- #1

Jimmy87

- 686

- 17

## Homework Statement

Determining which graphs technically use gradients and which do not. This is not a homework question but will help me with it so I put it here. My instructor said you have to be careful whether or not to call what you are calculating from the graph as the "gradient" or not. For example he said that most students think the gradient of a voltage vs current graph gives you the resistance but it does not - the ratio of voltage to current gives you the resistance. If you wanted to calculate the resistance on a curved pat of the graph you would literally do V/I but if it was a distance-time graph you would calculate the gradient of the tangent at that point. My question is - for curved graphs when would you draw a tangent and technically calculate 'gradient' and when would you just divide the 'y' by the 'x' value. It did some searching on google and it seems to say only rate changing graphs involve calculating the gradient - i.e. time on the x-axis. Are there any other examples where you would have to draw a tangent on a curved graph or is it only time?

Another question I had was about the force-extension graph for a spring. If you collect multiple load forces and extensions for a spring and plot a graph you get a straight line graph through the origin (force vs extension). We were told to calculate the gradient to find the spring constant using the whole line as it is more accurate than only using one set of y and x values. Is the gradient of a force-extension the spring constant? As I thought only graphs with time on the x-axis are gradients? So the spring constant is literally the ratio of force and extension isn't it? If you go past the elastic limit you wouldn't draw a tangent to find the spring constant you would do the ratio of the force to the extension i.e. one divided by the other. So why would you do change in y divided by change in x for a force-extension graph?