Teaching Physics with the Physics Suite Edward F. Redish

The cut pendulum

 A pendulum with a ball at the end is set swinging by holding it at the point marked A in the figure and releasing it. The x and y coordinate are shown with the origin at the crossing point of the axes and the positive directions indicated by the arrowheads. (a) During one swing, the string breaks exactly at the bottom-most point of the swing (the point labeled B in the figure) as the ball is moving from A to B towards C. Using solid lines sketch on the figure the path of the ball after the string has broken and sketch qualitatively the x and y coordinates of the ball and the x and y components of its velocity on the graphs at the right. Take t=0 to be the instant the string breaks.
(b) During a second trial, the string breaks again, but this time at the top-most point of the swing (the point labeled C in the figure). Using dashed lines sketch on the figure the path of the ball after the string has broken and sketch qualitatively the x and y coordinates of the ball and the x and y components of its velocity on the graphs at the right. Take t=0 to be the instant the string breaks.

Note to the instructor: The cut pendulum is a classic problem that is more difficult than it appears on the surface. I have seen some physics graduate students confidently get the path wrong. But I have also seen students in algebra-based physics figure it out by careful reasoning. If given on an exam, you have to be careful to grade for consistency with the chosen path and not cumulate errors in order not to be too Draconian.

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