A small ball of mass m is suspended from a string of length L . The ball revolve

Question

A small ball of mass m is suspended from a string of length L. The ball revolves with constant speed v in a horizontal circle of radius r as shown in the figure. (Because the string sweeps out the surface of a cone, the system is known as a conical pendulum.) Find an expression for v.

For the conical pendulum described above, determine the following if m = 15.0 kg and ? = 28? . (a) the horizontal and vertical components of the force exerted by the string on the object
FH = N

FV = N

(b) the radial acceleration of the object
ar = m/s

Explanation / Answer

mg = TCos and TSin = mv2/r

dividing both these, Tan = v2/rg

v = (rgTan)

a) Fh = mv2/r = m(rgTan)/r = mgTan = 15*9.81*Tan28 = 78.2 N

Fv = mg = 15*9.81 = 147.2 N

b) Radial acceleration = v2/r = (rgTan)/r = gTan = 9.81*Tan28 = 5.22 m/s^2

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