Problem $2$

A uniform $8\mathrm{.}00$m$,1500$kg beam is hinged to a wall and

supported by a thin cable attached $2\mathrm{.}00$ m from the free

end of the beam, as shown in the figure. The beam is fixed

to the wall by a hinge at an angle of $30\mathrm{.}0$@ above the

horizontal. The angle between the cable and the beam is

$40\mathrm{.}0""$

a$)$ What is the angle between the tension in the cable and the horizontal? $($Hint: angles in a

triangle add up to $180).$

b$)$ What is the direction of the torque exerted by the beam around the point where the cable is

attached to the beam?

c$)$ What is the magnitude of the torque exerted by the beam around the point where the beam

is fixed to the wall?

d$)$ What is the correct equation to balance the forces in the horizontal? $($ H$=$ hinge force; T$=$

tension, angle $=$ angle between T and horizontal$)$

e$)$ Starting from the force balance equation in the vertical and the torque balance equation

around the point where the beam is fixed to the wall: What is the correct expression for the

hinge force H $?$

PLEASE explain in depth