# Introduction to Hooke’s Law

Hooke’s Law states that the extension of an elastic object is directly proportional to the force applied to it up to the limit of proportionality (elastic limit).

Hooke’s Law can be represented by this equation:

## F = k x

• F is the force applied in Newtons (N)
• k is the spring constant in newtons per metre (N/m), the value for k can only be determined experimentally
• x is the extension of the spring in metres (m)

The equation is only valid until the limit of proportionality. If the spring is stretched beyond the limit, it will start to have a plastic behaviour and won’t return to its original length when the weight is removed.

# The Experiment

In the experiment that I have conducted, I investigated the behaviour of three different materials in relation to the force applied on them.

The apparatus used for the experiment were set up as such:

I started with a small mass and increased the mass used, measuring and recording the deformation (extension) of the material as I go. I used the same value of mass for all three materials to ensure consistency in my results.The results of the experiment were recorded in the table below.

# Data Collected

Table 1: Values obtained from the experiment

y1 and y2 represent the deformation for two different elastic materials, which are both still in their linear regions; whereas z represents the deformation for the third elastic material, which has gone past its limit of proportionality.

From the values in table 1, graphs can be plotted to show the relationship between the deformations (y1, y2, z) against the force applied (x).

# Graphs & Analysis

Figure 1: Graph of y1 and y2 against x

For the graph in figure 1, a linear line of best fit can be drawn and an equation in the form of y=ax+b can be derived. I have done so using Microsoft Excel and I had determined the equations for y1 and y2 to be y1=1.5583x+1.375 and y2=2.0583x+0.2 respectively.

Based on the graph the equations of the lines, it is evident that the deformation of the materials is proportional to the force applied as one increases with the other. However, the variables are not directly proportional as the graphs do not intersect the origin, (0,0). This can be seen as the value of “b” for the equation of y1 and y2 are 1.375 and 0.2 respectively instead of zero. This may be the result of systematic errors such as:

• Using a material that is already deformed
• Using faulty measuring equipment
• Incorrect method of measuring (human error)

Furthermore, there is also an anomalous point for the graph of y1 at x=7. This could be the result of random error or human error.

Upon further analysis, it can be seen that the gradient for y2 is greater than that of y1 as the value of “a”for the equation of y2 is larger. Based on this observation, it can be concluded that the second material has a smaller spring constant and is stiffer than material 1. Thus, making it easier to stretch.

In addition to that, it can also be seen that both graphs intersect at one point, meaning that at that point, both materials have the same deformation for the same force applied.

By using the graph from figure 1, I have estimated the approximate x-value of the intersection point to be x=2.3N. When I tried to confirm this estimation through calculations, I managed to obtain the value of x=2.35N.

### Working for the calculation:

I used the matrix method on excel to solve the simultaneous equations.

eqn 1 : y = 1.5586 x + 1.375

eqn 2: y = 2.0583 x + 0.2

First, I rewrote the equations in the form of a matrix as shown above, then I solved them using the “MINVERSE” and “MMULT” functions in Microsoft Excel, which is equivalent to solvinig by doing this:

AX = B

(A^-1)AX = (A^-1)B

X = (A^-1)B

X = 2.35N

Figure 2: Graph of z against x

For the graph in figure 2, a curve can be drawn and a third-degree polynomial equation can be derived. Once again, this was done using Microsoft Excel. The equation obtained for the graph is z=x^3-2(10^-12)x^2+4(10^-12)x+1.375 , which can be simplified to z=x^3+1.375 as the values of -2(10^-12)x^2 and 4(10^-12)x  can be considered negligibly small.

Based on this graph, it can be seen that the material does not obey Hooke’s Law as the line is not linear and the variables are not directly proportional to one another. This is because the material has already been stretched pass its elastic limit. Therefore, the third material will no longer return to its original shape after the weight is removed and  it will remain permanently deformed (plastic behaviour).

# Conclusion

Ignoring the systematic errors done, the first and second materials can be said to obey Hooke’s Law as the force applied is directly proportional to the deformation of the springs. However, the third material does not obey Hooke’s Law as the relationship between the force applied and the deformation of the spring is not directly proportional. From this experiment, it can also be concluded that Hooke’s Law only applies when a material is stretched within the elastic limit.

## References

BBC – GCSE Bitesize: Hooke’s Law, last updated/published in 【2014】, BBC – GCSE Bitesize: Hooke’s Law [ONLINE] Available from:

Dynamics – Hooke’s Law Experiment, by JL Stanbrough, last updated/published on          【6 November  2002】, Dynamics – Hooke’s Law Experiment [ONLINE] Available from:

http://www.batesville.k12.in.us/physics/phynet/mechanics/newton3/Labs/SpringScale.html

## Why People Should Study Engineering

Deciding on your future career is of utmost importance, it determines…… well…… your future!

However, doing so can be extremely difficult for some. In fact, some people don’t even have a clue to what they want to do in the future! In these cases, you should consider studying engineering!

