Auniform metal rod, with a mass of 3.7 kg and a length of 1.2 m, is attached to a wall by a hinge at its base. a horizontal wire bolted to the wall 0.51 m above the base of the rod holds the rod at an angle of 25 degrees above the horizontal. the wire is attached to the top of the rod.

find the tension in the wire.

a. find the horizontal component of the force exerted on the rod by the hinge.
b. find the vertical component of the force exerted on the rod by the hinge.

Explanation:

On the rod , three forces are acting .

1 ) its weight  from the middle point .

2 ) Tension in the wire in the horizontal direction

3 ) reaction force by the hinge which balances the other two forces

Now taking moment of forces acting on the rod about the hinge

and equating opposite moment

3.7 x 9.8 x .6 x cos 25 = T x .51 ( T is tension in the horizontal wire)

T = 38.6 N

a )

The horizontal component of the force exerted on the rod by the hinge

will balance the tension in the wire acting in horizontal direction so it will be equal to

38.6 N

b )  The vertical component of the force exerted on the rod by the hinge

will balance the weight of rod so it will be equal to

3.7 x 9.8 N

= 36.26. N

=