Download Solving problems at the (virtual) back of the envelope

Solving problems at the
(virtual) back of the envelope
Andy Buffler
UCT Physics
[email protected]
AIMS 2006
Estimation problems / order of magnitude calculations / ...
aka “Fermi problems”
... after Enrico Fermi ...
... who (amongst many other things) fingered out the yield
of the Trinity atomic bomb test from observing the
distance traveled by small pieces of paper dropped from
his hand during the detonation.
... and is associated with questions such as ...
“How many piano tuners are there in the city of Chicago?”
“How much faster or slower does a watch run when
carried up a mountain?”
How many golf balls would be
needed to completely fill this room?
How fast does your hair grow
(in km/hour)?
How many grains of sand are there
on Muizenberg beach?
Thinking about estimation problems:
•
•
•
•
•
What is really being asked?
Do I need a physical model?
If so, what idealizations or simplifications can I make?
Which parameters really matter?
How can I get reasonable values for these parameters?
• Is my answer reasonable?
If all the people of the world were
crowded tightly together, how much
area would we cover?
How many R100 notes are in
circulation in South Africa?
How many pencils would it take to draw
a straight line around the entire Earth,
following the equator (if you could also
draw on the surface of the ocean)
How many elastic bands will a
prisoner need to escape down a
10 metre high wall?
How small does a human need to
be in order to walk on water?
Homework
Answer all these questions before Friday
11:00. Bring your answers to class and be
prepared to defend them publicly. Discuss
things with your tutorial group and tutor,
but have your own answers ready.
Homework
1. What is the kinetic energy of a
drifting continent?
Homework
2. What is the heat output of a human?
Homework
3. How many commercial aircraft
are in the air right now?
Homework
4. How high can an elephant jump?
Homework
5. What is the photon flux at your
eye from a faint visible star?
Homework
6. How many atoms of Julius
Caesar do you eat every day?
Homework
7. Someone places 1 curie of
uranium on your chest...
... what do you die of?
Homework
8. A steel ball is dropped from a height
of 3 metres onto a concrete floor.
It bounces a large number of times but
eventually comes to rest. Estimate the
rise in temperature of the ball.
Homework
9. Invent a problem of your own
(you don’t have to know the answer).
Email this problem (only) to
[email protected]
before 17:00 on Thursday.
Solving problems at the
(virtual) back of the envelope
Part 2
Andy Buffler
UCT Physics
[email protected]
AIMS 2006
How far does a car travel before
one molecule layer of rubber is
worn off the tires?
What is the mass of air in
this room?
How many molecules are there in a
sample of 1 litre of air in this room?
What is the average spacing between
these molecules?
How many atoms are there
in the human body?
How much would the ocean surface
rise if the ice caps melted?
Physical theories
Abstract, acontextual, external.
Manifested in mathematical or linguistic form
particularization,
application
Physical models
Concrete, contextual, external
Manifested in many forms
idealization,
simplification
Real world
(Phenomena)
Concrete, experience, observation
How fast does your hair grow
(in km/hour)?
How many golf balls would be
needed to completely fill this room?
How many hairs are there on
your head?
Could Bill Gates buy the
whole of Muizenberg?
A golf ball is dropped onto a
concrete floor from a high flying
airplane.
How high will it bounce?
How long does it take for a light
bulb to turn off?
Tutorial
Answer the following 7 questions
(suggested by yoursleves).
Work within your groups and ask the tutors
for help if needed.
You have 1 hour to come up with reasonable
answers. Use whatever resources you have
available. You may leave the room.
Write full answers, stating all approximations
and assumptions you make.
Hand in one set of solutions per group.
Tutorial
1. How many people are born in
the world every minute?
Tutorial
2. How many bags of cement
were used to construct the AIMS
building?
Tutorial
3. How many words are used in
2 hour lecture if the lecturer talks
continuously?
Tutorial
4. What volume of rain fell on the
continent of Africa in 2006?
Tutorial
5. What distance have you walked
since the day you took your first steps?
Tutorial
6. What is the total distance covered
in a football game by all the players
on the field?
Tutorial
7. How much energy is required to
boil the Earth’s oceans?