Discover the Magnitudes and Angle Between Two Forces: Resultant Forces Homework

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The problem involves finding the magnitudes of two forces that sum to 24N, with one force being 12N and the resultant acting at a right angle to it. The equations used include R² = P² + Q² + 2PQcosΘ and tan α = QsinΘ / (P + QcosΘ). The initial attempt to solve the equations led to confusion regarding the correct formulation of the cosine term. After clarification, the correct equation was established, leading to the realization that the forces are actually 15N and 9N. The discussion highlights the importance of precise equation setup in solving physics problems.
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Homework Statement


The sum of two forces is 24N. There resultant is act right angle to the smaller of the two forces which is 12N. Find the magnitudes of the two forces & the angle between them.


Homework Equations



R2 = P2 + Q2 + 2PQcosΘ

tan α = QsinΘ/ (P+QcosΘ)

The Attempt at a Solution



R2 = P2 + Q2 + 2PQcosΘ

144 = (24-x)2 + x2 + x(24-x)cosΘ
0 = (2-cosΘ)x2 - 24(2-cosΘ)x + 432
cosΘ = 2x2 -48x +432/x(x-24) --------- (1)


tan90 = (24-x)sinΘ / [x + (24-x)cosΘ]
cosΘ = x / (x-24) ---------------(2)

from 1 & 2
x2 = 2x2 -48x +432
0 = x2 -48x +432
(x-12)(x-36) = 0
x = 12 or x = 36

Then both forces are 12N


I got this. But answer given as 15N and 9 N. Please tell me how to reach to this
 
Physics news on Phys.org
144 = (24-x)^2 + x^2 + x(24-x)cosΘ

The above equation should be

144 = (24-x)^2 + x^2 + 2x(24-x)cosΘ
 
thnx, i got it, the answer come
 
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