Question

Why are we so insistent that you include the origin in your plot points when plotting Equation 3 (∑F = T - f = ma₁). There are two very good reasons. One has to do with the (NSL) equation itself and the 2nd has to do with what happens when you apply a linear fit to only two points.

Answer 1

Including the origin in plots for Newton's Second Law is essential because it demonstrates the proportional relationship between force and acceleration, and it ensures the integrity of linear fits by providing a necessary reference point for two-point extrapolations.

Step-by-step explanation:

When plotting the points for Equation 3 (ΣF = T - f = ma₁), it is crucial to include the origin to ensure accuracy and reliability. The first reason is rooted in the Newton's Second Law (NSL) equation itself; the equation Fnet = ma represents the net force acting on an object is the product of its mass (m) and its acceleration (a). This establishes a proportional relationship between force and acceleration, which must pass through the origin (0,0) on a graph to accurately reflect that zero force results in zero acceleration.

The second reason relates to linear regression or fitting. If you only use two data points to perform a linear fit, excluding the origin can lead to incorrect extrapolation, especially for force and acceleration. The origin serves as a fixed reference point, anchoring the linear equation. Without it, the slope and y-intercept derived from just two other points may not represent the true physical relationship, potentially leading to substantial errors in predicting other points. Including the origin helps to maintain the integrity of the linear fit, assuming the underlying relationship is indeed linear and starts from a state of rest.