A Bus

[theleeroy55]

lets say a bus is travelling along a road at 40mph. whilst moving the bus hits a grain of sugar that is suspended in the air by the wind. does the grain of sugar cause the bus to slow down at all? even if it is of the smallest margin?

[jake-the-peg]

If you were talking about a spacecraft travelling in deep space the answer would definately be yes.

With a bus driving along the road there are many other factors such as slight random differences in air pressure. These factors will be much larger than the effect of the sugar grain and because they are random it means that if you were to run the whole experiment again you would not be able to measure any difference even if you had infinitely accurate equipment. The effect is lost in the "noise of the experiment"

So in theory there is a difference, but if you try to apply that to a bus that difference is swamped by other factors

[heathfield]

This is the old 'fly hits a train' paradox. Does the train stop?
The answer is 'No'.
There is no such thing as an instant change in velocity.
What happens is that a teensy-weensy part of the bus hit by the sugar will deform imperceptibly, (imagine the bus being made of rubber). The middle of the deformity will 'stop', then rebound, and carry the sugar forward. Energy gained from the collision will appear as heat, and will be dissipated.

[jake-the-peg]

And from a conservation of momentum perspective Heathfield?

[heathfield]

Vector of forces, Jake.

[Gef]

To answer the question - yes! But it would not be noticeable.

[lord molly]

newton was good at this sort of thing, so good infact he made up a load of laws



such as every action has an equil and opposite reastion, all proportional to its enertia of course

[jake-the-peg]

I think I misread Heathfields answer slightly.

Anyway what I was getting at is that the total momentum (mass times velocity) is the same before and answer.

If your bus weighs say 10,000 Kg and is moving at 20 m/s it has a momentum of 200,000 Kgm/s the sugar grain has 0.

If the mass of the sugar grain is say 0.00001Kg and ends up travelling at an angle to the bus with say 2 m/s in the direction the bus' travel ( we don't care how fast upwards - this is what heathfield means by vector of forces)
then

200,000 (total momentum before) = 10,000 x V Bus + (.00001x2)

So the final velocity of the bus is 19.999999998 m/s in theory. ( provided I've not miscounted the 9's)

But this is way too small for it not to be swamped by other effects that occur in the real world and that we've ignored in the example.