Figure 5.39 shows an apparatus used to verify Newton's second law. A "pulling mass" $m_{1}$ hangs vertically from a string of negligible mass that passes over a pulley, also of negligible mass and with nearly frictionless bearings. The other end of the string is attached to a glider of mass $m_{2}$ riding on an essentially frictionless, horizontal air track. Both $m_{1}$ and $m_{2}$ may be varied by placing additional masses on the pulling mass and glider. The experiment consists of starting the glider from rest and letting the pulling mass accelerate it down the track. Three photogates are used to time the glider over two distance intervals, and an experimental value for its acceleration is determined from these data, using constant-acceleration equations from Chapter $2 .$ The table in the next column lists the measured acceleration for a number of mass combinations. (a) Determine a quantity that, when plotted on the horizontal axis of a graph, should result in a straight line of slope $g$ when acceleration is plotted on the vertical axis. (b) Make your plot, fit a line to the plotted data, and report the experimentally determined value of $g$.
CAN'T COPY THE FIGURE
$$\begin{array}{ccc}
\hline m_{1}(\mathrm{g}) & m_{2}(\mathrm{g}) & a\left(\mathrm{m} / \mathrm{s}^{2}\right) \\
\hline 10.0 & 170 & 0.521 \\
10.0 & 270 & 0.376 \\
10.0 & 370 & 0.274 \\
20.0 & 170 & 1.06 \\
20.0 & 270 & 0.652 \\
20.0 & 370 & 0.534 \\
\hline
\end{array}$$