Lab: Acceleration versus Force and versus Mass

Newton's second law says a = F_net/m. Hold mass constant and change force, and acceleration changes in direct proportion, so a graph of a versus F is a straight line through the origin with slope 1/m. Hold force constant and change mass instead, and acceleration drops off as mass grows, but not in a straight line, because a = F/m is an inverse relationship. Plotting a versus m gives a curve that looks like it is decaying toward zero without ever quite getting there.

The standard setup uses a cart on a track connected by a string over a pulley to a hanging mass, which provides the applied force through gravity. For the first run, you add small masses to the hanger to change the force while keeping the total mass of the system (cart plus hanger plus masses) fixed, usually by shifting masses between the cart and the hanger so the total never changes. You measure acceleration with a motion sensor or timer for each force value and plot a versus F. For the second run, you keep the hanging force fixed and instead change the mass of the cart, plotting a versus m, which curves, then plotting a versus 1/m, which straightens into a line because a = (F/m) means a is directly proportional to 1/m when F is constant.

This lab turns the abstract equation F = ma into something you measure directly, and it sets up the next ideas in the unit: reading slopes and intercepts off real data to find mass or detect friction, and treating the cart-hanger-string system as a single object with one net force acting on it.