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

Question

The height of a tower is measured by attaching a simple pendulum to its ceiling, whose length is barely enough to stay off the floor. The pendulum is let go from a small angle, and takes 13 s to return to the same location it started from.

a.) How tall is the tower?


41.95 m

If the pendulum mass is let go 0.2 m above the floor,

b.) How fast is the mass travelling as it grazes the floor?


1.98 m/s

c.) From what angle (measured from vertical) was this pendulum released?


5.597 degrees


0.0977 radians

I got all of those right, but i have no idea about d), -- small angle approximation, help plz.. Thanks




d.) How much % error is incurred in the pendulum's initial angular acceleration by using the small angle approximation? (Remember to use radians here.)
%
(Does the error in the angular acceleration get worse or better as the pendulum swings towards equilibrium?)

Explanation / Answer

Reviewing your text/equations...you will that the 'period' of the pendulum is 13 s. p=2pi(1/sq.rt g/l) l=length =height of tower ...... g/l=(2pi/p)^2 .....l=g/(2pi/p)^2 l=9.8/.2336=41.95m

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