reach the edge, assuming there is no friction at all.
4. The orbiting Hubble telescope was recently repaired by a crew of astronauts from the Space Shuttle Endeavor. The Hubble is in a circular orbit 600 km above the surface of the earth. For half of the Hubble's orbital period, it is in sunlight and for half, it is in the darkness of the earth's shadow. As a result of the change in fit of the various parts of the Hubble due to heating and cooling of the telescope, the astronauts could only work on certain repairs while the Hubble was in darkness. Estimate how much time the astronauts had to work on these repairs before having to stop "for a sun-break".
5. According to Newton's law of universal gravitation, the earth's gravity gets weaker as we go further from the earth. But when we drop a ball near the top of the lecture hall it doesn't seem to fall any differently than we drop it near the floor. Let g_t stand for the gravitational acceleration observed at the top of the lecture hall and g_b for it at the bottom. Estimate how much Newton's universal gravitation theory predicts g_t will be less than g_b. (Hint: It's easier if you estimate the fractional change, g_b/g_t - 1.)
6. Suppose the Army Corps of Engineers decided to put a dam across the Potomac River in order to provide power for the Washington area. Assume the dam was built to hold back the water into a lake to a height of 15 m behind the dam. (Ignore the fact that this lake would cover land occupied by houses and cities.) Estimate the total force the water would exert on the dam. (Hint: If you have never seen the Potomac and have no idea as to how wide it is across, make a reasonable guess.)
7. A ballistic rocket is shot straight up from Cape Canaveral. Its rockets fire briefly. After the firing, it has a velocity of 8 km/sec and a mass of m. How far up will it go before it begins to fall back to earth? Calculate your answer to within 10%. Ignore the distance it travels while its rockets are firing, the resistance of the atmosphere, and the rotation of the earth. (Hint: If you don't remember the radius of the earth you can solve for d/R_e where d is the distance it reaches measured from the center of the earth and R_e is the radius of the earth.)
8. For next year's Physics Open House, the Department is planning to set up a bungee jump from the top of the physics building. Assume that one end of an elastic band will be firmly attached to the top of the building and the other to the waist of a courageous participant. The participant will step off the edge of the building