I understand that they have two similar but different formula’s that both scale differently with velocity. I also understand that momentum has a direction ie. Vectored, and kinetic energy is directionless. What I can’t wrap my head around is how they are seperate properties with differing values and how it interacts with forces on an object.
For example, when an object collides with a wall, momentum drops to zero, the change in momentum requires the wall to exert force on the object and it involves some work done, and therefore energy. At the same time, the kinetic energy of the object is also released as heat(?)
In: 1
Momentum = mass * velocity
Kinetic energy = 1/2 * mass * velocity^2
In a collision, momentum is conserved, but if the collision is inelastic, some of the energy is converted to heat.
For example you have two pairs of 1kg and 10kg balls, one pair perfectly bouncy, the other is clay that sticks together when it touches.
If the small ball is moving left at 10m/s and the large ball is moving right at 1m/s and they hit squarely, the bouncy balls will just reverse their direction, the clay balls will become a stationary lump, with all the energy converted to heat.
Now, all the balls might start out with the same amount of momentum, but the small balls have more kinetic energy than the big balls. When you’re accelerating an object, the momentum is force * time, but kinetic energy is force * distance. The smaller balls move a longer distance in the same amount of time, so they require more energy to get the same momentum.
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