Question

A steel bar (mass 762 kg, length 88.3 m) is supported by a horizontal wire attached to a wall. The wire is tied to the beam distance 28.96 m from the top end. The center of mass of the bar is 23.5 m from the bottom. The bar is held at the bottom by a hinge, and makes an angle θ = 46.5^o with the horizontal. Find F_hinge, the magnitude of the force exerted by the hinge on the bar, in N.        

Answer 1

The diagram of the situation in the problem is shown below.

Given the mass of steel bar M = 762kg, its length L = 88.3m, x1 = 28.96m, x2 = 23.5m and

For the system to be in equilibrium, the net torque acting on the syatem should be zero. Taking torque about the pivot A, we get

So the tension in the wire is 2806.65N.

Again for the system to be in equlibrium, the net force acting on the syatem should be zero. Let Fx and Fy be the components of hinge force on the bar in the x and y directions respectively. Now taking forces in the x-direction,

Taking forces in the y-direction,

So the resultant hinge force is given by,

So the magnitude of force exerted by the hinge on the bar is 7977.61N.