A 20 kg uniform door has a width of 12 m and a height of 25

A 20 kg uniform door has a width of 1.2 m and a height of 2.5 m. The door is mounted on a post by a pair of hinges, marked 1 and 2, at the top and bottom of the door. An external force of 60 N, at an angle of 30° above the horizontal, is applied to the doorknob, as shown. The doorknob is 1.0 m above the bottom of the door. In the figure, the x-component of the force, exerted on the door at the top by hinge 1, is closest to

Solution

reactions at hinge 1=Rh₁,Rv₁

reactions at hinge 2=Rh₂,Rv₂

60cos30+Rh₁+Rh₂=0

Rv₁+Rv₂=20g-60sin30

moment about hinge 2

60cos30x1-60sin30x1.2+20g(0.6)+Rh₁x2.5=0

Rh₁=-53.42N

-Rh₂=60cos30-53.42=1.46N

the x-component of the force, exerted on the door at the top by hinge 1=-53.42N is approximately=-55N