Static force and Torque?

Question

A window of mass 5 kg and length 0.75m is being held open at an angle of 40 from the vertical by a duck pushing it out horizontally from the bottom.

a) How much force must be provided to hold the window statically?

b) What horizontal and vertical reaction forces must the hinges at the top provide when the window is held open?

Answer 1

Ok, what I have understood, is that there is a windows, let's consider it like a wire, a heavy wire, that is being held by a horizontal force in one of its ends, in other words let's graph a line, with the horizontal force.

The horizontal force is making an angle of : 90 - 40 = 50º

We must find that force, so we apply torques respect the other end.

Horizontal force = F

F*cos(50)*0.75 = 5*9.8*cos(40)*0.75/2

F = 29.19 Newtons

b) To find the reaction, we can apply torques respect the center of mass, so this time we will not consider the mass when we use torques :

Ry and Rx :

Ry*cos(40)*0.75/2 = F*cos(50)*0.75/2

Ry*cos(40)*0.75/2 = 29.19*cos(50)*0.75/2

Ry = 24.5 Newtons

Rx = F

Hope that helped