Workshop 1C

How long will it take a ball to roll down a BIG ramp? You will perform some extrapolation to see first-hand just how dangerous it is....

At the end of class today, I will roll a ball down a ramp which is about 9.4 meters long, tilted at about 4.6 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. In order to use these measurements to predict the time down the long ramp, you will need to extend the data beyond the range of measurements: we call this extrapolation. The further beyond the actual measurements you extrapolate, the more and more uncertain your estimates become.

You will measure the time it takes a ball to roll down a short ramp tilted at 4.5 degrees, but for only three distances: 20 cm, 50 cm, 110 cm. Make a graph of your measurements, and use it to estimate the time for a ball to roll about 9.5 meters. Actually, split your team into two units and make two graphs

Take two pieces of paper, tape them together to make a single lo-o-ong sheet of graph paper. Plot distance on the horizontal scale, running 0 m to 10 m; all your measurments will be squished on the left side. Plot time on the vertical scale -- leave plenty of room. Draw a curve through your measurements, and extend it to a distance of 10 meters.
On a single sheet of paper, plot distance on the horizontal axis, running from 0 cm to 120 cm. On the vertical axis, plot time squared, running from 0 square seconds to about 4 square seconds. How can you use this graph to predict the time to roll 9.4 meters?

Make a prediction which includes a range, like this:

                    12.8 +/- 0.5 seconds

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 ....