Topic 1 – Physics and physical measurement

Scientific Notation

We can express small and large numbers using scientific notation.

This can be written as

6.02 x 1023

The number of atoms in 12 grams of carbon is approximately:

602,000,000,000,000,000,000,000

Order of magnitude

We can say that the number 6 x 1023 is, to the nearest order of magnitude,

1024

Round to the nearest power of 10

Order of Magnitude

Similarly, the length of a virus is 2.3 x 10-8 meters. We can say to the nearest order of magnitude the length of a virus in meters is:

10-8 2.3 is less than 5, so we round down to 10-8

Ranges of sizes, masses and times

You need to have an idea of the ranges of sizes, masses and times that occur in the universe.

Size

On your paper can you write in order of decreasing size the names of 3 very small things.

Size

Which is the biggest? What size is it, in meters (m), to the nearest order of magnitude?

Size

The smallest objects that you need to consider in physics are subatomic particles (protons and neutrons).

These have a size (to the nearest order of magnitude) of

10-15 m

Size

On your paper write in order of increasing size the names of 3 very large things.

Size

Which is the smallest? How small is it, in meters, to the nearest order of magnitude?

SizeThe largest object that you need to consider in physics is the Universe.

1026 m

The Universe has a size, to the nearest order of magnitude, of:

Ratio of biggest to smallest

How much bigger is the universe than a proton?

1026 m10-15 m

= 1041 times

or 41 orders of magnitude bigger

Mass

On your paper estimate the masses, in kilograms, of the 3 smallest objects you wrote down earlier.

Smallest mass

The mass of the electron:

10-30 kg!(0.000 000 000 000 000 000 000 000 000 001 kg)

Biggest Mass

We have already decided that the Universe is the largest object. What do you think its mass is?

1050 kg(100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 kg)

Ratio of most massive to least massive

How much more massive is the universe than an electron?

1050 kg10-30 kg

= 1080 times

or 80 orders of magnitude bigger

Time

Now think of 3 small time intervals

(For example, the time it takes sound to travel 1 meter is a small time interval. Can you think of smaller?)

Time

Can you add order of magnitude estimates for your time intervals?

(For example, the time it takes sound to travel 1 meter is 10-3 seconds to the nearest order of magnitude)

Shortest Time

The smallest time interval you need to know is the time it takes light to travel across a nucleus.

Can you estimate it?

10-23 seconds

Longest Time

What’s the longest time interval you can think of?

Time

The age of the universe.

Any ideas?

1018 seconds

or 13.8 billion years

Ratio of longest to shortest

How much longer has the universe existed than the time it takes light to cross a proton?

1018 s10-23 s

= 1041 times

or 41 orders of magnitude longer

Copy please!

Size10-15 m to 1025 m (subatomic particles to the

extent of the visible universe)Mass

10-30 kg to 1050 kg (electron to the mass of the Universe)

Time10-23 s to 1018 s (time for light to cross a

nucleus to the age of the Universe)

One common ratio – Learn this!

Hydrogen atom ≈ 10-10 mProton ≈ 10-15 m

Ratio of diameter of a hydrogen atom to its nucleus

10-10 m10-15 m

= 105 times

or 5 orders of magnitude bigger

Estimation

You have to be able to make order of magnitude estimates.

Estimation/Guess

What’s the difference?

Estimate the following:

1. The mass of an apple(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple2. The time it takes your heart to beat 100

times.

(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple2. The time it takes your heart to beat 100

times. 3. The speed a cockroach can run.

(to the nearest order of magnitude)

Estimate the following:

1. The mass of an apple2. The time it takes your heart to beat 100

times. 3. The speed a cockroach can run.4. The number of times the earth will fit into the

sun (Rs = 6.96 x 108 m, Re = 6.35 x 106 m)

(to the nearest order of magnitude)

10-1 kg

102 s100 m/s

(6.96 x 108 m)3 (6.35 x 106 m)3

= 106

Let’s do some more estimating!