The height of a tower is measured by attaching a simplependulum to its ceiling,

Question

The height of a tower is measured by attaching a simplependulum to its ceiling, whose length is barely enough to stay offthe floor. The pendulum is let go from a small angle, and takes12 s to return to the same location itstarted from. The tower is 35.75 m tall = L. If the pendulummass is let go 0.3 m above the floor,

How fast is the mass travelling as it grazes the floor? ______m/s
The height of a tower is measured by attaching a simplependulum to its ceiling, whose length is barely enough to stay offthe floor. The pendulum is let go from a small angle, and takes12 s to return to the same location itstarted from. The tower is 35.75 m tall = L. If the pendulummass is let go 0.3 m above the floor,

How fast is the mass travelling as it grazes the floor? ______m/s

Explanation / Answer

Let h be height of pendulum above floor when released d = ((L2 - (L - h)2)  where d is the horizontal distance of the pendulum from itsequilibrium position                                     since is small d ˜ L d2 = 2 h L - h2 ˜ 2 hL    since h2 is small d = (2 * .3 * 35.75) = 4.63 m v = d    maximum speed for simpleharmonic motion = 2 f = 2 / 12 = .524 v = .524 * 4.63 = 2.42 m / s Or by conservation of energy m g h = 1/2 m v2     v = (2 g h) = (.6 * 9.8) = 2.42 m/s v = (2 g h) = (.6 * 9.8) = 2.42 m/s

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