Q1.2 Making estimates (S)
Estimate (give the order of magnitude of) the following:- the volume of your body;
- the thickness of a single page of Halliday Resnick and Walker (not so bad, eh?);
- the surface area of a CD-ROM needed to accommodate one bit of information;
- the speed of a point on the equator, due to the earth’s rotation.
Hint
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Hint
For many purposes the human body can be thought of as a bag of water.
A typical CD-ROM holds about 700Mb of data; 1 Mb =8×106 bits.
Think of the radius of the earth and the length of the day.
Solution
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Solution
- Assuming a mass m∼102 kg and a density ρ∼103 kg⋅m-3 (we are indeed mainly water!) implies a volume V=m/ρ∼10-1 m3, which seems reasonable when I contemplate my geometry.
- HRW has ∼ 1000 pages (‘sides’) and thus 500 sheets and is about 4 cms thick (ouch!), implying a sheet thickness of ∼10-4m.
- The area of a CD-ROM (of radius r∼5×10-2m) is A=πr2∼10-2 m2. The number of bits it accommodates is N∼1010. So the area per bit is A/N∼10-12 m2
- As a result of the earth’s rotation, a point on the equator will move a distance 2πR in time T where R is the earth’s radius, and T its rotational period. Its speed is then v=2πR/T (which some will recognise as v=Rω, where ω=2π/T is the earth’s angular velocity). We all know T=1 day; you probably have to remind yourself that R∼107 m. Then we find v∼102 m⋅s-1.