Help with circular motion question

[Chenpionn]

In an adventure park ride, people are strapped in a small cage that is whirled in vertical circles as shown in picture. The cables make an angle of 30 degrees with the vertical. The radius of the circle (shown as dotted line) is 8.0m. The cage and its occupants has a mass of 250kg. At the top of the circular motion, the cage is traveling at 10m/s.

Show the tension in each of the cables is very close to 360N.   


Could anyone please explain how to get the tension? All help appreciated [:

Chenpionn

[availn]

First find the net centripetal force at the top of the circle

F = mv²/r = 250 x 10² / 8 = 3125N

As we know, at the top of the circle, the cage's weight contributes to the centripetal force because it is pointing towards the centre. If we subtract the weight from the net centripetal force, we are left with the amount of force the cables must provide downwards.

3125 - 250x10 = 625N

The is the net force inwards both cables must provide through tension. So one cable must provide half of that force inwards.

625/2 = 312.5N

One cable must produce this much force directly downwards, but the cable is on an angle. The vertical component of one cable must produce this much force, so the tension of the cable is a bit more than this. Draw a triangle, with the cable's tension on the hypotenuse, and solve for this tension.

cos(30) = 312.5 / T
T = 360.8N

[Chenpionn]

thanks man [: