Question

Exploration 2.1 Suppose the cart and masses can be changed by adding masses to the cart. Sketch a graph of the acceleration plotted vs. cart masses in the space below based on your equation in part 1.1e. Equation is   mhg=(mc+mh)a. a=mhg/mc+mh

Exploration 2.2 If you were to take data, measuring the acceleration of the cart for different masses added to the cart, what could you plot that would give you a straight line? What would be on the x-axis? What would be on the y-axis? What would the slope be? What physical quantity does the slope represent? Show your work and explain.

Answer 1

The acceleration is always a fraction of g (gravity's acceleration) but this fraction grows smaller when we make the cart mass larger. The graph would look something like this

Based on the equation given, If instead we were to plot the acceleration of the system (y axis) against the ratio mh/mc+mh (x axis) we'd get a straight line, and the slope of this line would be the value of the acceleration of gravity g.