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
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.
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