E202: CONSERVATION OF MOMENTUM: THE BALLISTIC PENDULUM

FRISNEDI, Nadine T.

OBJECTIVE

The experiment aims to accomplish its two main

objectives. The first one is to use the principles of

conservation of energy and momentum in

determining the velocity of the steel ball. Through

the experiment, the students will be able to gain

more knowledge and appreciation about the

concepts of conservation of momentum and how it

is helpful in determining the velocity of moving

objects and even the distances it covers. The

experiment can also help the students understand

on how the angular displacement of an object is

important in getting its initial velocity. The

experiment will also show how Kinetic Energy and

the Gravitational Potential Energy is closely

related with the conservation of momentum and

during a collision.

The second objective is to be able to validate the

initial velocity of the steel ball through projectile

motion. The students will not just learn how to

compute for the velocity of the steel ball using the

ballistic pendulum but also though the use of

projectile launcher. The experiment will help the

students be able to understand the applications of

the given laboratory formulas in solving problems

involving Physics and will surely be helpful in

studying other concepts about it. Another thing

about this experiment is that it is very easy to

conduct and it is not time consuming, thus

students will enjoy doing it.

The significance of this experiment is that it a way

of showing how an inelastic collision happens,

what are the things happened afterwards and

lastly it shows how fast an object in two

dimensions is moving.

MATERIALS AND METHODS

(Figure 1. The materials and equipment used in

the experiment. )

Before the experiment was actually performed, in

which the ballistic pendulum with the steel ball

were tested first to prevent accidents since a few

of them are releasing the ball accidentally even

before the release. The projectile launcher with

ballistic pendulum was set up away from the class

and pointing towards a bag to prevent it from

hitting anything else or a person. The level or

range assigned for the group was medium.

At the beginning of the experiment, angle marker

on the ballistic pendulum was set up to 0°. Since

group had trouble making it stay at that angle, the

group decided to check first if the working table is

leveled and when it finally becomes at 0°, we

started gathering the required data. To get the

initial height of the ballistic pendulum, the distance

from the base to the center of the pendulum while

at the reference point 0 is measured using the

meter stick

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(Figure 2. Setting the reference point to zero and

measuring the initial height.)

(Figure 3. Measuring the initial height of the

pendulum.)

After getting the measurement, the steel ball was

loaded to the spring gun on the medium level

which is said to be the second click heard and then

fired to the pendulum holder. The pendulum

moved and made an angular displacement. This

displacement was recorded. The bob was placed

back to zero and then the steel ball was again

fired. This part was done for a total of five trials.

The mean or the average angle was computed by

adding the five angles and dividing it by five. The

pendulum bob was set to the computed average

angle. And while it is in the mean angle, the

pendulum was set up on to that angle. The final

height of the pendulum was measured from the

base to the center of the pendulum.

(Figure 4. Measuring the final height of the

pendulum based on the computed mean angle)

The increase in height was calculated by

subtracting the initial height of the pendulum from

the final height of the pendulum. The increase in

height was then used for determining the velocity

of the steel ball and the pendulum. The mass of

the steel ball is used to compute for its velocity.

The mass of the pendulum was also needed in

order to compute for the velocity including the

additional 100 grams in it.

In the second part, the pendulum placed and

locked upward so that the ball can be fired to the

floor in horizontal direction. The spring gun was

then placed at the end of the table. The vertical

distance, y of the firing position which is the center

of the hole of the spring gun on the table down to

the floor was measured using the meter stick.

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(Figure 5. Setting up the spring gun at the end of

the table while the pendulum is placed upward.

(Figure 6. Measuring the vertical height of the

firing position.)

The computed velocity from the first part of the

experiment was then used to predict in how far

horizontally the ball will land and to test it further,

the group launched the ball and knew which part

it will land. The group then placed a bond paper

beneath a carbon paper. Taped the papers

securely which will be used to determine the

horizontal distance of the ball’s landing since upon

landing onto the carbon paper the ball will leave a

black mark on the bond paper. The black marks in

the bond paper will show how far the steel ball

travelled horizontally. For this part, a total of five

trials was done.

