Unit $3$ Progress Check: FRQ $3$

spring and block are on a table which is a height $\backslash ($ h$=0\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash )$ above the floor. They push the block to the right, compressing the spring a distance $\backslash ($ X $\backslash )$ from equilibrium. The block is released from rest, follows the trajectory shown, and strikes the floor a horizontal distance $\backslash ($ D $\backslash )$ from the edge of the table. Air resistance and all frictional forces are negligible. The students record the initial displacement $\backslash ($ X $\backslash )$ of the block and the horizontal distance $\backslash ($ D $\backslash )$ traveled by the block before hitting the floor. The students repeat the experiment, changing $\backslash ($ X $\backslash )$ each time. The following table shows the data collected by the students.

The students correctly determine that the relationship between the compression of the spring $\backslash ($ X $\backslash )$ and the horizontal distance traveled by the block $\backslash ($ D $\backslash )$ is given by $\backslash ($ D$=$X $\backslash$sqrt$\{\backslash$frac$\{2$ k h$\}\{$m g$\}\}\backslash ).$ The students create a graph with $\backslash ($ D $\backslash )$ plotted on the vertical axis.

$($c$)$

i$.$ Indicate which measured or calculated quantity could be plotted on the horizontal axis to yield a linear graph whose slope can be used to calculate an experimental value for the acceleration due to gravity $\backslash ($ g $\backslash ).$ You may use the remaining columns in the table, as needed, to record any quantities $($including units$)$ that are not already in the table.

Vertical: D Horizontal:

ii$.$ On the grid shown in Figure $3,$ plot the data points for the quantities indicated in part $($c$)($i$)$ that can be used to determine $\backslash ($ g $\backslash ).$ Scale the graph as appropriate. Clearly label the horizontal axis, including units.

Unit $3$ Progress Check: FRQ $3$

Figure $3$

iii. Draw a best$-$fit line for the data.

$($d$)$ Calculate an experimental value for the acceleration due to gravity $\backslash ($ g $\backslash )$ using the best$-$fit line that you drew in part $($c$)($iii$).$