- #1
E_Man
- 9
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Every kid has asked the question on a swing, could I go all the way around? How fast would I have to go? I wanted to find the answer.I’ve taken the first year of calculus, and I have been having trouble with the math of this problem . I am not sure there is an algebraic solution to this problem. :surprise:
You are on a park swing with radius R. What must your minimum speed be at the bottom of your circular trajectory such that you perfectly traverse the circular path created by the rotating swing?
Note: There are several parts to this problem. First you must calculate the rate of change of theta. You must then integrate the deceleration of gravity over the swing’s circular path. At all times the upward vector of centrifugal force, (V^2)/R must be greater than the acceleration of gravity so that you stay on your circular path.
Thanks, Elias
You are on a park swing with radius R. What must your minimum speed be at the bottom of your circular trajectory such that you perfectly traverse the circular path created by the rotating swing?
Note: There are several parts to this problem. First you must calculate the rate of change of theta. You must then integrate the deceleration of gravity over the swing’s circular path. At all times the upward vector of centrifugal force, (V^2)/R must be greater than the acceleration of gravity so that you stay on your circular path.
Thanks, Elias