Question

The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle θ = 43o by a brace that is attached to a pin. The beam has a weight of 336 N. Three additional forces keep the beam in equilibrium. The brace applies a force to the right end of the beam that is directed upward at the angle θ with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component and a vertical component . Find the magnitudes of these three forces.

Answer 1

`F_b = 246.3 N`

`F_x = 180.15 N`

`F_y = 168 N`

Step-by-step explanation:

Let the force exerted by the brace is given as

`F_b` along its direction of length

also the two components at the end of the pin is given as

`F_x , F_y`

now by vertical force balance we have

`F_y + F_b sin43 = mg`

`Fx = Fb cos43`

Now by torque balance about the hinge point we have

`F_bsin43 * L = mg *(L)/(2)`

so we have

`F_b = (mg)/(2 sin43)`

`F_b = (336)/(2sin43)`

`F_b = 246.3 N`

now we have

`F_x = 246.3 cos43`

`F_x = 180.15 N`

similarly by Y direction equation

`F_y + 246.3 sin43 = 336`

`F_y = 168 N`