Wednesday, September 14, 2011

A stationary ....?

A stationary 0.1-g fly encounters the windshield of a 1200-kg automobile traveling at 120 km/h. (a) What is the magnitude of change in momentum of the car due to the fly? (b) What is the magnitude of change of momentum of the fly due to the car? (c) Approximately how many flies does it take to reduce the car's speed by 1 km/h?A stationary ....?
Momentum is mv or mass times velocity, now the fly has zero momentum initially and the car has 1200kg * 120/3.6 m/s = 40,000 kg m/s of momentum. Now due to conservation of momentum and with the assumption that the fly gets stuck on the car and begins to travel with it as the same speed all you do is say [ 40,000 = (1200 + 0.0001) v ] to solve for the new total velocity. Solving this you get v = 33.333330555555787037017746915188 m/s.



The change in momentum in the car is 40,000 - (1200*33.333330555555787037017746915188) = 0.0033333330555555787037017746915188 kg m/s.



This momentum change for the fly is 33.333330555555787037017746915188*.0001k?= 0.0033333330555555787037017746915188 kg m/s. (The same as that for the car)



To reduce the cars' speed by 1km/h you do this calculation: 40,000 = (1200 + 0.0001*x) (119/3.6)... solving for x gives 100840.33613445378151260504201681 flies or 100841 flies to be practical. So it takes just over one hundred thousand flies to reduce the speed of that car by 1 km/h.



Cheers
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