AP Physics 1 : Pendulums
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Example Question #21 : Pendulums
Consider the following system:
If the length of the pendulum is 
We can use the equation for conservation of energy to solve this problem.
If the initial state is when the mass is at its highest position and the final state is when the mass is at its lowest position, then we can eliminate initial kinetic energy and final potential energy:
Substituting expressions in for each term, we get:
Canceling out mass and rearranging for height, we get:
Thinking about a pendulum practically, we can write the height of the mass at any given point as a function of the length and angle of the pendulum:
Think about how this formula is written. The second term gives us how far down the mass is from the top point. Therefore, we need to subtract this from the length of the pendulum to get how high above the lowest point (the height) the mass currently is.
Substituting this into the previous equation, we get:
Rearrange to solve for the angle:
We have values for each variable, allowing us to solve:
Example Question #22 : Pendulums
Matt Damon is once again trapped on Mars. He must measure the length of rope he has using only a stopwatch. Please solve the problem below.
A pendulum on Mars has been measured to have a period of 
To find the answer one must manipulate the equation
Where 
To solve this for 
Now plugging in our numbers
Keep in mind that the most accurate method is to round numbers at the very end of calculations (above this isn't done from the start of pi for simplicity).
The unit calculation above will end with meters as we are taking 
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