A 5.69-kg ball hangs from the top of a vertical pole by a 2.23-m-long string. Th

Question

A 5.69-kg ball hangs from the top of a vertical pole by a 2.23-m-long string. The ball is struck, causing it to revolve around the pole at a speed of 4.59 m/s in a horizontal circle with the string remaining taut. Calculate the angle, between 0° and 90°, that the string makes with the pole. Take g = 9.81 m/s2.

Find Tension in string.

(I've been working on this problem for quite a while) I know that tan(theta)=v^2/(piGsin(theta)

I know that this then equals sin^2(theta)/cos(theta)=v^2/piG.

I don't know how to solve for theta from here.

Explanation / Answer

use the condiition o equillibrium as force = tesion =T

centriopetal acceleration = mv^2 /R

a = m*4.27^2/ ( 2.13 sin(angle) )

force balance in x axis, Tsin(angle) = m*4.59^2/ ( 2.33 sin(theta)

force balance in y axis, T cos theta = Mg

divide these equations, tan( theta ) = 4.27^2/ (9.8 *2.13)sin( theta)

angle = 39.9 degrees

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so Tension T = 5.69 * 9.8/(cos 39.9)

T = 72.68 N

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