Class 050824

pendulum, synchronization of pendulums, time down track, time down track changes with slope, time for rotating rod to come to rest

Based on the observations made in class, here is a graph of pendulum period vs. length.  The function that according to this graph relates period and length is T = .23 L^.48, approximately.

If a complete cycle of a 'bracket pendulum' of a certain length would take .5 seconds, then how much time elapses between its release and the fourth 'hit'?

If your 'bracket pendulum' requires .6 seconds for every cycle, and if the time required for a marble to roll down the track coincides with 5 'hits' after release, then how long does it take the marble to roll down the track?

If a marble rolls down a track of length 30 cm in 5 seconds, then

• How fast is the marble moving?
• Does the speed of the marble change?
• How would you prove that the speed of the marble changes?
• How fast do you think the marble is moving at the instant you release it?
• Would the speed of the marble at the end of the ramp be greater than, less than or equal to its average speed as it moves down the ramp?
• How fast would the marble therefore be moving at the end of the ramp?

If we were to make a graph of the speed of the marble vs. clock time, as the marble rolls down the ramp, what do you think the graph would look like?  Sketch the graph as you think it would be:

If we were to make a graph of the distance of the marble from its starting point vs. clock time, as the marble rolls down the ramp, what do you think the graph would look like?  Sketch the graph as you think it would be:

If we had three ramps, each with a slope greater than the one before it, then what do you think the corresponding three velocity vs. clock time graphs would look like?  Sketch the three graphs you would expect and indicate which corresponds to the greatest and which to the least ramp slope.

What aspect of the velocity vs. clock time graph changes as the ramp slope changes?