Question

In the figure shown, one end of a uniform beam that weighs 827. N is attached to a wall with a hinge. The other end is held up by a wire. So the beam is in static equilibrium. There is an unknown horizontal and an unknown vertical force on the hinge.

(a) Find the tension in the wire.
N
(b) What is the horizontal component of the force of the hinge on the beam?
N
(c) What is the vertical component of the force of the hinge on the beam?
N

Answer 1

Use the FBD to find the forces,

Figure 1

or,

Figure 2

(a)

Use the equation of rotational equlibrium to find tension,

Take moment about hing,(use figure 2),

Take length of beam L,

(b) Use figure 1 to find horizontal equlibrium equaiton on the beam,

c) Use figure 1 to find vertical equlibrium equlibrium equaiton on the beam,

Therefore,

a) Tension in wire is 716 N,

b) Unknown horizontal hing force is 358 N

c) Unknown vertical hing foce is 207 N,