c . ô
!"# V g=the gravitational constant y=the height of the launcher to the A ballistic pendulum is a device for measuring a ground bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. It is We had to compare the results of part 1 and 2 so useful in demonstrating properties of momentum we computed for the percentage difference using and energy. The basic calculations for a ballistic the equation pendulum do not require any measurement of time, but rely only on measures of mass and distance. The ballistic pendulum can be used to
measure any transfer of momentum. V V The ballistic pendulum is a device where a ball is In part 1 of the shot into and captured by a pendulum. The experiment, we first pendulum is initially at rest but acquires energy identified the mass from the collision with the ball. Using of the ball and the conservation of energy it is possible to find the pendulum. We also initial velocity of the ball. In this ball-pendulum measured the initial system we cannot use the conservation of height of the mechanical energy to relate the quantities pendulum. After because energy is transferred from mechanical to setting the non-conservative forces. pendulum bob to 0° and putting the ball Part of this experiment is determining the change in place, we then in potential energy. It is done by first getting the fired the steel ball change in height, the difference of the final and to the pendulum initial height. To get the change in potential holder. We noted energy, the equation below is used: the angle. We did this procedure several times. ë After seeing that the values were close to each where g= acceleration due to gravity (9.8 ) other, we then got the mean angle of the 5 y= the increase in height ( ) values. We then computed the velocity of the steel ball before collision with the equation
where m1 =mass of the ball m2 =mass of the pendulum y= increase in height of the pendulum In part 2 of the experiment, we used kinematics to get the initial velocity of the ball with the equation
with x =the average horizontal distance travelled by the ball
Next, we manually set the pendulum to the computed mean angle then we determined the final height of the ballistic pendulum. We determined the increase in height by getting the difference of the measured initial and final heights. This value was used to get the change in potential energy. We also got the
velocity of the ball and pendulum after and before collision.
projectile. We can then validate velocity with the trajectory method.
Part 2 of the experiment required us to get the initial velocity of the ball through projectile motion. This was done by first attaching bond papers and carbon papers on the floor. We measured the vertical distance of the launching point to the ground. We now launched the ball and did this five times. We measured the horizontal distance travelled by the ball then computed the average.
Possible errors occurred due to measurements especially the measuring of the height and horizontal distance of the projectile motion and the initial and final height of the pendulum. We also may have misaligned the launcher which caused discrepancy. Another source of errors includes misreading of the angles.
We determined the initial velocity then compared it with the first result. ]VV V V Methods Ballistic Method Trajectory Method
Velocity of ball before collision 363.24 cm/s 349.61 cm/s
Percentage difference= 3.82% This table presents the results for initial velocity of the steel ball for both methods. This shows that our velocities for both experiments closely matched. When the ball collides with the pendulum bob, the projectile remains embedded in the pendulum bob- a completely inelastic collision. Using conservation of momentum to the collision yields the initial velocity of the ball. After the collision, the pendulum bob will swing upward until all of its kinetic energy is converted into gravitational potential energy. With the vertical distance traveled by the pendulum bob, conservation of energy will give us the velocity of the pendulum-
This experiment focuses on using the principles of conservation of energy and momentum in determining the velocity of the steel ball with the use of a ballistic pendulum. The result is then validated using projectile motion. The laws of conservation of momentum and energy are used with the ballistic pendulum to measure the velocity of a projectile. In this experiment, the steel ball, which has an initial momentum, is fired into a ballistic pendulum, which is initially at rest therefore having zero momentum. The ball collides with the pendulum and remains fixed with the pendulum. They both start to move with a final velocity and therefore a final momentum. After the pendulum catches the ball, the laws of conservation of energy are taken into account. Once they start to move together, they have a kinetic energy. The pendulum will start to gain height as it moves about its axis, thus losing kinetic energy but gaining potential energy until it reaches its maximum height where all the kinetic energy has been transferred into potential energy. Since energy is conserved, the velocity of the pendulum with the ball can be computed. Using conservation of momentum, on the other hand, the velocity of the ball before impact with the pendulum can be determined. In the case of the trajectory method, the velocity can also be computed through kinematics equation, taking into account both the horizontal and vertical components of the ball. As conclusion, we can say that the laws of conservation of momentum and energy were verified in the experiment and we can use projectile motion to validate the initial velocity. c I again want to extend my heartfelt thanks to Professor de Leon for the simulating discussion about this topic. I also express my gratitude to my mom Rachel for the support and my brother for impatiently waiting for his turn on the laptop and making me type faster. Just the same, I thank my groupmates for their help during the
accomplishment of the experiment. And again, thanks to Cean for tagging us the pictures to be used in this report. ] Voung, H., Freedman, R., $ % $, 12th Edition, 2008 Vhttp://en.wikipedia.org/wiki/Ballistic_pendulu m Vwww.cabrillo.edu/~cfigueroa/4B/4Blabs ±VV ;V Physics is becoming so unbelievably complex that it is taking longer and longer to train a physicist. It is taking so long, in fact, to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them. ± Eugene Wigner ;V i:What is horsepower? A:The power it takes to drag a horse a given distance in a given amount of time. ;V i: What's the difference between a mathematician and a physicist? A: A mathematician thinks that two points are enough to define a straight line while a physicist wants more data.