A bob of mass m = 0.200kg is suspended from a fixed point with a massless string

Question

A bob of mass m = 0.200kg is suspended from a fixed point with a massless string of length L = 20.0cm . You will investigate the motion in which the string traces a conical surface with half-angle = 21.0 degree.

What tangential speed v must the bob have so that it moves in a horizontal circle with the string making an angle 21.degree with the vertical?

A bob of mass m = 0.200kg is suspended from a fixed point with a massless string of length L = 20.0cm . You will investigate the motion in which the string traces a conical surface with half-angle = 21.0 degree . What tangential speed v must the bob have so that it moves in a horizontal circle with the string making an angle 21. degree with the vertical?

Explanation / Answer

Let tension in the string be T

Hence Tcos(theta) = mg

Tsin(theta) = mv^2/r

where r = Lsin(theta)

Hence dividing we get

tan(theta) = v^2/rg

tan(21 degrees) = v^2/(20 * 10^-2 * sin(21 degrees) * 9.8)

v = sqrt(tan(21 degrees) * 20 * 10^-2 * sin(21 degrees) * 9.8) = 0.519 m/s

Hence speed required is 0.519 m/s

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