CAPM Challenge

CAPM Challenge - Table Sliding

Find the acceleration of a ball rolling down a table using only a ball, chalk, and ruler.

Also, predict the velocity of the ball after 4 seconds.

To begin, Valentina and I set up our experiment. We raised a table up on wooden blocks to create a slant. Then, using a metronome, we marked the position of the ball at each half second as it rolled down the table.

We then measured the ball's travel from 0 seconds to 3.5 seconds. We took three trials of data and averaged all of the results. Them, we took these results and graphed the averages. 

Afterwards, we converted the centimeter measurements to meters so, when we test our data with the motion detector, it will be easier to compare. 

The equation for our line is X = 0.011t^2 + 0.0081

We know that acceleration is equal to the change in velocity/the change in time. Half the slope is equivalent to the acceleration. Since the slope of the line is equal to the velocity, we multiplied 0.011 by 2 and found the acceleration to be .022 m/s.

Then, to predict the rate of acceleration at 4 seconds, we used instantaneous velocity. 

We took our original equation X = 0.011t^2 + 0.0081 and plugged 5 in for t as well as 3.

0.011(5)^2 + 0.0081

= .2831

0.011(3)^2 + 0.0081

= .1071

Next, we subtracted the results at 5 from the results at 3. That number was then divided by two to find the instantaneous velocity of 4.

  (.2831 - .1071) / 2

= .088

We predict that the acceleration at 4 seconds will be .088 m/s