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Old Oct 19th 2008, 04:19 PM   #1
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pendulum problem

Hello everyone,

Could someone please show me how to do this one?

4. Suppose a pendulum is swinging back and forth. If the highest point is 12.5 cm above the lowest point, what would be the speed of the bob when it passes the lowest point?

Thank you very much
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Old Oct 19th 2008, 05:16 PM   #2
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Could someone please show me how to do this one?
Yes. You will have to use the conservation of energy. You know that when the pendulum reaches its highest point, its velocity is $\displaystyle 0 \frac{m}{s}$.
Consider a system with an origin centered at the lowest point.
The mechanical energy is given by $\displaystyle \frac{mv^2}{2}+mgy$.
So when the pendulum reaches its lowest point, there's no potential energy ($\displaystyle mgy=mg0=0$) but kinetic energy.
So $\displaystyle E=\frac{mv^2}{2}$.
At its highest point there's no kinetic energy, so $\displaystyle E=mgy=mg\cdot 12.5cm=mg\cdot 0.125m$.
You have that $\displaystyle E=\frac{mv^2}{2}=mg\cdot 0.125 \Leftrightarrow \frac{v^2}{2}=g\cdot 0.125$.
Solve for $\displaystyle v$ and you're done.
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