I have been doing research and the explanations don’t make sense. Kinetic energy is based off of velocity, and so is momentum. If the kinetic energy decreases, the momentum would also have to decrease, because the objects in the collision have less energy and therefore move at slower rate, and therefore have less momentum. It seems like momentum and energy are one, but but in reality it isn’t? And here’s my thought experiment:
Two objects collide and lock together. They maintain their original momentum, but are now locked together as one. According to what I am currently learning, they have lost kinetic energy, but they have maintained their total momentum. Now, the locked objects hit an equal copy of themselves in front of them, except the copies are unlocked. Due to conservation of momentum, the locked object stops, and the copies are now at the same point the two objects were at the start of the experiment, before they collided. How can energy be lost, and then gained? Where did they go? If someone could simply explain what I’m missing, that would be very helpful as I have a test in 12 hours. Thanks!!
In: Physics
Hi,
Energy is never lost, period.
Kinetic energy might be lost to heat in a collision, but the total energy before the collision (all kinetic) will be the same as the energy after the collision (kinetic plus heat in this example.)
Momentum is always conserved in a collision, regardless of whether the total kinetic energy changes.
From a math perspective, the kinetic energy is proportional to mass * velocity * velocity, and the momentum is mass * velocity, so it is completely plausible that one can be constant while the other changes.
I found this answer to be fairly clear:
https://physics.stackexchange.com/a/132763
But you really should give one example, with details, of a collision that is confusing you. Your multiple collision example is tough to follow and is surely not helping your understanding. Break it down to small bits, understand the small bits, and then the total situation will be clear.
You thought experiment is horribly explained because I’ve read it 4 times and can’t follow it. You’re leaving out way too much information I think like the actual mass and velocity of the objects.
Because that’s another thing, kinetic energy and momentum also both depend on the mass of the objects too.
But you’re describing, no energy has been lost or gained at all, it’s all just kinetic energy in the moving of the objects, all that is changing is what objects currently have the energy.
For example, say you have 4 bowling balls of the same mass, if you roll ball A into ball B, the kinetic energy is just getting transferred form ball A to ball B. Then if ball B hits ball C and D at the same time, the kinetic energy is getting transferred for balls C and D and just getting split between C and D.
So even tho balls A and B aren’t moving anymore, and balls C and D are moving slowly, no kinetic energy has been gained or lost.
The kinetic energy of a moving object is 1/2*m*v^2 but the momentum is m*v.
That means that if an object’s speed is halved, the momentum is also halved, but kinetic energy is quartered.
So, let’s say we have one object with mass m and speed v hit an object also with mass m and speed 0. That means the total kinetic energy of the system is 1/2mv^2 and the total momentum of the system is mv.
Then they collide and stick together. Since momentum has to be conserved, the two objects must be moving with speed v/2, because there’s twice as much mass moving now.
But the kinetic energy is 1/2*(2m)*(v/2)^2 which is equal to 1/4mv^2 which is less than the initial energy.
Simply, kinetic energy isn’t generally conserved, momentum is.
Total energy is conserved (as long as we’re not invoking nuclear reactions or relativity), total momentum is conserved, but there’s no particular reason to think kinetic energy by itself would be conserved.
In your thought experiment it’s too open to be sure, but one of your assumptions about an intermediate state isn’t right.
Clap your hands together in front of you, trying to be as symmetrical as possible. The moment before they connect, they have the same non-zero kinetic energy (same mass, same speed); the moment after they connect, they have zero kinetic energy. Where’d the energy go? Where’d the momentum go?
I think what you’re missing is that momentum is technically based off of velocity *in a specific direction*, while kinetic energy is a scalar (aka just a number). Momentum to the left is different than momentum to the right. When you clapped your hands, your leftward momentum plus your rightward momentum always added to zero.
In your thought experiment, if I’m reading it right, I think you’re combining an inelastic collision to start with an elastic collision at the end, so you’re going to end up seeing some weird results when you flip from one to the other.
Say you’ve got a big block of concrete moving to the right. It’s got a mass M and a velocity V, and that calculates out to kinetic energy K and momentum P. Then you’ve got a snowball that you’ve thrown to the left with mass m, velocity v, kinetic energy k, and momentum p. Because it’s ELI5 we’ll ignore all those pesky things like friction and air resistance.
Snowball hits concrete, and the combined object keeps moving to the left. Turns out a snowball isn’t enough to stop a concrete block. However, because of Newton’s Laws of Motion, we know that the snowball applied a force to the block, which accelerated it – changed its velocity. Meanwhile, the combined object as a whole now has mass M+m, velocity V1 (which is slightly slower than the block’s original V), kinetic energy K1 (which is lower than the original K), and momentum P+p. Total mass is conserved, total kinetic energy is conserved, the rest change.
The key there is that kinetic energy isn’t typically conserved. It just doesn’t work that way. Imagine dropping a buttered piece of bread onto the floor, it just goes thwack and stops moving.
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TLDR: Momentum is conserved, but kinetic energy is not; since KE is just a measurement of how much moving is happening it can appear and disappear without causing problems. (There’s typically something converting to or from KE, such as potential energy turning into kinetic energy when you drop a ball, but it can also just be that it makes heat or a sound – like clapping hands – but that aspect is often ignored in physics homework).
The lost kinetic energy heats up the objects, turning into thermal energy (motion of individual atoms with no net momentum). You can’t ever get it all back again.
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