(Figure 7. After the steel ball was fired, it landed

on the carbon paper which left a mark on the bond

paper.)

The horizontal distances were measured carefully

stating from the tip of the spring gun to the end of

the table and from the end of the table to the black

marks left on the bond paper using the meter

stick.

(Figure 8. Determining the horizontal distance

from the tip of the spring gun to the tip of the

table.)

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(Figure 8. Determining the horizontal distance

travelled by the steel ball.)

These distances were recorded. The average

horizontal distance was then computed by adding

all the five distances and also dividing it by five.

The average horizontal distances and the

measured vertical height was then used to

compute for the velocity of the steel ball.

OBSERVATIONS AND RESULTS

The first part of the experiment was focused in the

determination of the velocity of the steel ball after

the inelastic collision with the pendulum bob. Upon

completing the five trials, the group calculated for

the average angle. Upon completing the data to be

gathered, the group then calculated the increase

in height by subtracting the initial height of the

pendulum to the final height of the pendulum. The

group then used the increase in height y, in

determining the change in potential energy which

is also said to be the velocity of the steel ball and

the pendulum right after collision. The group then

used the given formulas from the laboratory

manual in order to compute for the initial velocity

of the steel ball before its collision with the

pendulum.

Table 1, Getting the Initial Velocity of the

Steel Ball, Ballistic Method

Mass of the steel ball, m1 = 65.875g

Mass of pendulum, m2 = 241.6g

Trial Angle

1 26° Initial height of the

pendulum 𝑦1=8.5cm

2 25.5° Final height of the

pendulum 𝑦2=11.7cm

3 26° Increase in height

𝑦 = 𝑦2 − 𝑦1 𝑦= 3.2cm

4 26°

Velocity of the

steel ball and the

pendulum right after collision, 𝑢 =

√2𝑔𝑦

𝑢=

79.196

cm/s

5 26°

Velocity of the

pendulum before

collision

𝑣2=0cm/s

Average

Angle: 25.9°

Velocity of the

steel ball before collision, 𝑣1 =

(𝑚1+𝑚2)

𝑚1√2𝑔𝑦

𝑣1=

375.061

cm/s

Sample computations:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑔𝑙𝑒 = 𝜃1 + 𝜃2 + 𝜃3 + 𝜃4 + 𝜃5

5

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑔𝑙𝑒 = 26° + 25.5° + 26° + 26° + 26°

5

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐴𝑛𝑔𝑙𝑒 = 25.9°

𝑦 = 𝑦2 − 𝑦1

𝑦 = 11.7 𝑐𝑚 − 8.5 𝑐𝑚

𝑦 = 3.2 𝑐𝑚

𝑢 = √2𝑔𝑦

𝑢 = √(2) (980𝑐𝑚

𝑠2) (3.2𝑐𝑚)

𝑢 = 79.196 𝑐𝑚/𝑠

𝑣1 = 𝑚1+𝑚2

𝑚1(√2𝑔𝑦)

𝑣1 =65.875𝑔 + 241.6𝑔

65.875𝑔(√(2)(

980𝑐𝑚

𝑠2)(3.2𝑐𝑚)

𝑣1 = 375.061 𝑐𝑚/𝑠

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The second part is mainly about validating the

computed initial velocity of the steel ball through

projectile motion. The group measured the vertical

distance of the firing position which is from

reference point to the ground. The velocity in the

first part was used for predicting the horizontal

distance. When the ball was fired and landed to

the carbon paper, it left a black mark that will

indicate the horizontal distance it covered after

being launched. After doing the five trials, the

average of the horizontal distance was then

computed. After getting the average, and all the

necessary data, the group then computed for the

initial velocity using the given formulas in the

laboratory manual.

