15. A 20.0kg uniform door has a width of 1.20m and a height of 2.50m. The door i

Question

15. A 20.0kg uniform door has a width of 1.20m and a height of 2.50m. The door is mounted on a post by a pair of hinges, marked 1 and 2 in the figure, at the top and bottom of the door. An external force of 60.0N, at an angle of 30.0 degree above the horizontal, is applied to the small doorknob, as shown in the figure. The doorknob is 1.00m above the bottom of the door.

(a) Find the x component of the force that hinge 1 exerts on the door at the top.

(b) Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.

Please explain number 15 in detail.

Ans: (a) -53.4N, (b) 166N

Explanation / Answer

Let the angle is the angle from the cg of the door to the top edge portended by the top hinge
and the angle is the angle from the cg of the door to the bottom edge portended by the bottom hinge
and the angle is the angle from the bottom hinge to the door knob to the bottom edge

=atan(2.5/1.2)
and = atan(1/1.2)

sum torque about the bottom hinge

F*sin(30-)*sqrt(1^2+1.2^2)+
h1x*2.5-m*g*cos*sqrt(1.2^2+2.5^2)/2=0 , F = 60 N given
Now, solve for h1x

then sum forces in the x , Given F = 60N
h1x-F*cos30-h2x=0
Now, solve for h2x

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