tension in a string with mass rotating around a point?

Question

A conical pendulum consists of a mass M attached to a light string of length L. The mass swings around in a horizontal circle, making an angle Θ with the vertical, as shown below. What is the tension, T, in the string?

I thought I have to take the centripetal force, F=mv^2/r in the x direction, F=mg in the y direction.... What should I actually do?

Avinash · Accepted Answer

T cos(Θ) = m g ---------------(1)
T sin(Θ) = m v^2/r ------------------(2)

Solve the above two equations.
I do not see any diagram with the question. But if you need to find T in terms of m, v, and r, then do as follows:

Squaring equations (1) and (2)
T^2 cos^2(Θ) = m^2 g^2
T^2 sin^2(Θ) = m^2 v^4/r^2
Adding,
T^2 = m^2 (g^2 + v^4/r^2) (because cos^2(Θ) + sin^2(Θ) = 1)
_________________________.

biire2u · Answer

You take a vector (a right triangle) between the x forces and the y forces and that resultant vector will be the tension in the string

Shuddhasattwa Paul · Answer

Balance the forces

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tension in a string with mass rotating around a point?

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