00:01
For this problem on the topic of equilibrium of rigid bodies, we are given a lever which is hinged at point c and attached to a control cable at point a.
00:12
Now we are told the horizontal force that the lever is subjected to at b and we are asked to determine the tension in the cable as well as the reaction at c.
00:22
So first we draw our free body diagram and we can see that triangle a, c, d is isosceles.
00:33
Angle c equal to 90 degrees plus 30 degrees, which is 120 degrees.
00:43
So that's the angle from cy to the line that is parallel with the lever.
00:54
Now angle a is equal to angle d and this is a half into 180 degrees minus 120 degrees, which is 30 degrees.
01:17
And hence, da forms an angle of 60 degrees with the horizontal axis.
01:24
Now for part a, we will resolve fad into components along ab and perpendicular to ab as follows.
01:34
And now we will take anti -clockwise moments as positive and we'll take the sum of the moments about point c and we know this the sum must be zero since the system is in equilibrium.
01:50
So this is f -a -d times a sign of 30 degrees at a distance of 250 millimeters, minus the force of 500 newtons times 100 millimeters must equal to 0...