1. Mathematical and Graphical Techniques
IB Physics
1.3

2. Estimation Estimating measurements is important.
If you develop an innate feeling for the common units of physics (eg time, length and mass) you will be able to get a gut feeling if something is reasonable or nonsense.
This will be particularly important when doing practical work.

3. Try this quick quiz - estimation
Instructions: For each of these examples write down your estimate and then find the actual value.
You will be given a box with samples or tools to help you in your mission.
Task
How far is it from the floor to the ceiling in the Physics Kingdom?
Using a stopwatch estimate 30 seconds – obviously you are not allowed to look at the stopwatch or any other time pieces in your field of view.
What is the mass of the toy in your box? Use the electronic balance to check your estimation.
Compare your answers with others in the class.

4. I bet your answers differed from others in the class.
That’s why we have standards!
The importance of measurement grew as societies became more complex.
Now imagine yourself back need the dawn of human evolution.
What do you think was the first measurement you would have used?

5. Answer: the day (this came well before length or mass)
As civilizations progressed so too did their need for new units of measurement.
The need for a new unit comes before the unit is invented.
Homework: The barn is a relatively new unit of measurement. What is it and why was it invented?

6. 1.3.1 Estimate approximate values of everyday quantities to one or two significant digits and/or to the nearest order of magnitude.
Reasonable estimates for common quantities, eg
dimensions of a brick =
mass of an apple =
duration of a heartbeat =
room temperature =
Are expected.

7. ‘Fermi’ Estimations
Physicists should be able to estimate the order-of-magnitude of anything. How many atoms of Julius Caesar do you eat every day? How much waste does a nuclear power plant generate?
Physicist Enrico Fermi drove his students crazy with questions such as these and those in the following slides.
In these questions Fermi considered the process to be as important, if not more important, than the answer.

8. How to do Fermi Questions
The Nobel-prize-winning physicist, Enrico Fermi, came up with this simple and intuitive way to deduce the circumference of the earth.
1. How many time zones do you pass through when you fly from New York to Los Angeles? Answer, 3
2. How many miles is it, about, over that same distance? Answer, about (note: we have used miles here because it makes the calculations easier)
3. How many miles per time zone, on average? Answer, about 1000
4. How many time zones must there be around the world? Answer, 24 because there are 24 hours in a day
5. How many miles around the world? Answer, 24 time zones x 1000 miles per time zone = miles Yes, it is about miles around the world.

9. So how do I get the diameter of the Earth?
1. the formula for a circle is 2 pi r, right? where r is the radius and pi is about 3
2. so mi = 2 x 3 x r = 6 x r
3. therefore mi / 6 = r = 4000 mi
4. the diameter of the earth is 2 x r = 8000 mi, where the diameter is 2 times the radius
5. 1 mi = 1.6 km so 8000 mi x 1.6 km/mi = km
(the correct answer is ~12742 km)
So you can always figure out the dimensions from your basic knowledge of travelling!

10. How many toy whistles can you fit into an atom?
Try these on for size!
Task: Get into groups of two or three and tackle the following Fermi brain busters! You may need to research some data on the internet.
1. How many seconds are there in a year?
2. How many piano tuners are there on the Central Coast?
3. How many ping pong balls can you fit in a suitcase?
4. How many ping pong balls would fit in the library foyer?
How many toy whistles can you fit into an atom?

11. 1.3.2 State and explain simplifying assumptions in approaching and solving problems.
For example, reasonable assumptions that certain quantities may be neglected, others ignored (eg heat losses, internal resistance), or that behaviour is approximately linear.

12. 1.3.3 Estimate results of calculations.
We have dealt with these when doing Fermi problems.
Examples: 176/118 ≈ 180/120
= 3/2 = 1.5
or 6.3 x 7.6/4.9 ≈ 6 x 8/5
= 48/5 ≈ 50/5 ≈ 10.