Galileo experimented with falling objects. By meas-uring the distance fallen as a function of time he was able to conclude that the velocity is a linear function and that the acceleration is constant. This applet mir-rors his experiments.

Select various times from the pull-down list, and observe the collected data. As the ball drops the distances are listed and average velocities and accelerations are com-puted and plotted.

Click here for more instructions below.

First observations: Select a time step from the pulldown list. As the ball drops the distances s are listed and average velocities and average accelerations are computed. Supposing the s-values to be measured positions of the falling ball, what can you deduce by examining the average velocities? What about the average accelerations?

Computing average velocity: Using the s-data from the second column, with the time step set to 0.5 seconds, compute by hand the first several values of the average velocity given in the third column. Do your computations agree with those given by the applet? Do the same for the fourth column, computing by hand the first several values of the average acceleration.

Experimental errors: The initial display assumes that all the values in the s column are exact. Note that the error field is initially set to 0. In a real laboratory situation, of course, no measurements can be exact. More typically a scientist will present data along with an estimate of the error in the measured values. For example a skilled experimenter may claim that the measured values of s are accurate to within 0.1%. That would be extraordinary. More likely the error would be 0.5%, 1.0%, or greater. Errors in the measured values of s result in errors in the computed values of average velocity and acceleration. It is an unpleasant fact of life that even small errors in the original data may result in much larger errors in the computed values. You may gain some feeling for this by setting the experimental error value to, say, 0.1%, 0.5%, 1.0%, or 5.0%. Do this with the time step set to 0.1 seconds, and note the effect on the plotted values of average velocity and acceleration. How accurately do you think Galileo could have measured the values of s? For him to be able to draw the conclusions that velocity is a linear function and acceleration is constant, how accurate do you think his data must have been?

Return to top