15. Two forces P and Q act at an angle a and have a resultant R. If each force is increase
R, prove that the new resultant makes with R an angle
tan-1
((P-Q) sin a/
P+Q+R+ (P+Q) cos a)
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Two force P and Q act at such an angle that R=P. Show that if P is doubled, the new resultant is at right angles to Q.
Step-by-step explanation:
Let the angle between the forces P and Q is α.
The resultant force is given as,
P
2
=P
2
+Q
2
+2PQcosα
cosα=−
2P
Q
When the P is doubled, let the new resultant make an angle θ with Q.
It can be written as,
tanθ=
Q+2Pcosα
2Psinα
=
Q+2P(−
2P
Q
)
2Psinα
tanθ=∞
θ=
2
π
Thus, the new resultant is at right angles to Q.
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