A uniform metal rod, with a mass of 3.4 kg and a length of 1.3 m, is attached to

Question

A uniform metal rod, with a mass of 3.4 kg and a length of 1.3 m, is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.44 m above the base of the rod holds the rod at an angle of 20 degrees above the horizontal. The wire is attached to the top of the rod.


A.Find the tension in the wire.

T=_______N


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

Fhor=__________N

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


Fver=___________N

Explanation / Answer

A) Weight mg = 3.4 x 9.8 = 33.3 N Let T = tension in the wire Calculate torques about the hinge. Torque of T = T * 0.44 Torque of weight = mg * L/2 cos(20 deg) These torques are in opposite directions. Net torque = 0 Therefore T * 0.44 = mg * L/2 cos(20 deg) T = mg * L/2 * cos(20 deg) / 0.44 = 33.3 * 1.3/2 * cos(20 deg) / 0.44 = 46.25 N Ans: 46.25 N Can round it to 46 N B) Net horizontal force = 0. Therefore horizontal component of foce by the hinge = T = 46 N C) Net vertical force = 0 Therefore vertical component of force by the hinge = mg = 34.3 N

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