# Acceleration vs mass graph shape?

1. Mar 2, 2009

### sean-820

I know acceleration vs mass graphs are curved, but why?
also, how would i calculate an uncertainty?

2. Mar 2, 2009

### LowlyPion

Can you put those questions in some more context?

3. Mar 2, 2009

### sean-820

well,
there is a constant applied force, but their is more and more mass added. As the mass increases, the acceleration decreases.
This has to do with newtons second law that a is inversly related to mass and directly related to force (i think thats it). The graph forms a hyperbola.
Im not sure why its a hyperbola as opposed to a straight like that shows the a decreases as the mass increases

for the level of uncertainty, i have to find the level of uncertainty of the applied force over 6 tests.Would it just be the average force+- 1/2 the difference between the max and min

4. Mar 2, 2009

### Delphi51

It looks like you did an experiment where you applied the same force to a series of different masses and measured the acceleration. The formula that applies is F = ma or a = F/m. This is the same mathematically as y = k/x - a hyperbola.
To analyze this data, you would compare a = F/m to the formula of a straight line:
y = slope*x. This suggests graphing 1/m (make a column for it in your table) on the x-axis and acceleration on the y-axis. Then the graph should be a straight line with slope equal to the Force. If the data points form a perfect straight line, then you have no uncertainty in the force. If the points don't fit a straight line very well, then you have a lot of uncertainty .

One way to measure the uncertainty is to draw a straight line through the middle of the cloud of points as best you can. Then draw another straight line that is as steep as you can draw while still coming close to all the data points. Ideally, you would have error bars instead of data points and make your extreme slope line come within the range of most of the error bars. The difference between the best slope and the extreme one is your uncertainty in the force.

A more sophisticated approach is to put all the data points into a graphing calculator and let it draw the graph and calculate the variance or standard deviation - these are good measurements of the uncertainty.

5. Mar 2, 2009

### LowlyPion

I think the better way to determine uncertainty is to develop the uncertainty from the methodology of your experiment, - i.e. finest units you can measure with your instrument, the accuracy of your weights, your reaction times in making time measurements, etc.

Then if your variances lie within that, you know you have a sounder confirmation of your theoretical to actual.