51 Newton force acting perpendicular to QP shown, is required to hold the bonnet at to the horizontal
From the information given,
mass of bonnet = 12kg
Weight = mass x acceleration due to gravity
Thus,
Weight of hat is 12 times 9.8, or 117.6 N.
Thus, 117.6 N of force is exerted downward.
Remember that moment equals force times the distance from the pivot perpendicular to the force's line of action?
The PB is the separation between the pivot and the force's path of action. Applying the cosine trigonometric ratio, which is denoted as, would allow us to determine PB.
Cosθ = adjacent side/hypotenuse
Considering triangle GBP,
hypotenuse = 1
adjacent side = BP
Cos30 = BP/1
BP = 1Cos30 = 0.866
Thus,
Moment: 101.845 Nm = 117.6 x 0.866
The unidentified force, F, is 2 meters away from the pivot and perpendicular to it. This force produces a moment of 2 * F = 2F.
Since the mass operates in the center and the bonnet is in balance, it follows that
2F = 101.845
F = 101.845/2
F = 51 N
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