Mere and Ruth investigated the relationship between the applied force, F, and the extension, x of a spring. The results they obtained are shown in the table below.
Force F (N) Extension x (M)
0.0 0.0
2.0 0.033
4.0 0.066
6.0 0.099
8.0 0.132
10.0 0.165
state the type of relationship between force and extension.
calulate the gradient of the graph line. Show your working and give a unit with your answer.
State the equation of the relationship between F and x.
The spring constant is the force required per metre of extension of the spring (k = f/x)
Use this formula and your equation to find the value of the spring constant of the spring. Show your working and give a unit with your answer.
Once again, no table appears
To determine the relationship between force and extension, we can examine the data provided in the table. By looking at the values of force (F) and extension (x), we can determine if there is a pattern or trend. Let's plot the data points on a graph to visualize the relationship more easily.
1. Plot the data points:
On a graph, plot the force (F) values on the y-axis and the extension (x) values on the x-axis. Each data point will have an x and y-coordinate, representing the extension and force values, respectively.
2. Determine the type of relationship:
After plotting the points, observe the pattern or trend formed by the data. In this case, if the line connecting the points is linear and passes through the origin (0,0), it indicates a direct proportionality. A linear graph where the points are closely aligned suggests a direct relationship.
3. Calculate the gradient:
The gradient of the graph line will help in understanding the relationship between force and extension. The gradient represents the "steepness" or slope of the line. To calculate the gradient, choose any two points on the line and use the formula:
Gradient = (change in y / change in x)
Select two points that are easy to work with, such as (0,0) and (2.0, 0.033).
change in y = 0.033 - 0 = 0.033
change in x = 2.0 - 0 = 2.0
Gradient = 0.033 / 2.0 = 0.0165 N/m (unit of force per unit of extension)
4. State the equation of the relationship between F and x:
Based on the pattern or trend observed, we can say that the relationship between force (F) and extension (x) is directly proportional. The equation of a straight line relationship can be written as:
F = k * x
Where F is the force, x is the extension, and k is the constant of proportionality (spring constant).
5. Calculate the spring constant, k:
To find the value of the spring constant, substitute any of the force (F) and extension (x) values from the table into the equation F = k * x. Let's choose the first data point (0.0 N, 0.0 M):
0.0 N = k * 0.0 M (since k * 0 = 0)
We can see that when the force is zero, the extension is also zero. This confirms that the spring constant k is indeed zero.
Therefore, the spring constant of the spring in this experiment is 0 N/m (unit of force per unit of extension).