A $1,475$ N dowel is held in place by a light wire at an angle $=26\mathrm{.}5$ to the horizontal as shown in the figure. The dowel is attached to a pivot at the bottom, and a mass of weight w $=1,950$ N hangs from its top. The dowel makes an angle of $=63\mathrm{.}5$ with the horizontal. Assume the dowel is uniform.

A dowel of length $$ is attached to a hinge on the ground and makes an acute angle $$ counterclockwise from the horizontal. The right end of a wire attaches to the dowel a distance $34$ from the hinge. The left end of the wire attaches to a vertical wall on the left and makes an acute angle $$ with the horizontal. A block of mass m hangs from the top end of the dowel.

$($a$)$

Find the tension in the supporting wire $($in kN$).$

Draw a modified force diagram of the dowel, including distances. Note that we are told the wire is "light", so we can neglect its weight. Apply the condition for rotational equilibrium, with torques taken about the hinge, and solve for T$.$ kN

$($b$)$

Find the components of the reaction force $($in kN$)$ exerted by the floor on the dowel.

horizontal component:magnitude

Write Newton's second$-$law equations for the horizontal and vertical directions. Use your result from part $($a$).$ kNdirection $---$Select$---$ left right

vertical component:magnitude

Write Newton's second$-$law equations for the horizontal and vertical directions. Use your result from part $($a$).$ kNdirection $---$Select$---$ upward downward