Would a Force vs. Acceleration Graph Lie in Both Quadrants One and Three?

[Physicsguru21]

If plotting F=ma on a graph with F as one axis and a as the other, would the line be in both quadrant one and three since the force vector, and subsequent acceleration vector, could be negative?

 

[Chandra Prayaga]

Yes. Certainly. It will all depend on whether you can exert forces in both directions in your particular experimental set up, but if you can, the line will be in both quadrants.

 

[Physicsguru21]

Thanks. Thats what I thought. I guess it is just not very common since it is essentially redundant to plot the data in both quadrants.

 

[Physicsguru21]

Ok, I have an extension of this question. If my resultant force vector is F=-3i+4j, how would I plot that on the F vs a graph?

 

[Chandra Prayaga]

In your original question, you changed the force to have several values, and for each value, you calculated, or measured the acceleration. Then you plotted the force vs. acceleration. Now you are giving me only one value for the force. Why do you think that will generate a graph?

 

[Physicsguru21]

It is a poorly worded problem. The actual problem says that I am given the resultant force on a body and am asked to plot that force vs acceleration. Then I am asked what shape is plotted, if the shape that is created passes through the origin, and what quadrant(s) it is in? Since I wasnt given an actual value for force, I originally varied the force value and plotted F=ma. However, I now don't see how that is not correct. The force can only be on point on the X axis and the resuting line if you vary mass will be vertical. Since no value for force is given, there is no way of knowing where that point will be.

 

[Chandra Prayaga]

In any case, whatever the force may be, you can only plot force vs. acceleration on a single graph if it is a problem in one dimension. If it is in one dimension, and you plot the force vs acceleration, it is always a straight line passing through the origin, and lying in the 1st and 3rd quadrants. If it is a problem in two dimensions, you need two graphs. F_x vs. a_x and F_y vs a_y. Both will be identical straight lines through the origin, with the same slope.