Question

A spring is stretched and the work recorded as shown in the table below.

Work (joules)	Stretch (m)
0.11	0.1
0.44	0.2
0.99	0.3
1.76	0.4
2.75	0.5
3.96	0.6
5.39	0.7

Graph this data to find the spring constant, k, of the spring. Give your answer in N/m.

Hint #1: What is the formula work and spring displacement?

Hint #2: You can cut and paste the table into a spreadsheet to save time!

• This data is NOT linear. You'll need to add a column and modify the data to graph a straight line or graph the actual data and pick the correct type of trend line.

Make sure:

• Your trend line includes an equation (set the intercept to 0)
• Your axes and equation are labeled correctly
• On your spreadsheet OR on a separate piece of paper, show HOW you came to your answer with the values from the graph.

Answer 1

When a force acts on the spring to stretch/compress the spring (amplitude reasonable to keep the spring maintain it's springy-nature, i.e., when the force is withdrawn it goes back to its original form), the equation of motion for the same is given by, $F = -k \cdot x.$ Here is the spring constant. is the force and the displacement.

Now work,$W = F \cdot x \implies F = \frac{W}{x}.$ So if we find the force and plot it versus the displacement, the slope should give us our spring constant,

The data is, (first coulumn is displacement (m) and second column is Force applied (N)).

0.1   1.1
0.2   2.2
0.3   3.3
0.4   4.4
0.5   5.5
0.6   6.6
0.7   7.7

Ofcourse one needs to fit that data into a linear fit to get the slope. The red dashed line gives the fit. The fitted linear line is given by, $y = 11.0 \times x+ 1.34279955 \times 10^{-15}.$ Here x denoted the values along the x-axis (horizontal) and y denotes the values along the y-axis (vertical). From the line equation (straight line linear equation) you can read the slope as So

合 4 21 0.1 0.2 0.3 0.4 0.5 0.6 0.7