Collisions

1) Introduction
This Lab is about conservation of momentum. It is to investigate the difference of momentum before and after collisions. Using the photo gates record the velocity of each cart, comparing momentum and kinetic energy to find the law. The experimental apparatus are two red carts in approximately same weight and a gold cart in lower weight than the red ones, a stable air track (blow a constant stream of air out through numerous tiny holes) with low friction and two photo gates.
2) Project description
2.1) Theory
We should have the concept of momentum to disassociate velocity and momentum. The linear momentum of an object is the product of the object’s mass and velocity. Linear momentum is a vector quantity that in the same direction as the velocity. P = m * v (kg. m/s) During a collision, it is usually straightforward to measure the mass and velocity of an object, so that its momentum just after the collision and just before the collision can be found. The collisions include elastic collision (one in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision, ideally with no loss of energy due to sound, heat, light, or deformation) and inelastic collision (one in which the total kinetic energy of the system is not the same before and after the collision; if the objects stick together after colliding, the collision is said to be completely inelastic).
In this lab, we should measure the length of the tapes which will interrupt the photo gate laser on the carts. The measurements will enter into the data studio to measure the velocity is value of the tape’s length divided by the time. Then, we push a cart to collide another one on the track.
2.2) Experiment
To start, perform some billiard style collision. That means two objects of the same mass which connect, then break back apart. The actual physical term for this is a perfectly elastic collision. The objects bounce off of each other, ideally with no loss of energy due to sound, heat, light, or deformation.
There are totally three cases in this lab. In the first case, we investigate elastic collision. We use two red carts in the same mass. In this condition, we should only consider velocity. The carts will ideally interchange their velocity, due to the conservation of momentum formula. (m1v1 + m2 v2=m1 v’1 + m2 v’2) Then, we replace one of the red carts by a lighter gold cart to now have two carts of different mass, and perform the same experimental collision. Compare velocities of the pair of carts before and after. Also compare the momentums of the pair of carts before and after. In these cases, we may need more space past the photo gates for the carts to travel post-collision. We lift a cart off the track after it has recorded final velocity if it appears the other cart needs room to move. Finally, we will investigate perfectly inelastic collisions. In these collisions, the two objects collide, and do not separate after the collision. Leaving only a single object(and thus velocity) post collision. Perform the same series of tests you did previously, making note of initial and final velocities and masses.
2.3) Discussion
Through the data in the form below, we can observe that in the first case, the differences of velocities, momentums and kinetic energy of the carts are small. It means that there is almost no external force in the system. The carts exchanges velocity with each other, because they are in same mass. P = m v, they have same mass and velocity, so they have approximately same momentum, same as the kinetic energy.
In the second case, the two carts have different masses. They have different velocities, because their momentums are same, as there is almost no external force in this system. Ek = 1/2 m v^2, so they also have different kinetic energy. In the last case, the carts make inelastic collision different from the last two cases. So the velocities, momentums and kinetic energy of the red cart and red with gold cart are different.
3) Conclusion
1-- The elastic collision shows the conservation of momentum, because the momentums of the carts are same before and after the collision.
2-- The same velocity don’t represent same momentum. The different velocities also can’t mean the different momentums, taking case one and two as examples.
3-- As we know, the conservation of momentum occur in the special conditions, without any other external force in the system.