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How to Determine the Value of Acceleration Due to Gravity g Through Newton’s Laws

Word Count: 1458

TABLE OF CONTENTS

Abstract -----------------------------------------------3

Introduction-------------------------------------------4

Theory-------------------------------------------------5

Apparatus----------------------------------------------7

Procedure----------------------------------------------8

Data Collection and Processing--------------------9

Conclusion and Evaluation-------------------------12

Bibliography------------------------------------------13

ABSTRACT:

This experiment is about finding the value of acceleration due to gravity with the application of Newton’s Laws of Motion. This paper discusses the theory involved which was demonstrated mainly through mathematical equations. The set-up that was used was the cart and pulley experiment but using a toy crane instead of a normal cart. The independent variable (controlled variable) was the distance and the amount of weights applied to the toy crane as well as to the weight hanger. The dependent variable was time which was from the time taken of the toy crane to pass the marked starting point as well as the ending point. The trials were executed 10 times per weight increments on the hanger. There were three sets of the experiment done, for 30 g, 40 g and 50 g hanging weights. The equation to find the value of g discussed in the earlier parts of the essay was the formula to which the data collected was substituted. The value of g that was acquired from the experiment was proofed for percentage error against the theoretical value of 98.1 cms-2. The conclusion of the experiment found that the actual value of the value of g ranges from 149.4 cms-2 and 103.3 cms-2. Word Count: 210

INTRODUCTION:

According to our textbook, Physics for the IB Diploma, Newton’s Second Law asserts that the net force on a body is proportional to the body’s acceleration where the constant of proportionality is the mass of the body. (K.A. Tsokos,2010) This can be understood better when it is demonstrated in an equation. The mathematical translation of this law is: F = ma

F stands for force, m for mass in kilograms (kg) and a for acceleration in metres per second squared (ms-2). The result of this equation is N, newtons, which is the unit of force. The net force on a free falling body will be its weight W and the equation to find this value is: W = mg

W stands for weight and m for mass as I mentioned earlier, and g stands for acceleration due to gravity. If we apply Newton’s Second Law to this equation this is what we will find: ma = mg

a = g

The value of g is normally regarded as a constant with the value of 98.1 cms-2 thus a is the value solved for Newtonian equations. Since that is so, the aim of this experiment is to find out the value of g through finding out the components of the equation applicable and solving for it.

SET-UP:

Theory

The net force of the system in the set-up above will be tension T and we can see this from the free body diagram of the system:

In this diagram, T stands for tension and the small m for m1 and the capital M for m2 and f stands for kinetic friction force. With Newton's Second Law equation F = ma we can deduce from the free body diagram of the system that: m1g - T = m1a

T = m1g – m1a

That will be our equation one, and we can alo see from the diagram that: T - f = m2a

T = m2a + f

That is now the equation 2 to find T and combining the two equations we find that: m1g - m1a = m2a + f

m1g = m1a + m2a + f

g=(m1a + m2a+ f) / m1

Since f is not negligible in this experiment, the kinetic friction force will be coming from the mass m of the hanging mass and this comes from applying the principle of Newton’s First Law that the toy crane will move in constant velocity once set in motion if the weight of the string produces a force equal in magnitude...