A beam with a length of 8.00 m and a mass of 100. kg is attached by a large bolt to a supp...

SKETCH:

The figure shows that the beam makes an angle with the horizontal.

RESEARCH:

The first condition for the static equilibrium:

The net force acting on the system must be zero when the system is in static equilibrium.

The second condition for the static equilibrium:

The net torque acting on the system about the pivot point must be zero when the system is in static equilibrium.

SIMPLIFY:

When the system is in equilibrium, then the torque acting on the beam about the pivot point must be zero.

Therefore, the tension in the rope can be expressed as

. . . . . . (1)

Let be the force acting on the beam by the bolt in horizontal direction.

Let be the force acting on the beam by the bolt in vertical direction.

When the system is in equilibrium, then the net force acting on the beam in vertical direction must be zero.

Therefore, the force acting on the beam by the bolt in vertical direction can be expressed as

. . . . . . (2)

Similarly, the net force acting on the beam in horizontal direction must be equal to zero.

So, the force acting on the beam by the bolt in horizontal direction can be expressed as

. . . . . . (3)

CALCULATE:

Given data

The length of the beam,

The mass of the beam,

The mass is attached with a rope to one end of a beam,

The beam makes an angle with the horizontal,

The distance between pivot point and the left end of the beam,

Using the equation (3), the force exerted on the beam by the bolt in horizontal direction can be calculated as

Using the equation (2), the force exerted on the beam by the bolt in vertical direction can be calculated as