Suppose the impact coefficient k is similar, it does make a difference whether a bike crashes into a standing car (case 1) or a car crashes into a standing biker (case 2).
Sorry I don’t have much time today to get into it. Seems to me you can’t solve for case 2 here since in this case m2 and m1 are switched. But it does not matter, I am not trying to solve for speed before and after.
The force of the impact does not depend on the mass, I agree, but the energy to dissipate (in the cyclist body) is much higher.
I’m just saying that inertia plays a role as it contribute to the energy necessary to stop either vehicule. I am happy to be proven wrong, I just don’t think this is the right equation to do so.
The thing is: You are using velocities v1, v2 which are relative to Earth. But none of the two vehicles collide with Earth - they collide with each other, thus the thing that matters is their relative speed, thus the difference of their velocities relative to Earth.
(That’s also why the speed at which both Earth, the car, and the motorized bike move around the sun does not matter - relative speed is all what matters).
The other thing is that a human colliding with an object of several tons weight with a speed of, say, 36 km/h is not “elastic”. 36 km/h is 10 meter per second, which is equal to about one second of free fall (accelerating with a= 9.81 meter per square second to the ground), which is equivalent to a fall height of h = a/2 * s ^2 or 5 meters.
Somebody falling from 5 meters hight on hard concrete ground will not bounce up but will likely have some broken bones, or a broken skull. What happens is that all parts of thier body is decelerated to a speed of zero within a distance of one or two centimeters, which involves massive forces that easily break bones.
And a speed of 14 m/s, or 54 km/h corresponds to a fall of ten meters depth - almost certainly lethal if hitting a two-ton concrete block.
@Alerian@sh.itjust.works
Suppose the impact coefficient k is similar, it does make a difference whether a bike crashes into a standing car (case 1) or a car crashes into a standing biker (case 2).
Sorry I don’t have much time today to get into it. Seems to me you can’t solve for case 2 here since in this case m2 and m1 are switched. But it does not matter, I am not trying to solve for speed before and after.
The force of the impact does not depend on the mass, I agree, but the energy to dissipate (in the cyclist body) is much higher. I’m just saying that inertia plays a role as it contribute to the energy necessary to stop either vehicule. I am happy to be proven wrong, I just don’t think this is the right equation to do so.
The thing is: You are using velocities v1, v2 which are relative to Earth. But none of the two vehicles collide with Earth - they collide with each other, thus the thing that matters is their relative speed, thus the difference of their velocities relative to Earth.
(That’s also why the speed at which both Earth, the car, and the motorized bike move around the sun does not matter - relative speed is all what matters).
The other thing is that a human colliding with an object of several tons weight with a speed of, say, 36 km/h is not “elastic”. 36 km/h is 10 meter per second, which is equal to about one second of free fall (accelerating with a= 9.81 meter per square second to the ground), which is equivalent to a fall height of h = a/2 * s ^2 or 5 meters.
Somebody falling from 5 meters hight on hard concrete ground will not bounce up but will likely have some broken bones, or a broken skull. What happens is that all parts of thier body is decelerated to a speed of zero within a distance of one or two centimeters, which involves massive forces that easily break bones.
And a speed of 14 m/s, or 54 km/h corresponds to a fall of ten meters depth - almost certainly lethal if hitting a two-ton concrete block.