15. A 20.0kg uniform door has a width of 1.20m and a height of 2.50m. The door i
ID: 1494272 • Letter: 1
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
a)
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
b) F= m g - F sin 30 = 20*9.81 - 60*0.5= 166.2 N
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