UNIVERSITY OF SANTO TOMAS HIGH SCHOOLNatural Science Department

Academic Year 2013 – 2014

A STUDY TO DETERMINE THE PROPORTION OF THE WEIGHT OF A BALL TO THE FORCE NEEDED FOR IT TO ACCELERATE

An Investigatory ProjectPresented to the Faculty of the Natural Science Department

University of Santo Tomas High School

In Partial Fulfilment of the Requirements in Physics

Griffin Kelly CruzLiam Ruther CugalDither John Nabor

Joshua Nathaniel PadrigoRachelle Pua

Krish Jill TalagtagAngelica Tria

GROUP 2 – SAINT DIONYSIUS

Mr. Ruben SinugbuhanRESEARCH ADVISER

February 26, 2014

ABSTRACT

The group decided to use Newton's Laws of Motion as their inspiration for the

research. This research is for the determination of proportion between acceleration and

mass, as stated in the second law. The group built an experiment set-up to help in the

measurement of variables, particularly distance and time. Prior to the experimentation,

the metal balls used were weighed. The group also tried to derive from formulae to get

the inspiration for the unit Newton (N). The group did several trials to ensure a patterned

data. At the end of the experiment, the group was successful in answering the questions

stated.

CHAPTER 1: INTRODUCTION

I. Background of the Study

Sir Isaac Newton was a mathematician and physics scholar who transformed our

scientific world. In 1666, Sir Isaac Newton started to develop the theories of gravitation

when he was just 23 years old. Then in 1686, he presented three laws of motion in the

Principia Mathematica Philosopae Naturalis1. It is believed that he first started studying

the effects of gravity after watching the apple fall. His curiosity for the fall of an apple

and seeing stars and planets above without falling to the ground, led him to develop three

laws of motion. The first motion is the definition of inertia; the second law explains how

the velocity of an object changes when an additional force is applied; the third states the

action-reaction law. The book was published in July 1687.

‘The “Laws of Motion” is the main topic that is covered in physics. These laws

are considered as one of the basic principles in the subject. The computation in the

second law, on the other hand, is the application of math in this paper.

This study is part of the requirements in Physics IV. Considered as a major

requirement, all students shall accomplish this paper and defend in front of a panel,

headed by the Physics teacher. Upon the completion, the students may now be considered

as candidates for graduation in their secondary studies.

1 https://www.grc.nasa.gov/www/k-12/airplane/newton.html

II. Problems

What is the proportion of the mass of an object to the force required for it to

accelerate?

How does the angle of the paddle affect the amount of force applied?

III. Objectives of the Project

To determine the proportion of the weight of an object to the force required for it

to accelerate

To identify action-reaction forces when given an interaction

To state Newton’s three laws of motion and motion and display an understanding

of their applications

IV. Scope and Limitation

This study covers the connection of a uniformed object and an external force

being reacted and applied to the object. It shows the relationship of the mass of an object

together with its acceleration and applied force. It covers friction, and the deeper

interaction between every action omitted by it. This study does not go beyond the study

of the three laws of motion.

CHAPTER 2: REVIEW OF RELATED LITERATURE

Sir Isaac Newton

Isaac Newton was born in 1642, the same year that Galileo Galilei died. His work

on motion was published in 1686 entitled Philosophiae Naturalis Principia Mathematica

(The Mathematical Principles of Natural Philosophy). This book was the result of

investigations when Newton was a student and continued during his tenure as a Lucasian

Professor of Mathematics at Cambridge University.2

History of Newton’s Laws of Motion

Before Newton, Aristotle believed that all objects have a natural state in our

universe, the heavy are to be at rest on earth, the light objects are to be at rest at the sky

and the stars are to remain at the heavens. He thought that the object would remain at the

state until an external agent will affect and continue to affect it to be in straight motion,

otherwise the object would stop moving. However, Galileo Galilei observed that an

external agent would make an object at rest move but not necessary for it to continue

moving. He called it inertia; this was the basis of Newton’s Law of Motion or the law of

Inertia.

Also, Aristotle predicted that an object of Greater mass would fall faster and hit

the ground first; however, Galilei proved this wrong. He conducted an experiment atop

the leaning Tower of Pisa. He tried to drop a cannon ball and musket ball at the same

2 Thomas Grissom, The Physicist's World: The Story of Motion & the Limits to Knowledge (Baltimore, Maryland: The Johns Hopkins University Press, 2011), 99.

time, but found out that the objects fell at the same rate and hit the ground at roughly the

same time. The Experiment has inspired Newton’s Second Law of Motion.3

The Laws of Motion

First Law of Motion (Inertia)

“An object at rest will remain at rest and an object in motion will remain in motion, with

constant velocity, unless acted upon by an external, non-zero force.”

