Abstract. In this paper, we aim to use one of the most important and frequently used principles of physics: the law of conservation of momentum and energy in determining the velocity of a steel ball using a ballistic pendulum. We do so by comparing results from two experiments. The first is conducted with a ballistic pendulum and the next through projectile motion. In part A, we use the ballistic pendulum and derive a projectile velocity using conservation of momentum and energy principles. In the second, we use kinematics methods to determine the initial velocity for a projectile. After the experiment, our results show that momentum and kinematics methods produce almost similar results with a percentage difference of 3.82%.

IntroductionA ballistic pendulum is a device for measuring a bullet's momentum, from which it is possible to calculate the velocity and kinetic energy. It is useful in demonstrating properties of momentum and energy. The basic calculations for a ballistic 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.

The ballistic pendulum is a device where a ball is shot into and captured by a pendulum. The pendulum is initially at rest but acquires energy from the collision with the ball. Using conservation of energy it is possible to find the initial velocity of the ball. In this ball-pendulum system we cannot use the conservation of mechanical energy to relate the quantities because energy is transferred from mechanical to non-conservative forces.

Part of this experiment is determining the change in potential energy. It is done by first getting the change in height, the difference of the final and initial height. To get the change in potential energy, the equation below is used:

u=√2 gywhere g= acceleration due to gravity (9.8

m

s2 )

y= the increase in height ( y2− y1)

We then computed the velocity of the steel ball before collision with the equation

v1=(m1+m2)m1

√2gywhere m1 =mass of the ball

m2 =mass of the pendulumy= 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

v1=x√ g2 y

with x =the average horizontal distance travelled by the ball

g=the gravitational constanty=the height of the launcher to the

ground

We had to compare the results of part 1 and 2 so we computed for the percentage difference using the equation

%=¿EV 1−EV 2∨¿

( EV 1+EV 22 )×100% ¿

MethodologyIn part 1 of the experiment, we first identified the mass of the ball and the pendulum. We also measured the initial height of the pendulum. After setting the pendulum bob to 0° and putting the ball in place, we then fired the steel ball to the pendulum holder. We noted the angle. We did this procedure several times. After seeing that the

values were close to each other, we then got the mean angle of the 5 values.

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

pendulumlau

ncher

metal ball

potential energy. We also got the velocity of the ball and pendulum after and before collision.

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.

We determined the initial velocity then compared it with the first result.

Results and Discussion

Methods Velocity of ball before collision

Ballistic Method 363.24 cm/sTrajectory Method 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-projectile. We can then validate the initial velocity with the trajectory method.

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.

ConclusionThis 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.

AcknowledgmentsI 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.

References[1] Young, H., Freedman, R., University Physics

with Modern Physics, 12th Edition, 2008[2] http://en.wikipedia.org/wiki/Ballistic_pendulum

[3] www.cabrillo.edu/~cfigueroa/4B/4Blabs

Free Space Physics is becoming so unbelievably complex

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Q:What is horsepower?A:The power it takes to drag a horse a given distance in a given amount of time.

Q: 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.