Question

What do the slope and intercept represent in a Mass vs 1/acceleration graph?

I have run a cart+fence along a level air track. I have been told to make the graph shown here of mass against reciprocal acceleration. What is the significance of the m/a slope, and what is the significance of the intercept?

The equation in the legend is of the trendline for these data.

Answer 1

Gradient: Force
Y-Intercept: Systematic Error

Explanation:

The gradient of a graph is `"rise" / "run"`, `(deltay)/(deltax)`, so in this case your y-axis variable is mass (m) and your x-axis variable is inverse acceleration (`1/a`) , so substitute these into the equation for the gradient of a straight line.

`m / (1/a)`, which is the same as `m -: 1 /a`, to do this we multiply be the reciprocal so `m xx a`.

Which is equal to Force (`F = ma`)

So the gradient represents the constant force applied.

A y-intercept occurs when there is a error that applies to all tests (systematic error). This is because our equation `F = ma` has no constant added onto the end meaning the graph should pass through (0,0).

In this case you have a small positive y-intercept.

This could have been caused by a range of errors when conducting the experiment. A few possible ideas are an extra force applied to hold the cart in place which could be due to the ramp being on a slight slope, holding the cart with your hand. The error could have also be used by the scale being calibrated incorrectly, you measuring the mass incorrectly.

There are a range of possibilities that could cause the intercept. I suggest thinking of something that affected all tests and using that as a reason.