When two equal forces are inclined at an angle 2a their resultant is twice as great as
when they are inclined at an angle 2B. Show that cosa = 2 cosß.

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mathmate mathmate · Answer 1 · 2019-07-05T12:17:37+02:00

Step-by-step answer:

Referring to the attached diagram, the resultant of two forces each with magnitude F and inclined to each other at 2a equals

Ra = 2Fcos(a) ..............................(1)

Similarly, the resultant of two forces each with magnitude F and inclined to each other at 2b equals

Rb = 2Fcos(b)..............................(2)

We are given that

Ra = 2Rb ....................................(3)

Substitute (1) & (2) in (3) gives

2Fcos(a) = 2(2Fcos(b))

Expand

2Fcos(a) = 4Fcos(b)

Simplify

cos(a) = 2 cos(b) QED

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