F6 App Math~Statics & Friction

Please refer to the following link first:

http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld01Mar032134.jpg


For the system to be in equilibrium, the weight W, the reaction R and the tension in the string T must be concurrent.

That is T passes through the centre O.

Hence, OPA is a striaght line.

OA = 9 + 6 = 15 cm

Hence, angle OAB = sin^-1(9/15) = sin^-1(3/5)


Now, by Lami's theorem, rearrange the forces.

http://i601.photobucket.com/albums/tt95/physicsworld9999/physicsworld02Mar032134.jpg


W / sin[90* - sin^-1(3/5)] = T / sin30*

W / cos(sin^-1(3/5)) = 2T

W / (4/5) = 2T (Since cos(sin^-1(3/5)) = 4/5)

Hence, tension in the string, T = 5W / 8


Tips: For statics problems, you should tackle it by taking moments, forces equilibrium, considering the geometric relations or applying Lami's theorem.

2009-03-03 21:38:26 補充：
Lami's theorem can only be used when there are three forces acting on the object.