4 ms·

This tripped me up too, but one of the StackOverflow answers pointed out something I hadn't considered. If the cars are moving towards each other and you choose

This tripped me up too, but one of the StackOverflow answers pointed out something I hadn't considered. If the cars are moving towards each other and you choose one of them as the reference frame. After they collide and "stop" on the road the reference frame keeps moving (because we're using Newtonian physics and "inertial" reference frames[1] here). This means the cars are still "moving" relative to the reference frame and this kinetic energy needs to be subtracted from the energy of the collision since it's residual kinetic energy in the chosen reference frame (and the velocity vectors of the motion before and after collision point in the same direction relative to the reference frame as well). This is in contrast to car vs. brick wall where choosing the brick wall as a reference frame means that the car is not moving relative to the reference frame after the collision and the kinetic energy is 0. And if you think about it further, the difference is not that you're choosing one object as still and one as moving but that in the car vs. car case, the second car takes on some of the energy from the collision, whereas the wall does not. This makes some intuitive sense if you imagine this collision happening. Forget all the crumple zone stuff - a car hitting a stationary car is going to make that car move - and if you ignore friction and assume the cars stick together the two cars will be moving in the same direction as the initially moving car, just slower. This means not all the initial kinetic energy from the moving car was "used up" in the collision. [1] https://en.wikipedia.org/wiki/Inertial_frame_of_reference https://en.wikipedia.org/wiki/Inertial_frame_of_reference

LegionMammal978 2y ago
The difference is whether the collision is allowed to make the wall move. A 100-mph car won't be halted by a physical brick wall, but will just bust right through it. Afterward, both the car and wall remnants will be moving at 50 mph (minus however much energy it takes to tear the section of wall from the ground). In that case, the change in kinetic energy will be not much more than in the car/car case. For a truly immovable wall, the ground has to exert a lot of force to keep it in place, which goes into the car, causing the entire discrepancy.
roarcher 2y ago
Kinetic energy is relative too. Two cars moving at 100MPH in the same direction (relative to the reference frame) have no kinetic energy relative to each other. You're right that if you match your reference frame to one car, that car becomes "stationary" until the collision, but after the collision it is moving relative to the reference frame. But that's the key--it now has kinetic energy relative to the reference frame, but not to the other car. As far as the pair of cars is concerned, all of the kinetic energy between them has been expended, because they are now moving together. Of course this is assuming a scenario where the cars crumple into a single mass, i.e. they don't "bounce". I think part of the confusion in these comments stems from the problem being poorly defined. Some people are considering crumple zones, others are considering whether a brick wall is movable and still others replace it with another car for simplicity. I do think the driver's ed manual is correct in some Spherical Cow sense, but I don't think its authors ever intended for the problem to stand up to Hacker News scrutiny. It's quite funny to me how innocuous things like this can generate these "unladen swallow"-type discussions on here, even though I'm participating.
- s1artibartfast 2y ago
  Kinetic energy is relative to the frame of reference, but Changes in kinetic energy is never relative to fixed reference frame. I think people dont realize they are changing their reference frames, and getting insane results like the amount of kinnetic energy release in the collision depend on what frame you pick. two crumple zones don't matter for head on collision, which is another thing that trips people up.

LegionMammal978 2y ago

The difference is whether the collision is allowed to make the wall move. A 100-mph car won't be halted by a physical brick wall, but will just bust right through it. Afterward, both the car and wall remnants will be moving at 50 mph (minus however much energy it takes to tear the section of wall from the ground). In that case, the change in kinetic energy will be not much more than in the car/car case. For a truly immovable wall, the ground has to exert a lot of force to keep it in place, which goes into the car, causing the entire discrepancy.

roarcher 2y ago

Kinetic energy is relative too. Two cars moving at 100MPH in the same direction (relative to the reference frame) have no kinetic energy relative to each other. You're right that if you match your reference frame to one car, that car becomes "stationary" until the collision, but after the collision it is moving relative to the reference frame. But that's the key--it now has kinetic energy relative to the reference frame, but not to the other car. As far as the pair of cars is concerned, all of the kinetic energy between them has been expended, because they are now moving together. Of course this is assuming a scenario where the cars crumple into a single mass, i.e. they don't "bounce". I think part of the confusion in these comments stems from the problem being poorly defined. Some people are considering crumple zones, others are considering whether a brick wall is movable and still others replace it with another car for simplicity. I do think the driver's ed manual is correct in some Spherical Cow sense, but I don't think its authors ever intended for the problem to stand up to Hacker News scrutiny. It's quite funny to me how innocuous things like this can generate these "unladen swallow"-type discussions on here, even though I'm participating.

s1artibartfast 2y ago
Kinetic energy is relative to the frame of reference, but Changes in kinetic energy is never relative to fixed reference frame. I think people dont realize they are changing their reference frames, and getting insane results like the amount of kinnetic energy release in the collision depend on what frame you pick. two crumple zones don't matter for head on collision, which is another thing that trips people up.