The magnitude of two forces acting at a point is 16N.If the resultant force is 8N and its direction is perpendicular to the.samller force,then the forces are.
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let A and B are two forces acting at a point . A< B
A + B = 16 ------(1)
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A( A + B) = 0
A² = - A.B
A.B = -A² -----(2)
| A + B | = 8
√(A² + B² + 2A.B) = 8
√( A² + B² -2A²) = 8 from eqn (2)
( B² - A²) = 64
(B + A )( B - A) = 16
16 ( B - A ) = 64
B - A = 4 --------(3)
from eqn (1) and (3)
B = 10N and A = 6N
A + B = 16 ------(1)
question ask
A( A + B) = 0
A² = - A.B
A.B = -A² -----(2)
| A + B | = 8
√(A² + B² + 2A.B) = 8
√( A² + B² -2A²) = 8 from eqn (2)
( B² - A²) = 64
(B + A )( B - A) = 16
16 ( B - A ) = 64
B - A = 4 --------(3)
from eqn (1) and (3)
B = 10N and A = 6N
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