Predict the motion of a ball down a big ramp

How long will it take a ball to roll down a BIG ramp? You can use 1-D kinematics to answer this question; however, you may discover that extrapolation of results can be dangerous ...

At the end of class today, I will roll a ball down a ramp which is about 9.6 meters long, tilted at about 2.5 degrees. Your job is to estimate how long it will take the ball to make the trip. However, the only measurements you may make are of balls rolling down a much shorter ramp.

You will measure the time it takes a ball to roll down a short ramp tilted at 2.5 degrees. You must decide what to measure and how many measurements to make. Using your measurements, compute the acceleration of the ball as it moves down the ramp; be sure to include an uncertainty.

An example of computing the uncertainty in a ball's velocity

Now, assume that the ball will have the same acceleration as it rolls down a longer ramp tilted at the same angle. Make a prediction of the time it will take for the ball to roll 9.6 meters; include a range, like this:

                    12.8 +/- 0.5 seconds

Be sure to justify your uncertainty.

At the end of the class, I will roll the ball down, and every group will measure the time. The prediction which includes the actual time within its range and has the smallest range is the winner! Winning group members will receive a prize ....