Newton's second law: lab?

Question

he slope of the linearized acceleration vs. mass graph should be equivalent to the net force, and the slope of the acceleration vs. net force graph should be equivalent to one over mass. Explain why. Calculate the %error for each slope
how do i do this?
and for the % error i keep on getting 91% no matter how i tried

Answer 1

In your lab you are dealing with the relationship of:
f=m*a
so a=f/m

If you plot the values of acceleration versus mass holding force constant, this is a non-linear graph, so it will depend on the range of your data. As m gets large, the slope will approach zero. As m gets small the slope will approach infinity, which makes sense. The instantaneous slope of this line is -f/m^2. So your error will depend on the relative magnitude of the mass with respect to the net force.
If you plot the values of acceleration versus net force while holding the mass constant, the slope of this line is 1/m. Your error will depend on the accuracy of the system. If the coefficient of kinetic friction is not a constant, or the force applied is not a constant, then error will be introduced into the system.

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