f5 add nath project

8/14/2019 f5 add nath project

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Sometimes, error may occur either the random error or systematic error

when the measurements are taken due to the inaccuracy of instruments andmisinterpretation of the observer. Therefore, when the variables of the linear

equation are plotted, not all points fix exactly on a straight line. In this

situation, a line of best fit is drawn.

The two main principles of the line of best fit are:

I. The line must pass through as many points as possible.

II. The number of points that do not fit on the straight line must be fairly

equally distributed on both sides of the line.

In addition, linear law can also be applied to non-linear relations or equation

in which the non-linear equation is reduced to linear form to obtain a straight

line graph. For example, y2 = x2 + 12 is a non-linear equation as it has the

power of two in the variables. So, by applying this powerful law, the highest

power of the equation is reduced to one to form a linear equation by

substitute X and Y into y and x respectively. As a result, Y= X + 12 is formed.

In short, this law is believed to help mankind in solving problems especially

for science and mathematics. This invention may contribute to us so we must

appreciate it and it also must be upgraded to its maximum function and

usage


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Acknowledgement

Undoubtedly, I am grateful that I can complete this Additional Mathematics

project in time. Many people had helped me in this project. I would like to

take this opportunity to express my sincere gratitude towards those who had

helped me out to succeed the project.

First of all, I would like to thank my Additional Mathematics teacher, Mrs.

GOH for providing his guidance and assistance which enabled me tocomplete the project in time.

Besides, I would also want to thank my friends for helping me by providing

moral support. They had helped to search for relevant information in the net

for the project. Hereby, I truly appreciate their contributions. 1 would also

like to thank my parents for supporting me.

Lastly, I would also thank my teammates for willing to spend their precious

time and energy by finishing each of their tasks to complete this project. This

project has given me a chance to venture into the world of additional

mathematics.


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The Experiment for additional math

projectA simple pendulum consists of an object suspended by a string from a fixed

point. When displaced, and then released, the object will swing back and

forth in a vertical plane under the influence of gravity. This periodic motion

can be used as a basis for measuring time.

The simple pendulum as shown in Diagram 1 is set in motion by releasing the

object through a small angle of displacement, 6(10to 15)from the vertical.

Procedu re1) Set up a simple pendulum by attaching an object to a string of length

60cm.

2) Set the pendulum in motion and measure the time taken, ts, for 20

complete oscillations.

3) Calculate the period, Ts, that is the time taken for one complete

oscillation.4) Repeat steps 1 to 3 using at least 10 different lengths of strings with the

minimum length of 5 cm

5) Record the readings in a suitable table.


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DATA FOR EXPERIMENT

I/cm T1/s T2/s average T/20 t2 VI

5.00 6.7 6.9 6.8 0.34 0.12 2.24

10.00 10.8 10.8 10.8 0.54 0.29 3.16

15.00 14.2 14.2 14.2 0.71 0.50 3.87

20.00 16.9 17.1 17.0 0.85 0.72 4.47

25.00 19.7 19.9 19.8 0.99 0.98 5.00

30.00 22.0 22.0 22.0 1.10 1.21 5.48

35.00 23.3 23.9 23.6 1.18 1.39 5.92

40.00 25.0 25.3 25.2 1.26 1.59 6.32

45.00 26.8 27.2 27.0 1.35 1.82 6.71

50.00 28.3 28.5 28.4 1.42 2.02 7.07

Data tor the exper imen t

6) Plot a graph of period (T s) against length(l cm). Comment on the graph

obtained.

The graph obtained is a curve graph

7) The relationship between period and length is given as

where g is the gravitational acceleration.

(a) Suggest at least two different pairs of variables for the horizontal and

vertical axes to obtain a linear relation. For each pair, plot the graphs and

draw lines 01 best fit manually and by using ICT.


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The relationship between the period and the length is

The gravitational acceleration g is constant (not variable)- Therefore the

variable is

T and l.

[f we square both sides of the equation, it become


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Hence the 2 variables are T2 and 1. The 2

pairs of variables are:

T and Vl (T as vertical axis and Vl as horizontal axis) T2 and

1 (T2as vertical axis and 1 horizontal axis.)


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(b) Estimate the gradient of each graph. Hence, write an equation relating

period and length for each of the graphs.

Graph of T against Vl

Graph of T2 against 1

0.35

= 4.571mj-2

The equation of the graph T2 against 1 is y=4.571x. JThe

gradient of the graph is 4.571. [The equation relating the period

and the length is

(c)Use the gradient of each graph to determine the respective value of the

gravitational acceleration, g ms".Comment on the values obtained.

