SAMPLE COMPUTATIONS(Fig 1.1) Velocity of the steel ball and the pendulum right after collision,u= u = u= 82.43 cm/s(Fig 1.2) Velocity of the steel ball before the collision,V1= V1= V1= 413.66 m/s(Fig 2)Velocity of the steel ball before the collision,V1= V1= V1= 478.68cm/s(Fig 3)Percent Difference 100% = 100% = 14.57%(Table 1) Getting the Initial Velocity of the Steel Ball, Ballistic Method

mass of the steel ball, m1= 65.875g mass of the pendulum, m2= 245.8g

Average angle (from 5 trials)35.6 degrees

Initial height of the pendulum7.1 cm

Final height of the pendulum11 cm

Velocity of the steel ball and the pendulum after collision, u87.43 cm/s

Velocity of the steel ball before the collision413.66 cm/s

(Table 2) Getting the Initial Velocity of the Steel Ball, Trajectory Method

Average x (from 5 trials)57.62 cm

Height from the reference point to the ground7.1 cm

Velocity of the steel ball before collision478.68 cm/s

ANALYSISThis experiment is about the law of conservation of momentum. This law states that for a collision occurring between two objects in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision, which also means that the momentum lost by object 1 is equal to the momentum gained by object 2. In our case the momentum of the steel ball must be equal to the momentum of the pendulum, because the ball and the pendulum will have an inelastic collision (their velocity after the collision will be equal) and it was stated in the law that momentum is conserved in an inelastic collision. The experiment aims to find the initial velocity of the steel ball using two different principles, first is the one that Ive already mentioned which is the law of conservation of momentum and second is the projectile motion. In the part 1 of the experiment we used the Ballistic Pendulum to determine the initial velocity of the steel ball. Set-up 1 was made, the steel ball is fired to the pendulum holder and the displaced angle from the swinging of pendulum was recorded. Five trials were made in getting the angle; this angle will be used as a reference in measuring the initial height and final height of the pendulum. The initial and final height will be used in computing for the velocity of the steel ball and pendulum right after the collision, a sample computation was presented earlier at Fig 1.1. A formula using the law of conservation of momentum was derived in order to solve for the initial velocity of the ball, a sample computation was also presented earlier at Fig 1.2. There were no difficulties encountered while performing the experiment, the instructions in the manual was clearly written in a way that it was easy to follow. (Set-Up 1) The ballistic pendulum

In the part 2 of the experiment using the projectile motion, we will verify the result of the initial velocity that weve obtained in the first part. The pendulum was fixed upward so that we can fire the ball horizontally as shown in Set-Up 1. The vertical distance of the firing position was recorded. In our group we tried two different set-ups, we tried to fire the ball from the spring gun above the table down to the floor (211 cm) so the vertical distance is affected by the height of the table and we also tried firing the ball from the spring gun down to the surface of the table only (7.1 cm). A carbon paper was placed to the predicted area of where the ball will land, then horizontal distance was measured. Five trials were made to get average horizontal distance which will be used in computing the initial velocity by projectile motion, a sample computation was shown in Fig 2 earlier. We compared the results that we got from the two set-ups that we made. We computed for the percent difference using the formula in the sample computation at Fig 3. The percent difference of our first set-up (which is when we allow the ball from the spring gun to land at the floor) is larger than the percent difference that we get in our second set-up (which is when we just allow the ball to land at the surface of the table) so we decided to just record our data in the second set up. The possible cause of high percent difference in the first set-up is the inaccuracy in measurements because the distance to be measured in the second set-up becomes larger, the margin of error also becomes higher. (Set-Up 1) The ballistic pendulum in projectile method

From the experiment that weve done, I could say that in determining the initial velocity of the ball, the ballistic method is the more convenient and more accurate because we can get a lot of source of inaccuracy in the trajectory method like when we are measuring the horizontal and vertical distance.

CONCLUSIONThe objectives of the experiment are: to use the principles of conservation of energy and momentum in determining the velocity of the steel ball using ballistic pendulum and to validate the initial velocity of the steel ball through projectile motion. The experiment make use of the principle that the total momentum and energy of a closed system does not change. We can use the principle of law of conservation of momentum in solving for the initial velocity of the steel ball since the pendulum and the steel ball will be having a completely inelastic collision, they stick together after the collision and their velocity after the collision will be the equal. It was in the law that in all kinds of collision, the momentum is conserved, therefore the formula in solving the final velocity of the steel ball and the pendulum is can be derived from the equation of the law of conservation of energy which is . In addition if we have a completely inelastic collision, the kinetic energy is not conserved, instead it was converted to gravitational potential energy so together with the equation of the law of conservation of energy above we can use the formula of the gravitational potential energy which is to obtain the formula for the velocity of the steel ball and the pendulum, . When the formula for the final velocity of the steel ball and the pendulum was already known it was now possible for us to find for the initial velocity of the steel ball. All this principles were proved to be true when weve used another method in calculating for the initial velocity of the ball which is the trajectory method, in this method the principle of projectile motion was used. The results of the initial velocity of the steel ball that we obtained from two different methods appears to be almost the same, so we conclude that momentum is really conserved in a collision.

APPLICATIONOne example of real life application of the momentum and collisions is the use of air bags in automobiles. Air bags are used in automobiles because they are able to minimize the effect of the force on an object involved in a collision. Air bags accomplish this by extending the time required to stop the momentum of the driver and passenger. When encountering a car collision, the driver and passenger tend to keep moving in accord with Newton's first law. Their motion carries them towards a windshield that results in a large force exerted over a short time in order to stop their momentum. If instead of hitting the windshield, the driver and passenger hit an air bag, then the time duration of the impact is increased. When hitting an object with some give such as an air bag, the time duration might be increased by a factor of 100. Increasing the time by a factor of 100 will result in a decrease in force by a factor of 100. Now that's physics in action.

The same principle explains why dashboards are padded. If the air bags do not deploy (or are not installed in a car), then the driver and passengers run the risk of stopping their momentum by means of a collision with the windshield or the dashboard. If the driver or passenger should hit the dashboard, then the force and time required to stop their momentum is exerted by the dashboard. Padded dashboards provide some give in such a collision and serve to extend the time duration of the impact, thus minimizing the effect of the force. This same principle of padding a potential impact area can be observed in gymnasiums (underneath the basketball hoops), in pole-vaulting pits, in baseball gloves and goalie mitts, on the fist of a boxer, inside the helmet of a football player, and on gymnastic mats. Now that's physics in action.

Fans of boxing frequently observe this same principle of minimizing the effect of a force by extending the time of collision. When a boxer recognizes that he will be hit in the head by his opponent, the boxer often relaxes his neck and allows his head to move backwards upon impact. In the boxing world, this is known as riding the punch. A boxer rides the punch in order to extend the time of impact of the glove with their head. Extending the time results in decreasing the force and thus minimizing the effect of the force in the collision. Merely increasing the collision time by a factor of ten would result in a tenfold decrease in the force. REFERENCE[1] (1996).The Physics Classroom. Real World Applications. Retrieved from http://www.physicsclassroom.com/class/momentum/Lesson-1/Real-World-Applications