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
Draw a graph of force against extension using graph paper.
(b) State the type of relationship between force and extension.
(c) Calculate the gradient of the graph line. Show your working and give a unit with your answer.
(d) State the equation of the relationship between F and x.
(e) 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.
Your table does not appear in your powt. Neither does any question about the data
To draw a graph of force against extension, you can follow these steps:
1. On a sheet of graph paper, label the horizontal axis as "Force (N)" and the vertical axis as "Extension (m)".
2. Mark the appropriate scale on each axis. In this case, you could start with a scale of 1 unit (e.g., cm or squares) on the horizontal axis representing 2 N, and a scale of 1 unit on the vertical axis representing 0.033 m.
3. Plot the data points from the table. For example, the first data point is (0.0 N, 0.0 m). Locate this point on the graph and mark it. Repeat this step for all the other data points.
4. Once all the data points are plotted, connect them with a straight line to create the graph of force against extension.
Now let's move on to the other questions:
(b) To determine the type of relationship between force and extension, examine the graph. If the graph is a straight line that passes through the origin (0,0), then the relationship is directly proportional.
(c) To calculate the gradient of the graph line, you'll need to determine the change in extension (Δx) and the change in force (ΔF) between any two points on the line. Then, divide the change in force by the change in extension: Gradient = ΔF / Δx. Choose two points on the line, calculate the differences in force and extension, and then use the formula to find the gradient. Remember to include the units in your answer.
(d) The equation of the relationship between F and x can be determined by examining the form of the graph. In this case, since the graph is a straight line passing through the origin, the relationship is directly proportional, and the equation can be written as F = kx, where k is a constant (spring constant).
(e) The formula provided to find the spring constant is k = F / x. Now that you have the equation of the relationship between F and x (F = kx), you can substitute the values of force and extension from the table to solve for k. Choose any data point from the table, plug in the values of F and x, and solve for k. Make sure to use the corresponding units for your answer.