A uniform metal rod, with a mass of 3.7 kg

 and a length of 1.0 m

, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.59 m

 above the base of the rod holds the rod at an angle of 36 

 above the horizontal. The wire is attached to the top of the rod.

 

Find the tension in the wire.

Find the horizontal component of the force exerted on the rod by the hinge.

Find the vertical component of the force exerted on the rod by the hinge.

The detailed solution is explained below:

Step-by-step explanation

Metal rod mass= 3.7 kg

Length of metal rod = 1.0 m

Vertical distance above the base of the rod= 0.59 m

• The tension in wire is calculated by the expression using the equilibrium balance condition, the calculation is shown below:

?T(0.59)−mg(2l?cos36)TTT?=0=0.59mg(2l?cos36)?=0.863.7(9.8)(21?cos36)?=24.860N??

The tension in the wire is 24.860 N

• The horizontal component of the force exerted on the rod by the hinge is the tension 24.860 N.
• The vertical component of the force exerted on the rod by the hinge is calculated as shown below:

?F=mgF=(3.7)(9.8)F=36.26N??