Q1.2 Making estimates (S)

Estimate (give the order of magnitude of) the following:
  1. the volume of your body;
  2. the thickness of a single page of Halliday Resnick and Walker (not so bad, eh?);
  3. the surface area of a CD-ROM needed to accommodate one bit of information;
  4. the speed of a point on the equator, due to the earth’s rotation.
Hide

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

Reveal
Hide

Solution

  1. Assuming a mass m102 kg and a density ρ103 kgm-3 (we are indeed mainly water!) implies a volume V=m/ρ10-1 m3, which seems reasonable when I contemplate my geometry.
  2. HRW has 1000 pages (‘sides’) and thus 500 sheets and is about 4 cms thick (ouch!), implying a sheet thickness of 10-4m.
  3. The area of a CD-ROM (of radius r5×10-2m) is A=πr210-2 m2. The number of bits it accommodates is N1010. So the area per bit is A/N10-12 m2
  4. 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 R107 m. Then we find v102 ms-1.