“Why?”, you ask. Here’re a few reasons:

## 1) Less Risk

Engineering is one of the jobs out there that bears the least risk. The world NEEDS engineers, so the demand for engineers is high and the growth rate for the job is also increasing rapidly. Therefore, you don’t need to worry about landing a job after you get your degree because ENGINEERING JOBS ARE EVERYWHERE!!! Furthermore, the job provides you with financial security, which I will talk more about in the next section.

## 2) Financial Security

Engineering is known to be one of the jobs with high pays. So, you won’t need to worry about those pesky expense bills anymore if you become an engineer. But you do need to worry about how and where to keep all that money though.

According to statistics, engineers get a median starting salary of approximately \$60,000 in the U.S and can earn as much as \$180,000 after a few years of experience working in the field! (Cool fact: You can buy more than 80,000 gallons of chocolate with that money)

## 3) Wide Career Progression Opportunities

Having an  engineering-based education allows you to cultivate specialist and transferable skills that you can use in almost any industry. This includes skills such as critical analysis skills, social skills, logical thinking skills etc.  In addition to that, it also allows you to work your way up to high-level management, that means better working conditions and more money in your wallet!

## 4) Get A Chance To Improve the World

Who do you think is responsible for the modernisation of the world, the invention of technology, the designing of sports shoes?

THE ENGINEERS!

Yes, even shoes are related to engineers. As a matter of fact, almost everything you see is related to engineering in some way. That’s why engineers play a crucial role in society today.

One of the best parts of being an engineer is improving and modernizing the world. You get to create new things that benefit society and the feeling of doing so is pure ecstasy.

## 5) It’s all worth it

When people think about engineering, they think about hard work, sleep deprivation, and generally stu-dying.

Yes, it’s true that engineering is a difficult course to take, but everything comes with a price. Would you rather study engineering for 4-5 years and enjoy the rest of your life in luxury or waste your time taking up an easy course that doesn’t benefit you much and regret it the rest of your life? You’re out of your mind if you choose the latter.

On a serious note, believe me, every drop of blood, sweat, and tears that you shed while trying to become an engineer will be worth while in the end.

## Reflecting on my Digital Identity

Have you ever stopped to think if what you posted last night on social media would impact your future career or your privacy? If your answer is yes, then keep on reading!!!

For all you know,  there could be someone out there who you have no clue existed who knows you better than most of your friends or even your family!

In this blog, I want to reflect on my digital privacy by:

1. Searching my name on web browsers, apps, and social media
2. Finding out who can view my profile and data
3. Attempt to improve my digital privacy by resetting my privacy settings to my liking.

# Googling Myself

Upon googling myself, there was only one link out of the first ten that were related to me. This is the case because there is a hawker stall with a similar name to mine and it is more well-known as opposed to me. Frankly, having less hits is a good thing to me as it means that less people will click and look at my profile and personal information accidentally. This will also mean that it is harder for others to obtain my personal information. However, having more hits on Google can have its benefits in the future, especially when you are trying to let yourself be known to the world. For example, if I were to form a company under my name in the future, it would be better if I have more hits as more people will know about the company and this may lead to an increase in sales and profits. My Google-presence may affect my future job prospects as my potential employer may be able to view my profile for social medias and everything on it, this of course includes pictures and posts from the past. I have never known about “Google Alert” so I have never thought about setting it up before.

By clicking on the “view as” section on Facebook,  the following information is available to the public profile

• photos
• personal information (where I studied, worked, lived…)
• friends

This makes me uncomfortable as most of the photos and posts viewed were from many years ago, when I was still ignorant and immature. So, to have someone else see it makes me feel embarrassed. If a potential employer were to see this page, he or she may be put off from the immaturity of the post and this may affect my employment.

# Reppler

I received one inappropriate content alert. Reppler flagged this as inappropriate as the was a swear word within the content. This would be relatively easy to explain to an employer as I was the one who posted the swear word, it was from a stranger who commented on a post I was tagged in, so it has no relation to me whatsoever. Furthermore, I didn’t receive any privacy or security risks from Reppler. This is good as it means that someone nefarious wouldn’t be able to cause harm or inconveniences for me as no security risk means a low chance of having my account hacked.

“The Faces of Facebook” doesn’t work

I think Facebook calculates for these through my recent activity on Facebook and the number of times I visit the page, group or person. The list doesn’t surprise me at all as most of the people and pages at the top of the list are things I had recently visited. I will neither be happy or unhappy if the list was shown to my Facebook friends as there is nothing special or bad about the list, it just shows them the sites and people I visit on Facebook recently

# Privacy Settings and Tidying Up

Only my friends can see posts that I make in the future. I wouldn’t be happy if everyone on Facebook could see everything I write as it would feel like an invasion of privacy. I would feel the same way if it was friends of friends as it would still be strangers viewing my posts. Everyone can look me up and search engines can link to my timeline and everyone can see my timeline when it is set to On.

A total of 36 apps are listed to having access to my data but I only remember authorising 20 of them. I do no trust all these applications to use my data responsibly as I have never heard or authorised some of the applications at all. If an app was taken over be another company, I would definitely remove the app from Facebook as the previous terms and conditions are no longer valid and the new company may exploit the data for nefarious purposes.