Question

A student developed an experiment to measure the gravitational acceleration. In this experiment, two photogates were used to measure the time it takes the object to fall from rest (at the first photogate) and reach the lower gate. The student recorded time (t) and the distance (y) between the two photogates as shown in the following table:

t (s)	y(m)
0.141	0.100
0.199	0.200
0.244	0.300
0.281	0.400
0.315	0.500
0.345	0.600
0.372	0.700

Use Excel to plot y versus t² and determine the acceleration of gravity from the slope.

Hint: remember that the relation between y and t can be understood using the following equation:

y = v_it + (1/2) g t²  

Where v_i is the initial velocity and considered zero in this experiment.

Answer 1

From the graph, slope is given as

Slope = BC/AC = (0.12 - 0.04)/(0.6 - 0.2) = 0.2

(0.5) g = 1/slope

(0.5) g = 1/0.2

g = 10 m/s²