Assuming this encounter between the two objects is elastic, the initial object that is moving towards the stationary object would transfer all of its kinetic energy and would stop moving while the other object would begin moving at the same speed.
In order to prove this, we need to define some concepts. First is the elastic collision, which is defined as a collision where all kinetic energy and momentum are conserved and no energy is lost/converted to another form by outside forces. We know this is elastic because there is no friction to lower energy in the system and convert it to heat energy and no other factors such as air resistance.
Another concept to define is Newton's Third Law: Every action has an equal and opposite reaction. This means that whenever a force is applied on an object, the object in turn applies a force in the exact opposite direction and in an exact amount. This is why a coffee cup doesn't fall through a table when set down. Gravity pulls the coffee mug towards the table and the table pushes backwards in an opposite but equal amount, causing the mug to stay stationary on the surface.
In our situation, I will use the analogy of two pool balls (on a friction-less table), one a cue ball which has been hit towards the other, a motionless 8 ball. Each ball has the following properties:
`Momentum = p = mv`
`KE = (1/2)mv^2`
The momentum of the cue ball is some number greater than zero, as it is moving and it has mass. It also has Kinetic Energy (the energy of movement) for the same reasons. The 8 ball on the other hand is not moving, thus velocity is equal to zero. This means the 8 ball has zero momentum and zero KE.
The two balls collide and, assuming zero friction and the cue is hitting the 8 as directly as possible (1-dimensional collision), the moving cue ball will act upon the stationary ball transferring all of its kinetic energy into the ball, causing it to move. Due to Newton's Third Law, the stationary 8 ball will also act upon the cue ball in an equal but opposite direction, or with all of the force the cue ball initially had but in the opposite way. This will cause the cue ball to stop and lose all momentum and KE.
Because this is an elastic collision, all KE and momentum of the system is preserved throughout the collision (energy in is equal to energy out). If the cue ball has come to a complete stop due to the reaction of the 8 ball we can assume all energy was transferred into the 8 ball and the 8 ball is now travelling at the same speed as the cue ball was before the collision.
In conclusion, due to Newton's Third Law and the understanding of elastic collisions, we can safely assume that if two objects (pool balls) on a friction-less surface were to collide in a 1-directional collision, the initial moving object would transfer all of its energy and momentum into the stationary object and would become stationary itself, while the initially unmoving object would begin to move at a speed equal to the speed of the once moving object before the collision. I hope this answered your question!
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