How do these values of g compare with the accepted value of g on earth(9.807 g

"2


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Comment

This value is slightly lower than the accepted value 9.807 ms"2

Error

Percentage of error

Explanation the Differences

Both of the values that we got is slightly lower than the accepted value. This

is most probably due to the presence of air buoyant force. Another possible

source of error is the pendulum did not oscillate in a plane but in circle. This

make the pendulum become a cone pendulum, where the calculation will be

different from a simple pendulum.


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(d)Use the graph with the least percentage error in g to determine the length

of string that will produce a complete oscillation in 1 second.

From the graph T against Vl, when t=\st

Vl=4.75

1=22.5625

8} A simple pendulum can be used as a device to measure time. Describe how you

can use it to measure your pulse rate.

Make a simple pendulum of length 22.565cm (So that 1 oscillation is

equivalent to 1 second).

Get a friend to count the number of oscillations for you.

Ask him to give instruction when should you start and stop (after 30

oscillation).

Start counting your pulse when your friend says start and stop counting after

30 oscillation.

Repeat this process for 3 times to get the average value. Pave.

The pulse rate = the Pave x 2.

9} If the length of the string is 4 times its original length, state the change in

the period, Ts


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When the length is 4 times its original length,

I1= 41

Substitute I' into the equation.

T* = 2T

Conclusion:

If the length of the pendulum increases by 4 times, the period, T will increase

by 2 times.

Since


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Further Exploration

1) If a simple pendulum with a period of 1 second is set in motion on

the moon, determine the new period of this pendulum.


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the gravitational field

strength ( or gravitational

acceleration) of the

moon,

Period of the pendulum on the surface of the earth, Tearth=ls

Gravitational acceleration of earth, gearth = 1.622 ms-2

Period of the pendulum on the surface of the earth = TH,^

Gravitational acceleration of earth, gmoon" 1-622 ms-2

2) (a) Investigate whether a simple pendulum will swing continuously in air.

Explain your

findings. Suggest the conditions required for a pendulum to swing

continuously.

Pendulum cannot swing continuously because there are air resistanceunless doing the experiment in vacuum.


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r is greater than original t

3 ) Sketch graphs on the same scale to illustrate the motion of simple

pendulum swinging

i, in air, ii. in water

and iii. in vacuum.

kj and k2 are the percentage of energy remain from previous oscillation

0


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P( ts density of pendulum

P is density of medium where pendulum oscillate

ReferenceBOOKSuccess Physics Reference Book. Oxford Fajar Sdn.Bhd. Foo Seng Teek, Yee

Cheng

Reference


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BOOKSuccess Physics Reference Book. Oxford Fajar Sdn.Bhd. Foo Seng Teek, Yee

Cheng Teik, Chong Geok Chuan, Lee Beng HinForm 4 Physics. Danaiis Distributors Sdn. Bhd. Tong Yoke Chai, Wan Faizatul

Shima Bt Ismayatim, Yoong Kai Seng, Rema Ragayan, Roslina Bt Ahmad

Form 5 Additional Mathematics. Chew Su lian,Khoo Ee Sin,Moy Wah Goon, Ooi Soo

Huat, Rohaiza binti Ramli

WEBS ITEhttp://en.wikipedia.org/wikiySimple pendulum

http://www.kettering.edu/-

HimsseU/Demos/Pendulum/Pendula.html http

://www.walter-fendt.de/ph 11 e/pendulum,htm


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Conclusion

Linear law is a very powerful law in which it helps the mankind to solve many

problems easily. We able to establish a relationship between the variables in the

experiment by using this law to help us to measure the corresponding values ofthe variables under different situations and by plotting the graph, the relationship

of the two variables is known easily.

So, after doing this project, I am quite impressed with the usage of linear law and

its ways to help us in solving problems although there are some errors occur.

Besides that, I also learn many things for this law which I can never find them in

the text book or reference book. I am doing many researches to understand its

usage and its principles when we apply this law.

Furthermore, I also able to interpret the relationship between the variables in the

experiments I did easily whether in Physics, Biology or in Chemistry. I am really

appreciating the government as they give us this opportunity to do this project in

the process of understanding and learning deeply into this law. I would also like

to thank my additional mathematics teacher as without his/her help, I am not able

to accomplice this project.

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f5 add nath project