rewriting/ paraphrasing job 1500 words DUE IN 4hrs

2. Theory

The spring, is defined as a mechanical device that can be deformed by a certain force, just like other elastic materials, they can be compressed either by compressing it with our hands, or by using machinery, once the force is released, it will return back to its original position. (Khan Academy)

According to the theory, in mechanics, the deforming of a certain material is done by any types of force, especially when it comes to Hooke’s law, it is defined as the amount of force required to stretch an elastic object, such as a spring, where the force is directly proportional to the extension of the spring, meaning that if the force is higher, the spring’s extension will be longer, here is the following formula for Hooke’s Law, where is the amount of force applied in Newtons, while is length of extension in meters, followed by is the spring constant, which is measured in N/m.

With my exploration topic “The relationship between temperature of a medium and the spring’s constant value.” The research question will be “To what extent do distinctive oven temperatures affect the spring constant towards steel springs.” due to my highly anticipated curiosity on exploring the springs in detail, so I’m looking forward to conduct this particular experiment for this exploration.

The aim of this exploration is to determine whether the spring constant will increase due to temperature, therefore according to my research question, my assumption that if the amount of heat applied is higher towards the springs, the value of spring constant will be larger, since I am assuming that if the spring’s temperature is higher, it will be proportional to the spring constant of a spring, so both of these combined will have a high correlation between them.

Here are the apparatuses that are going to be used for this following experiment:

· 7 Steel Springs

· Oven, with equally ranged temperature sets. (130, 150, 170, 190, 210, 230, 250℃)

· Newton Meter (Dynamometer)

· Tape Measure

The apparatuses are pictured below:

Figure 1. Apparatuses displayed below.

6. Experimental Variables

· Independent Variables: Temperature, Length of spring before and after extension

· Dependent Variable: Spring Constant

· Controlled Variables: (With reasoning)

1. Material of the spring:

a. The material of the spring has to be consistent throughout the experiment, which I will be using steel springs.

2. Newton Meter (Dynamometer):

a. Throughout the experiment, we will be using the same Dynamometer that has a maximum force of 10N / 1 Kilograms.

3. Temperature difference in oven:

a. By using the same range of temperature (20℃), it allows consistent results that are displayed in an ordered manner. (Fair test)

4. Time needed to heat the spring:

a. In each data, the time required to heat the spring has to be the same, as if we intake different timings in each data to heat the spring, it will result in inconsistent results if we degrade the spring’s temperature with the cooling agent.

5. Tape Measure

a. Throughout the experiment, only one tape measure will be used since different application of tape measures might give out inconsistent results, as I’m also using the same material of springs as well.

6. Stretching Distance

a. The stretching distance needs to remain the same throughout the experiment (150 mm), in order to prevent minimal to drastic change in results.

Here are the following steps to be taken:

· Prepare 7 steel springs, and each spring’s length has to be the same, with uncertainty ±0.5 cm.

· Heat up each spring with equally distributed temperatures. (130, 150, 170, 190, 210, 230, 250℃), followed by measuring the heating time, and each spring is required to have the same amount of heating time, which will be in total of 4 minutes each, or 240 seconds.

· Measure each springs with different temperature by using Newton Meter with same stretching length of force applied towards the spring.

1. E.g. Measure Spring with Temperature 130℃, followed by measuring the force by pulling its length up to 150 mm.

· Calculate all data, input final average value.

Once the experiment is completed, the following data is collected and are inserted below in order to determine the spring constant values that derived from different temperatures. (Table 1, 2, 3)

8.1 Data Collection 1 (Raw Data):

Table 1: Measured Initial Length, Temperature, Force applied and Spring Constant Value on each springs, and in order to count the spring constant value, I will applying the following formula:

Although the variable for the spring constant is negative due to the pulling force which goes towards the left side by the spring, and the pulling force is proportional to the stretching force (If pulling force is larger, the stretching force will also be larger.), but the final spring value will remain positive.

The following Raw Data is inserted below:

After measuring each initial length and force, each of the spring’s force is measured repeatedly for a total of 8 times from each temperature applied, followed by calculating the spring constant.

8.2 Data Collection 2 (Processed Data):

With the data collected, the average spring constant can be calculated for each designated temperature, this method is done by adding the total amount of trials (8 trials) divided by 8, the uncertainty for each average value can be calculated as follows:

But before we calculate that, we will calculate the average value, which goes as this:

Here is the following calculation below: (Sample Calculation for = 130℃)

8.3 Data Collection 3 (Final Data):

After analyzing the data from Table 1.4, a graph was created to represent the data plotted, followed by creating the best fit line, maximum and minimum uncertainty line:

Graph 1: Plotted the data points (Correlation between Temperature of Oven and Spring Constant)

As shown from the graph above, the error bares for Spring Constant (N/m) is clearly visible, whereas the gradient of the line of best fit can be calculated by selecting the two points that passes through. For instance, (120, 45.6) and (260, 53.8).With the variables given, the gradient can be found as followed:

From the result shown above, the value is coherent from the equation shown in the graph, and now the correlation coefficient is calculated, the following formula is shown below:

And now I proceed to calculate the correlation coefficient:

The value for correlation coefficient is 0.96, a very strong, positive correlation value.

After collecting the data from the experiment and processed, the hypotheses mentioned above can be proven that the temperature of the oven has it proportionality towards the spring constant’s value, as it can observed that from Graph 1, the relationship between Temperature of Oven and Spring Constant was plotted from average values that was taken from the Force of Spring. However, the line of best fit can be shown that there is a low precision on the data since there are only 8 trials that are conducted instead of 10 – 20 trials,

As mentioned before, there’s a low precision, but high accuracy on the data due to only 8 trials that are being conducted, where Graph 1 shows a demonstration that the temperature range is 10 Degrees Celsius, whilst after calculating the coefficient of correlation, the values display that there is a very strong, positive correlation between temperature of the oven and force of spring as the final value shows that , proving that the hypothesis “if the spring’s temperature is higher, it will be proportional to the spring’s constant value.” is correct.

Although the hypothesis proved to be correct, but in case if a similar experiment like this will be conducted in the future, the table below mentions the current method of experiment with the level of negligibility.