Answer to Question #204379 in Classical Mechanics for Bassie

Question

A door is 2.5m tall and 1.4m wide. It has a uniform density and weights 18kg. The door is supported

by two hinges, each 20cm from the top and bottom of the door as shown in the figure. A small child

weighting 30kg decides to start swinging from the doorknob which is 1m from the bottom of the door.

Find the total force (magnitude and direction) applied by each hinge on the door. Door knob is at the edge of the door.

Answer 1

$(a-20)F_1=Mg\frac a2,\implies \\ F_1=\frac{Mga}{2(a-20)}=98~N,$

$20F_2=Mg\frac a2+mgb+mgl,\implies\\ F_2=\frac{Mga+2mg(b+l)}{2\cdot 20}=4.7~kN.$