The “Giant Swing” at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 6.29 m long, the upper end of the cable being fastened to the arm at a point 4.34 m from the central shaft. Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 26.6 degrees with the vertical.

Give your answer in seconds to the second decimal place.

Question

The “Giant Swing” at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 6.29 m long, the upper end of the cable being fastened to the arm at a point 4.34 m from the central shaft. Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 26.6 degrees with the vertical.

Give your answer in seconds to the second decimal place.

jamesj · Answer

So you want to ask yourself: what speed of rotation is consistent with a 26.6 degree angle of the cable?

To do that, analyze the sum of the gravitational force and the centripetal force on each seat.

jamesj · Answer

What is the expression for the magnitude of the centripetal force?

anonymous · Answer

F=mv^2/r

jamesj · Answer

Right.  Now what's r here?  You'll need to figure that out.

Further in what direction does the centripetal force Fc act?  Horizontally.  
Gravity acts vertically.  Use these two forces and their directions to find the angle.

anonymous · Answer

Will it be r from the end of the arm or from the end of the cable that I need?

jamesj · Answer

r is always the distance from the axis of rotation. As the axis of rotation is vertical, r is a horizontal distance: it the sum of the length of the arm on which the cable is suspended, plus the horizontal component of the length the cable.

anonymous · Answer

I got it, Thanks!