Table of Contents

Conservation of the momentum is one of laws applied in physical science. It states that, when there is a collision between two different objects in an isolated system, the total momentum of the two objects is equal either before the collision or after the collision. Showing that the momentum lost by one object is the same momentum gained by the other object. This law, therefore, explains how the total amount of the objects collected together is conserved or is the value which cannot be changed. A practical study was, therefore, done to prove the statements as explained in the paper. The study was carried out in two cases. First case was between heavier cart and lighter cart. A collision was run with lighter cart striking the heavier cart which is at rest.

The velocities of each cart were recorded before and after the collision. The measurements were repeated three times in order to get accurate results. On the second case, the heavier cart and the lighter cart were used. The heavier cart strikes the lighter cart while moving backward. The strikes each other head on collision. The case was also done repeatedly. Both cases justify that momentum of both carts which are colliding is conserved since the momentum lost from cart one is the momentum gained by the second objects. This means the total momentum for the both carts before the y collide is the same as the total momentum of the same after the collision.

## Introduction

As implied by the Newton’s laws of motion (Goldstein, 1980), the law of conservation states that the total momentum of the collision of an object does not change. It is constant. It easily explains that the sum of both objects’ momentum equals to the sum of the same object’s momentum after the collision. This theory holds without the matter of compatibility of force between the particles. The momentum exchanged between several particles adds up to zero making the total change also to be zero. The theory of conservation law applies to all collisions, on separations caused by force of explosives and also interactions. When different objects collide, whether it is carts or locomotives, the results are complicated. As long as there are no external forces that are acting on the colliding forces, the conservation of momentum principle holds and provides the tool to understand the collision dynamics. This happens even in the most chaotic situations of collision. The following mathematical equation states the momentum conservation of the collision of the two objects.

pi = m1v1i + m2v2i = m1v1f + m2v2f=pf

The initials m1 and m2 represent the masses of the two objects. The velocities of the two objects before collision are represented by v1i and v2i. The final velocity after collision is represented by v1f and v2f. The total momentum of both objects before the collision is represented by pi while P_{f} represents the final momentum after the objects collides. This paper summarizes the lab practical study done to determine the facts of the theory of the conservation of momentum. The study involves recording the velocities of the objects used before and after the collision. This is to determine the total momentum and the percentage change of the momentum for the two objects. The study also reveals how the momentum is conserved in the case of collision.

The aim of the lab experiment is to illustrate the linear momentum conserved in the isolated systems. It also illustrates the Newton’s third law and how the momentum is conserved when comparing the collision in each object of different masses. The materials used in the lab experiment study consists two carts with different weight, one heavier than the other or of the same weight and add masses on one cart. Also, computers and photo gates to measure the velocity of the two carts. The procedure followed for the experiment is to have two carts.

Measure the masses of both carts and the velocity of each before the collision. After recording the velocity and masses of the objects before any collision, then run the collision with the lighter cart striking the heavier cart is standing. In this case, the heavier cart is standing. Record the velocity and mass of both objects after the collision. Then calculate the velocity of both carts before and after the collision. Then one can be able to calculate the momentum of both objects before and after the collision.

One can also determine how close the results are of total momentum of both objects either before or after the collision. The relative speed before and after the collision of both carts can be easily determined. On the second experiment, the same procedures are used, but the action of collision is different. The heavier cart strikes the lighter cart while moving backward. In the case, both the lighter and heavier carts are moving. So there occur the head-on collisions. The results of the lab study were recorded in the tables below:

All the results were recorded in the tables above. In Table 1a, 2a, 3a, and 4a shows all the results which were recorded during the experiment in the lab. The columns named trials indicate the repeated times of the same experiment. Mass 1 is the weight measurements of the first cart while Mass 2 shows the measurements in kilograms of the second cart. V2 Initial and V2 Initial are the velocity of both carts before the collision occurred. The total velocity of both objects is also recorded in the column V Both.

The momentum of both carts is recorded in P1 Initial and P2 Initial and the P Both columns shows the total momentum of both carts. In table 1b, 2b, 3b and 4b are different fro the discussed above. The table starts by categorizing the number of trials. In the column P1 Initial, the momentum value of the first cart is recorded before the collision and P1 Final shows the momentum value of the first cart after the collusion. Also, P2 Initial and P2 Final show the momentum of the second cart before and after the collision respectively. The total of the momentum for the both carts before the collision is recorded at Ptot1 column. The total momentum values of both carts after the collision are shows in the Ptot2 column.

The percentage difference between the total momentum of both carts after and before the collision is calculated and shown in P% diff column. Ki and Kf columns show the kinetic energy before the collision and after the collision respectively. The last column of the tables’ labeled %K lost shows the percentage kinetic energy lost after the collision. In Table 1b, trial one to three justifies the conservation momentum as the results shows that, the total momentum values of all trials are similar since the percentage difference is extremely minimal in elastic collisions. This is justified as shown in the Table 1b that the percentage difference of momentum in all trials ranges between 1 and 10 percent. This is because the kinetic energy loss is extremely minimal. There is a bigger percentage difference of momentum in Inelastic collisions between the initial momentum and the final momentum after collision since the percentage of lost energy was high ranging up to 80 percent.

The percentage error or the lost energy is the kinetic energy which is converted to forms like heat and sound on collision. These forms of energy cause the total momentum of both carts for either after or before the collision not to balance (Raymond & Jewett, 2012).

In conclusion, the total momentum of the two carts before collision is relatively similar to the total momentum of the same carts after the collision. The results show the opposite difference of the total momentum as justified by the results recorded in the tables above.

When the momentum difference in one object in the collision is one percent, the same difference change of momentum is lost directly opposite to the other. This shows that the forces acting between the two carts have the equal magnitude although the direction is opposite. This is because, the collision the impulse, which the first cart experienced, is the same as the momentum change experienced by the same cart. Since both carts experiences opposite collisions, though equal, so it is logical that they both have the opposite momentum change.

In summary, the first case where the light cart strikes the heavy cart, there is elastic collision where momentum is conserved as it remains constant. The second case where both carts collide head-on, there occurred inelastic collision where the momentum before and after the collision is opposite. This paper, therefore, has exhibited the law of momentum conservation. It has also demonstrated that, in a collision the change in the momentum of the first object is exactly equal to the opposite of the change momentum of the second object. Meaning that the lost momentum of the first object is the same to the momentum gained by the second object.

Most objects in the collisions lose momentum and slow down in speed while the other one gains the speed and gains the momentum. If the first object gains momentum by 1 unit, then the second object loses the momentum by 1 unit, But the total momentum of the both objects is the same either before of after the collision. Then, a conclusion is given that the momentum of the two objects is conserved.