Answer:
N = 167 Newtons
R = 727 Newtons
Explanation:
i) For static equilibrium, moments about any convenient point must sum to zero.
A moment is the product of a force and a moment arm length. Only the force acting perpendicular to a moment arm passing through the pivot point makes a moment.
ii) I will ASSUME the two moment arms are 0.05m and 0.15 m
CCW moments about the fulcrum are
190 N(0.2 m) + 280 N(0.05 m) = 52 N•m
CW moments are (N)N(0.15 m + 90 N(0.3 m) = 27 + 0.15N N•m
For static equilibrium, these must be equal
27 + 0.15N = 52
0.15N = 25
N = 166.6666666...
Sum moments about N to zero
(Same as saying CW and CCW moments must balance)
190(0.2 + 0.15) + 280(0.05 + 0.15) - R(0.15) - 90(0.3 - 0.15) = 0
R = 726.6666666...
We could verify this by summing vertical forces to zero.
R - 190 - 280 - 166.666666 - 90 = 0
R = 726.6666666...
