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How fast is a freight train travelling?

A train is travelling at 90mph and hits a fly travelling toward the train does the train stop temporarily?

  • if a train is travelling at 90mph and hits a fly travelling at 1mph, in the exact opposite direction (or -1mph in relation to the train), then the fly's speed would have to change to match the trains speed (+90mph) as it splats on the windscreen, and therefore at one point the fly must of been travelling at 0mph, and therefore the fly must temporarily stop the train. Is this true???

  • Answer:

    This is actually a great question, and I think most of the other responders are failing to appreciate the paradox. On the one hand, it seems obviously absurd to think that the train's speed could drop to zero. But on the other hand: 1. The fly's velocity is obviously zero at some point (namely when it's switching direction); 2. This happens when the fly and the train are stuck together; 3. Since the fly & train are stuck together, they must be going at the same velocity; THEREFORE: 4. The train must be going at 0 mph at the moment the fly is going at 0 mph. I think the paradox is resolved as follows: The fly and the train are not perfectly rigid (if they were, the fly would decelerate instantly, which requires an infinitely great force). So that means it takes a certain small time for the fly to decelerate to zero after its front part first touches the train; and also another small time to accelerate again from zero to 90 mph. And this means that Assumption #3 above is false. Because neither the train nor the fly is perfectly rigid, they can be going at two DIFFERENT speeds even while they're stuck together. (Non-rigidity means that your leading parts can be going at a different speed than your center of mass.) So, at the instant the fly's LEADING EDGE reaches zero, then indeed the train's LEADING EDGE is also at zero. But that simply means that the fly and the train are undergoing a slight, temporary deformation. Within a fraction of a second, the train's leading edge rebounds to 90 mph, carrying the fly with it; and the train's center of mass never notices any change. (Well, technically, the fly's collision would cause a small compression wave to travel backwards through the train at the speed of sound. As the wave pulse reached the train's center of mass, the center of mass would jiggle backwards for an instant, and WOULD come to a dead stop (relative to the ground) for just an instant--while the REST of the train continued on at 90. At no point would the WHOLE train stop.)

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no a fly will not temporarily stop a train it is absurd, A train travelling at 90 mph can hit a bus and not even slow down to much momentum and force when a train is moving

The Great Gazoo

No, because the fly can not create the equally opposing force required to stop the train so the train would not have to stop it's motion to cause the fly to change its direction of motion. The fly's motion would only be an opposing force equal to 1mph would not be enough to stop the train. And the flies mass would have to be equal to or greater than the mass of the train to be able to affect its forward motion enough to stop it. So the fly's forward motion would stop instantaneously, and in the same moment the fly would begin traveling in the direction and speed of the train without affecting the forward motion of the train.

I'm at work right now

No, As the fly hits the train it comes under opposite acceleration to it's motion and yes it will have a velocity of zero at a certain time, however it will not stop the train because the train is not experiencing change in velocity the fly is and the train will continue moving with it's constant velocity. However remember that F = ma . So the greater the mass the greater the force. If this fly was another object with a greater mass that could overcome the force of the train then it would stop the train.

Undefined

No. Think in terms of a canon ball, since there is only one force applied from the gun powder when the ball is initially fired. If it is temporarily stopped, it would fall out of the sky, since there is no additional force to get it moving again. Due to the huge difference in momentum (mass x velocity) the fly is mashed, and the canon ball keeps along its original path. Think of all the air molecules colliding with the canon ball as well. Same thing, it adds up to wind friction, but can not stop the canon ball right away.

Bobby Bo

No the train does not stop. The fly reverses direction which means at some point it's instantaneous velocity is zero relative to the ground. The train will technically slow down since the fly produces a force opposite of it's velocity vector, but it is too small to calculate. Since the train does not reverse direction it's instantaneous velocity will not reach zero.

Jason S

Even if you had some hypothetical train that was perfectly rigid and the fly collided with it perfectly elastically, there would be no need for the train to stop just because the fly has stopped, because in your scenario the fly is only stopped for an infinitely small period of time - the exact, infinitely small moment in which the collision occurs. Since we would also expect the distance traveled by the train to be zero over an infinitely small period of time regardless of its velocity, there is no paradox

arachdog

To answer this question, you will first have to understand the concept of "momentum". Now, momentum has to factors : 1)speed 2)mass It can be simply defined as the 'product of the speed and mass of a body.' (mass= weight) So, if mass=m speed=v (that is how speed is represented in physics) Thus, momentum = mv Let us take mass of train = 10,000kg (any big value, for that matter) Speed of train = 90m/h Thus, Momentum(train) = 90 * 10,000 = 9,00,000 kg m/h ------(1) Let mass of fly= 0.001kg (any small value) Speed of fly= -1m/h (-ve because its in opposite direction) Thus, Momentum(fly) = (-1) * 0.001 = -0.001 kg m/h ------(2) Now, after impact, total momentum = Mom.(train)+Mom.(fly) =9,00,000 + (-0.001) =+8,99,999.999 kg m/h ---------(3) Now, this gives us the total momentum of the fly and the train after impact. After the impact, we know that the fly and train would stick together. So, they form a single body, which has mass = mass of train + mass of fly = 10,000 +0.001 = 10,000.001 kg But, the final momentum of this body =8,99,999.999kgm/h Which is equal to = mv Thus, mv = 8,99,999.999 =>10,000.001 * v =8,9,999.999 (because m=mass of body) Thus, => v = 89.99 m/h Now, this final speed is the speed of the train (with the fly sticking to it) AFTER the impact. As we can clearly see, there has been negligible change to its speed, which was 90 m/h before the impact. So, we conclude by saying that although the speed of train decreased marginally, the train DEFINITELY DID NOT stop for any period of time. Hope that helps.

Arpit T

Let m <<<<<<<<< M; where m is the fly mass and M is the train mass. Then MV + mv = (M + m)v' from the conservation of momentum; wher V = 90 mph (132 ft/sec) and v = 1 mph (1.4 ft/sec). v' is the velocity after impact with the fly stuck to the locomotive's windshield. Solve for v' = (M/(M + m))V + (m/(M + m))v ~ V as we have m <<<<<<<<<<< M. In other words, within measurable limits, the train does not slow down.

oldprof

Let me answer your question with another one. If you're jogging/walking/running and a fly hits you in the chest, do you stop temporarily? Or if you're driving your car and a fly hits the windscreen, does the car stop temporarily? Of course not! The answer is definitely no.

Michael

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