…states, that if a body is at rest or moving at a constant speed in a straight line, it

will remain at rest or keep moving in a straight line at a constant speed unless it is acted

upon by an external, non-zero force. This Postulate is known as the law of inertia. The

Law of Inertia was first formulated by Galileo Galilei for horizontal motion on Earth and

was later generalized be René Descartes. Before Galileo it had been thought that all

horizontal motion required a direct cause, but Galileo Deduced from his experiments that

a body in motion unless a force (such as Friction) caused it to come to rest.4

Second Law of Motion (Acceleration)

“The Acceleration of an object is directly proportional to the net force acting on the

object and indirectly proportional to the mass of the object.”

…states that the behavior of objects for which all existing forces are not balanced.

The Second law states that the Acceleration of an object in dependent upon two variables

– the net force acting upon the object and the mass of the object. The Acceleration of an

3 https://www.grc.nasa.gov/www/k-12/airplane/newton.html4 http://global.britannica.com/EBchecked/topic/287326/law-of-inertia

object depends directly upon the net force acting upon the object, and inversely upon the

mass of the object. As the Force acting upon an object is increased, the acceleration of the

object is increased. As the mass of an object is increased, , the acceleration of the object

is decreased.5

Third Law of Motion (Interaction)

“For every action, there is an equal and Opposite Reaction.”

…states that in every interaction, there is a pair of forces acting on the two

interacting objects. The size of the forces on the first object equals the size of the force on

the second object. The direction of the force on the first object is opposite to the direction

of the second object. Forces always come in pairs – equal and opposite action – reaction

force pairs.6

5 http://www.physicsclassroom.com/class/newtlaws/u2l3a.cfm6 http://www.physicsclassroom.com/class/momentum/u4l2a.cfm

CHAPTER 3: METHODOLOGY

Materials:

- 2 meter Wooden Plank (for track)

- 3 balls (varying weights)

- Plywood (for paddle)

- Door Hinge (for paddles)

- Protractor (for measuring the angle of paddle)

Blueprint:

Paddle

Protracto

Procedure:

First, raise the paddle at the 30°. Place one of the balls at the start of the track.

Release the paddle. Record the time that from the paddle hit the ball until the ball stopped

rolling. Also, record the distance the ball rolled. Repeat this procedure for the 60° and

90° angle.

CHAPTER 4: RESULTS AND DISCUSSION

1. Data and Computation

MASS ANGLE DISTANCE

(cm)

TIME

(sec.)

FORCE

(N)

100g 30 90.33 3.53 0.72

60 200 3.78 1.39

90 200 3.27 1.87

200g 30 39.33 2.32 1.45

60 86 3.32 1.56

90 120 3.78 1.68

400g 30 31.67 3.23 1.22

60 32.33 2.11 2.9

90 41.67 1.83 4.97

v=dt

a=V f −V i

t=

V f−0t

=

d f

tf

t= d

t2

F=ma=m( dt 2 )

F=.1 kg( 0.3433 m(1.51 s)2 )=.1 kg ( 0.3433m

2.28 s2 )=.1kg(0.15 ms2 )=0.015 N

MASS AVERAGE

FORCE

ACCELERATION PROPORTION

100g 1.98 19.76 x 1

200g 1.98 9.88 x 1/2

400g 1.98 4.94 x 1/4

a= Fm

a=1.98.1

=19.76

19.7619.76

=1

2. Analysis of Results/Data

During the experimentation, the results show that the higher the angle’s degree,

the distance covered is longer and the force exerted becomes higher. The mass of the

metal ball bearing shows that the heavier it gets, it needs more force exerted to cover a

long distance.

For the ball with the smaller mass, it moves fast and covers a longer distance even

if there’s less force exerted.

For the second ball with the mass of 200g it took more time to stop but it didn’t

cover much distance unlike the first ball.

And the third ball with the mass of 400g it took more force and time to cover a

longer distance.

3. Documentation

CHAPTER 4: CONCLUSION AND RECOMMENDATION

Conclusion

Based on the experiments performed, the mass of an object is indirectly

proportional to the needed force to start acceleration. The rate is the reciprocal of the

mass used.

As for the other problem, the larger the angle of the paddle, the greater amount of

force it applies to the external body because of greater acceleration from gravity.

Recommendation

The group recommends that in the re-enactment of our experiment, to use a

smoother surface to lessen friction. Friction causes deceleration and could result to a

faulty computation of force. The group also recommends the further study of Force,

acceleration and other factors that the two aspects of motion.

CHAPTER 6: APPLICATION TO REAL LIFE

The prototype done by the group shows the relationship of force, distance and

time. Those elements made up the three laws of motion namely law of inertia,

acceleration, and reaction. The prototype can be related in various fields and one of it is

through sports like hockey, bowling, tennis, golf and many more. The prototype will help

the players to be aware what angle is most effective in striking the object. Industries that

produce sports equipment that will know of the relationship of weight and force can have

new model of their tools that can aid the concerns of their customer. Also, auto-making

companies can build more fuel-efficient cars because of their new understanding in the

relationship of force and mass.