Someone asked me whether Flies can stop trains, with the following explanation:
OK… You have a train traveling 100 mph in one direction and a fly traveling the opposite direction towards it at 10mph. When the fly hits the train’s windshield (presume it’s flat, not aerodynamically curved) there will be a point in time that the fly decelerates from 10mph to 0mph and then is accelerated up to the train’s 100mph speed. I think the laws of physics dictate that there is no way the fly can instantly change from 10mph in one direction to 100mph in the other, so there has to be one point when the Fly is stationary on the windshield. If the Fly is stationary and touching the windshield, then the windshield must at that time be stationary and therefore the train too. So, flies can stop trains…
Clearly not the case in reality, but why not? What’s the scientific (or emotional) explanation for the hypothesis?
Question from Tom Aldridge at Ringarogy island, Nr Skibberine, Ireland in 1990
This is where your reasoning goes off the tracks. The train and windshield are not a perfectly rigid body, nor is the fly.
The fly doesn’t instantly change direction or speed, nor does the train. Both the fly and the front of the train will deform under the force applied to both of them. Given the relative momentum and strength of each, the fly will deform a bit more than the train will, but nothing will happen “instantaneously”, just very quickly.
A small layer of molecules on the surface of the front of the train can move more slowly than the rest of the train for a tiny fraction of a second, then move most quickly for another tiny fraction of a second, without any observable effect on the rest of the train.
So what if they both “were” rigid? Say instead of a fly it were a stainless steel ball bearing and instead of a windshield it was the cast iron grill of the locomotive.
Or are you saying it doesn’t matter? The ball bearing will still deform (squash) like a nerf ball and reform to a sphere and that this reforming is it’s 0-100 acceleration independant of the train.
Right. There’s no such thing as a perfectly rigid object; there will always be some degree of deformation of both the object and the part of the train that’s hit.
Before the collision, the fly and the train are converging at 110 mph. After the collision they are both stationary. Although other nearby objects such as earth, track, and air may continue to fly by in various speeds and directions, they do not substantially affect the problem.
Even a steel ball bearing would flatten slightly. (A 20mm bullet hitting the train will still “squash”, lead being a little more, umm, elastic? Is that the right word? Less tensile strength?)
Your wondering how the tensile strengths of the two objects will hold up in kinetic impacts with near similar objects. That requires involving metalurgy as well as Newtonian physics.
A standard bb-sized steel ball bearing, 10 mph, has kinetic energy of mass * speed applied to front of an iron train. Since train weighs many tons, the speed effect on the train effect is not noticable. (But it is calculable.) The surface of the train at the point of impact will be effected based on the material the train is made of. Iron is reasonably strong. I expect a small ding, scratched paint in the case of an iron train vs steel bb.
The iron train, many tons, moving at 100 mph, applies it’s kinetic potential to the bb. The effect is more pronounced, even though steel is stronger than iron. (It had to absorb much more energy.) A deformity in the spherical shape of the bb, if you can find the bb in the grass afterwards.
Make the train out of Bleau Cheese however, and the bb may not show any deformity…
Motion is distance traveled over time. Remove time, and what are you trying to measure?
Besides, even if I could freeze time, the arrow will still have some kind of kinetic energy potential bound up in it, wouldn’t it? (Speed * weight, or something?) Which, if you knew how to measure that potential while frozen in time, would allow you to tell the diff between a stationary arrow and one in flight.
Value of E, elasticity, stiffness, modulus of elasticity, or Young’s modulus will all work. It’s defined by Hooke’s law, which states that the stress is equal to E times strain.
An depending on relative velocities this can be far more than you would think possible. I have seen some high speed video of impacts that show how truly elastic objects that we think of as solid are.
As was pointed out, the fly and locomotive front end aren’t rigid. They will deform so as to allow the fly’s change in velocity to take place. The whole fly does what the OP said, but only part of the locomotive does.
The deformation of the locomotive really happens. Raindrops will knock small pieces out of the leading edge of jet aircraft wins leaving them pitted. In that case, the deformation has exceeded the elastic limit, and even the ultimate strength of the material resulting in rupture.
Yeah. Just look at the super slo mo pictures of a golf ball when one of the touring pros hits it with a driver. The ball deforms by about 1/4" and then takes off. I suspect it’s similar to Colibri’s description of how a flock of birds changes direction. The deformation initiates a wave of motion that that travels through the ball and gets the whole thing moving.
Rats, late again. But surely if the locomotive were on the airplane’s treadmill it would end up going backwards (albeit, very very slowly) upon the collision with the fly, would it not? Provided the treadmill kept a constant speed.