Consider the conical pendulum, a mass on the end of a string, with the other end

Question

Consider the conical pendulum, a mass on the end of a string, with the other end of the string fixed to the cieling. Given the proper push, this pendulum can swing in a circle at an angle of 15.5 with respect to the vertical, maintaining the same height throughout motion. If the mass of the pendulum, M, is 7.4 kg, and the length of the string, L, is 0.7m, what is the speed in m/s of the mass as it swings? Hint: Radially: Tsintheta=mv^2/R; Vertically: Tcostheta=mg; Geometry: R=Lsintheta; solve for v

Explanation / Answer

Given

Tsin(theta)=mv*v/r...............1

Tcos(theta)=mg...............2

Dividing (1) by (2)

tan(theta)=v*v/rg

r=Lsin(theta)

So we got

v=sqrt(tan(theta))*Lsin(theta)*g)

We got

v=2.62sqrt(tan(theta)*sin(theta))

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