Well, I’m back in at work after a lovely Christmas break. Lots of sunshine (we dodged the bad weather by going southwards for Christmas and then back north for New Year), beaches, playing with baby, and hacking back the jungle that sprung in the back garden in our 10 days’ absence.<\/p>\n
Benjamin has now pretty-well mastered sitting upright, which makes playtime a bit easier. Sometimes he leans too far and falls over, usually as a result of over-reaching for something that’s caught his eye. A couple of days ago, he toppled backwards after a sneeze. Though it would be fun to think that the recoil from the momentum of the sneeze is what sent him over backwards, I think it is more likely that it just took him by surprise and he lost his balance.<\/p>\n
A quick estimate shows the situation. A sneeze, in physics terms, is a jet of air. We can think of it in terms of conservation of momentum. A jet engine on an aircraft sends a high speed stream of gas backwards, and at the same time the aircraft exhibits a forward force – the two are related – the force is equal to the rate at which momentum is transferred to the stream of gas. To work this out we need to think what mass is moved backwards every second, and what is its velocity; the product of these gives the momentum transfer every second.<\/p>\n
If we consider the jet as a cylinder whose ends are of area A (real jets aren’t cylindrical, but let’s not worry about that for a quick estimate), then in one second a length v metres of gas is emitted, where v is the velocity in metres per second. So the volume is Av, and the mass is pAv, where p is the density of the gas (for air it is conveniently about 1 kg per metre cubed). Since this gas moves at a velocity v, then the momentum per second is given by pAv times v, that is p A v squared.<\/p>\n