A car is travelling in one direction at 80 km/h and a fly is coming from the opposite direction at 5km/h. (So its velocity is -5 km/h, since it's in the opposite direction.)

The fly hits the windshield of the car and is now travelling at 80km/h. In order for the fly to achieve the speed of 80km/h it's speed must have passed from -5km/h to 80km/h. (Meaning it must pass through the speed of zero) Therefore if the fly passes through a speed of 0km/h and the car is in contact with the fly the car must also pass through that speed of 0km/h.

This seems to mean that everytime a car gets hit by a fly it will completely stop. Why is this not so?

You could either use Newton's 3rd Law (and 2nd) or the Conservation of Linear Momentum to explain this, but they both rely on the fact that there is a huge difference in mass.

Newton's 3rd Law says that they experience the same force in opposite direction when they come into contact. And his 2nd law says that F=ma. Because of the huge mass difference, the fly experiences a great acceleration while the car experiences virtually nothing. Therefore the fly accelerates to the speed of the car almost instantaneously.

The conservation of linear momemtum says that when they touch, their new speed becomes M*v0/(M+m), where M and v0 are the mass and speed of the car, respectively, and m is the mass of the fly. Due to the mass difference, this is essentially v0. Again, this means that the car slows down ever so slightly while the fly completely changes direction instantaneously.

But regardless of which law you use, it is mainly because the fly decelerates almost instanteously. During this infinitesimally small time, the speed of the car and the speed of the fly are not the same (only the forces are equal in magnitude). It's only after this time passes (after the contact force in the direction of travel is gone) that the car and the fly travel at the same speed.

Posted by np_rt on 2003-01-19 08:22:37