Question

The resultant of two forces p1 and p2 is p if p2 is doubled,the new resultant is perpendicular to pp1 . Show that p2 =p

Answer 1

Answer:

Resultant of two forces P and Q is R

R = P + Q

|R| = sqrt(P2 + Q2 + 2PQCosθ)

When Q is doubled new resultant R’ is

R’ = P + 2Q

Since it is perpendicular to P, dot product of R’ and P is zero

(R’).(P) = 0

(P + 2Q).(P) = 0

P^2 + 2PQCosθ = 0

(Dot product of P and P is P^2 and that of P and 2Q is 2PQCosθ)

Cosθ = -P/(2Q)

R = sqrt(P2 + Q2 + 2PQCosθ)

R = sqrt(P2 + Q2 + 2PQ*(-P/(2Q))

R = sqrt(P2 + Q2 - P2)

R = Q

Regards Arun

Explanation: