Understanding Tension in a Simple Bridge System

[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. We may assume that the bridge is horizontal and motionless.

My solution is :

Let y be distance between the rope and the mass 110kg

Thus, T x 6 x cos30 = y x mg

But I don't know what is value of y. Would you mind teach me? Thank very much. Good Bye

Billy

 

[Jer]

Since it's a static problem (no motion), you're just summing the moments, which equals zero (because it's static).

Anyway, since it seems you were using point A as your datum, the value for y would be 3 (because the force of the bridge acts at its center of gravity...the middle of beams/bridges/simple structures like that).

 

[Jer]

Oh, and it seems to me that it would be T*6*sin30, and not cos30.

When calculating moments, you use the component of force perpendicular to the object it is acting upon.

 

[BillyCheung]

http://ccp.homeip.net/~billy/phy1.jpg

Thank very much.

In Figure 2, I think that 6 x cos 30 is correct answer. Why is your answer 6 x sin30? Thank a lot. Good Bye

Billy