The figure to the right shows a diagram of a typical science museum demonstratio

Question

The figure to the right shows a diagram of a typical science

museum demonstration of a conical pendulum. It consists of

a metal sphere (known as the

The figure to the right shows a diagram of a typical science museum demonstration of a conical pendulum. It consists of a metal sphere (known as the "bob") on the end of string of negligible mass. Assume that the mass of the bob is M and that the length of the string is L. You have carefully measured the circumference of the circular path traced out by the bob to be s. Find an expression for the tension, FT, in the string as a function of the given quantities (M, L, and s) only. Find an expression for the period of the motion, T, as a function of the given quantities (M, L, and s) only. Find numerical values for FT and T if L=0.90 m, M=0.040 kg, and s is 0.94 m.

Explanation / Answer

radius of the path=circumference/(2*pi)=s/(2*pi)

let tension be T.

balancing vertical force ,T*cos theta=M*g

where theta is the angle between the cord and the vertical.

now,from the geometry,

we get sin theta=radius/L

theta=asin(s/(2*pi*L)

so T=M*g/vos theta=M*g*L/sqrt(L^2 - (s/2*pi)^2))

b)let speed be v.

then balancing force in horizontal direction:

T*sin theta=M*v^2/r

T*r/L=M*v^2/r

v=sqrt(T*r^2/(L*M))=sqrt(T*s^2/(4*pi^2*L*M))

period=circumference/speed=s/v=s/sqrt(T*s^2/(4*pi^2*L*M))

c)numerical value:

tension=0.397 N

time period=1.892 sec

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