Calculate the magnitude of this torque

[BillyCheung]

Dear all

A simple bridge made from uniform 6m long platform, whose centre of mass is at its midpoint. The mass of the bridge is 100kg. At one end A of the bridge, there is a frictionless hinge. A rope of negligible mass is attached to the other end B. This rope passes over a small frictionless pulley and supports a 110kg mass on its other end.

When the bridge is horizontal, the rope makes, at B, an angle of 30 degree to the horizontal. In answering all parts of this question, you may assume that the bridge is horizontal and motionless.

The tension in the rope has the same magnitude at all points. Calculate the magnitude of this torue.(Direction of the torque about A exerted ont he bridge by the rension in the rope.)

torque = r x Fsin30

Does = 6 x (tension - mg)sin30 ?

Thank a lot.

Billy

 

[ShawnD]

Sounds simple but a picture would really really help.

 

[sridhar_n]

Heres how u do it...

Since the mass of the bridge is concentrated at its centre, you can assume this to be a problem where the bridge is a single mass (do not consider length initially) connected to a rope making an angle of 30 degrees to the horizantal with a mass of 110 kg connected to the other end of the rope on the other side of the pulley. Now calculate the net force on the bridge's mass (You can do this by drawing free body diagrams for the bridge-mass-pulley system). This force times the length of the bridge will give the torque.

Got it?

Sridhar