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The resultant of two forces p and q is of magnitude p show that if p is doubled the new resultant is at rightangles to q and its magnitude Will be (4p^2-q^2)^2 answer from statics
The resultant of two forces p and q is of magnitude p show that if p is doubled the new resultant is at rightangles to q and its magnitude Will be (4p^2-q^2)^2 answer from statics

```
2 years ago

Arun
25768 Points
```							use the following resultant formulaR = [A 2 + B 2 + 2ABCosθ] 1/2where 'A 'and 'B' are two forces inclined at an angle 'θ' to each other giving a resultant force 'R'.in the first case caseR1 = pA = pand B = qso,p2 = p2 + q2 + 2pqCosθorq2 + 2pqCosθ = q + 2pCosθ = 0 (1)or in other terms-q2 = 2pqCosθ (2) and in the second caseA = 2pB = q thus,R22 = 4p2 + q2 + 4pqCosθ = 4p2 + q2 +2(2pqCosθ)orby using equation (1)R22 = 4p2 + q2 - 2q2or the new resultant isR2 = [4p 2 - q 2 ] 1/2 (3) the angle between R2 and q would beα = tan-1[qSinθ / (2p + qCosθ)]oraccording to (1),2p + qCosθ = 0thustanα = qSinθ / 0 = undefinedthus,α = 90 o so, the forces q and R2 are perpendicular to each other.
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2 years ago
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