Record----5 Physics Common Sense Problems in 30 minutes problem 2(not too easy)
Given that one has a conical pendulum of length 1 and angle between the z axis and "string" is 15 degrees,find the frequency of the pendulum.
Use a calculator for final approximations involving square roots and pi
If possible generalize how to find the period of a conical pendulum and why the approximation we are always told is 2pi*sqrtl/g.
Round to nearest thousandth
The answer is 1.972.
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1 solution
Since F=(mv^2)/r=Tension sin x and Tension cos x=mg (for no vertical movement ) we have F=T sin x = T cos x tan x =mg tan x.Now we have mg tanx = (mv^2)/r.We can form a right triangle and solve,making it obvious that r=l sin x.Simplifying we have v=sqrt(gl sin x tan x).So deriving for period(1/freq)we have 2pi r/v=2pi*sqrt(l cos x/g).Using addition/subtraction for cosine we have cos 15 =(sqrt6+sqrt2)/4.Using a calculator with the values and formula we just derived the answer is right there.