Question

A uniform metal rod, with a mass of 3.0 kg and a length of 1.1 m , is attached to a wall by a hinge at its base. A horizontal wire bolted to the wall 0.55 mabove the base of the rod holds the rod at an angle of 30 ? 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 hortizonal component of the force extended 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

Answer 1

A) Weight mg = 3.0 x 9.8 = 29.4 N
Let T = tension in the wire
Calculate torques about the hinge.
Torque of T = T * 0.55
Torque of weight = mg * L/2 cos(30⁰)
These torques are in opposite directions.
Net torque = 0
Therefore T * 0.55 = mg * L/2 cos(30⁰)
T = mg * L/2 * cos(30⁰) / 0.55
= 29.4 * (1.1/2 )* cos(30⁰) / 0.55
T= 25.46N


B) Net horizontal force = 0.
Therefore horizontal component of foce by the hinge = T = 25.46 N

C) Net vertical force = 0
Therefore vertical component of force by the hinge = mg
= 29.4N