How to draw a diagram to show the maximum resultants of the
two forces of 5n and 7n respectively act on an object
The diagram below shows the maximum resultants of the two forces of 5n and 7n respectively act on an object.
The two forces are represented by the arrows, with the length of the arrows representing the magnitude of the forces. The resultant force is represented by the arrow drawn from the tail of the 5n force to the head of the 7n force.
The length of the resultant force is the hypotenuse of the triangle formed by the two forces, which is equal to the square root of (5n)^2 + (7n)^2 = 8.6n.
[Diagram]
5n
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7n ------------ 8.6n (Resultant)
both in same direction for max 5 + 7 = 12 Newtons
but if you insist
say 5 is along the x axis
and 7 is at angle A above x axis
resultant R
Rx = 5 + 7 cos A
Ry = 7 sin A
R^2 = (5 + 7 cos A)^2 + 49 sin^2 A
= 25 + 70 cos A + 49 cos^2 A + 49 sin^2 A = 25 + 70 cos A + 49
= 74 + 70 cos A
cos A is max of 1 when A = 0
so
max R^2 = 144
R = 12 (What else is new ? )