Table 2. Getting the Initial Velocity of the

Steel Ball, Trajectory Method

Gravitational Constant, g = 980 cm/s2

Trial Horizontal Distance, x

Height from

the reference

point to the

ground

𝑦 = 88.9

cm 1 153.8 cm

2 153.2 cm

3 154.1 cm Velocity of the

steel ball

before collision,

𝑣1 = 𝑥√𝑔

2𝑦

𝑣1 =

362.113

cm/s

4 154.7 cm

5 155.4 cm

Average x:

154.24 cm

Sample computations:

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑥 = 𝑥1 + 𝑥2 + 𝑥3 + 𝑥4 + 𝑥5

5

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑥 = 153.8 + 153.2 + 154.1 + 154.7 + 155.4

5

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑥 = 154.24 𝑐𝑚

𝑣1 = 𝑥√𝑔

2𝑦

𝑣1 = (154.24𝑐𝑚)(√(980𝑐𝑚

𝑠2 )

(2)(88.9𝑐𝑚)

𝑣1 = 362.113 𝑐𝑚/𝑠

The group then computed for the Percent

Difference of the two computed velocities. This is

one way to know or confirm if the procedures were

done properly so that the group will arrive with

closely related results.

Table 3. Determining the Percentage

Difference

Percentage Difference,

% diff = |𝐸𝑉1−𝐸𝑉2|

(𝐸𝑉1+𝐸𝑉2

2)

Percent difference

= 3.513%

Sample Computation:

% 𝑑𝑖𝑓𝑓 =

|𝐸𝑉1 − 𝐸𝑉2|

(𝐸𝑉1 + 𝐸𝑉2

2)

% 𝑑𝑖𝑓𝑓 = |375.061 − 362.113|

(375.061 + 362.113

2)

%𝑑𝑖𝑓𝑓 = 3.513%

DISCUSSION & CONCLUSION

From the performed experiment, I could say that

it was a success. By following the procedures

stated in the manual properly gave us all the

relevant data that are needed. We have computed

properly all that was required for the experiment

too by using the appropriate formula for those.

In the first part of the experiment, we have used

the principles of conservation of energy and

momentum in determining the velocity of the steel

ball using a ballistic pendulum. Our data proves

that the conservation of energy and momentum

can be used in getting the velocity of the steel ball

and pendulum bob. Since the collision was

inelastic, the final velocity of the two masses will

be the same. This conclusion tells us that we have

achieved the first objective of the experiment.

For the second part, we have validated the initial

velocity of the steel ball through projectile motion.

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The velocity in the first part was also used in this

part for the determination of horizontal distance.

There were five trials and the average horizontal

distance is what we used to compute for the initial

velocity using the formula in the laboratory

manual. The result we got is really close from the

initial velocity we got from the first part of the

experiment. This only says that we have also

achieved the second objective of the experiment.

I believe that in terms of the errors made in the

experiment, it is somewhat minimal. The sources

of error can be from the measurement of the

vertical and horizontal distances. Since we

manually measured these components, there is a

high possibility that the measurements we got

were inaccurate. The percent difference we got

was 3.513% which is considered as small

difference.

ACKNOWLEDGMENT & REFERENCE

I would like to thank my groupmates for being so

cooperative upon doing the experiment. I

appreciate all of their efforts since without their

help, our experiment will have a great chance of

failure. I also thank our professor, Prof. Ricardo F.

De Leon, Jr. for guiding all throughout the

experiment. I thank him for instructing us on how

we should set up the materials and equipment for

our experiment. I also would like to acknowledge

the lab assistants for reminding us how to handle

the materials and equipment and telling us about

the important things to remember such as the

weights to be added. Lastly, I would like to thank

my family for supporting me in my studies as I

pursue my degree in Mapúa.

Reference:

Calderon, Jose C., (2000) College Physics

Laboratory Manual, Mapúa Institute of

Technology, Manila: Department of Physics.

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