A Collection of Estimation Problems
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 Sewanee 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
density of about 1 gm/cm^3 , 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/cm 3 .)
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 ($10 11 ).
(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 layed 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
9.Estimate the total number of sheets of 8.5 x 11 inch paper used by all Sewanee students 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 snow storms. Estimate the amount of
work a person does shoveling the walk after a snow storm. 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/cm^3 -- about one fifth that of water.
In doing this problem, you should estimate any other numbers you need to one significant figure. Be certain to state what assumptions you are making and to show clearly the logic of your calculation. (In this problem, the answer is only worth 2 points. Almost all of the credit is given for your showing correct reasoning clearly.)
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 layed out end-to-end, how many round trips from Detroit to Orlando could be made with the string?
19.How many drops of waters 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 Wood Labs 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.ow 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?
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 results 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 it 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 to be slowed and brought back up by the
elastic band before hitting the ground (we hope). Estimate the length and spring constant of
the elastic you would recommend using.
9.Estimate the angular momentum an automobile tire has about its axis of rotation while the car
is driving on the interstate.
10.In testing a design for a yo-yo, an engineer begins by constructing a simple prototype -- a
string wound about the rim of a wooden disk. She puts an axle riding on nearly frictionless
ball bearings through the axis of the wooden disk and fixes the ends of the axle. In order to
measure the moment of inertia of the disk, she attaches a weight of mass m to the string and
measures how long it takes to fall a given distance.
(a) Assuming the moment of inertia of the disk is given by I, and the radius of the disk is R,
find the time for the mass to fall a distance h starting from rest.
(b) She doesn't have a very accurate stopwatch but wants to get a measurement good to a few
percent. She decides a fall time of 2 seconds would work. How big a mass should she use?
Imagine you were setting up this experiment and make reasonable estimates of the parameters
11.According to some recent highly accurate measurements made from satellites, the continent
of North America is drifting at a rate of about 1 cm per year. Assuming a continent is about
50 km thick, estimate the kinetic energy the continental US has a a result of this motion.
12.While on travel this past summer, I passed through Charles deGaulle airport in Paris, France. The airport
has some interesting devices, including a "people mover" -- a moving strip of rubber like a horizontal
escalator without steps. It became interesting when the mover entered a plastic tube bent up at an angle to
take me to the next terminal. I managed to get a photograph of it. It is shown in the figure below. If
you were building this people mover for the architect, what material would you choose for the surface of the
moving strip? (Hint: You want to be sure that people standing on the strip do not tend to slide down it.
Figure out what coefficient of friction you need to keep from sliding down and then look up coefficients
of friction in tables in reference books in the engineering library to get a material appropriate for
the slipperiest shoes.)