The resultant of two forces is 250 N and the same are inclined at 300
and 450 with resultant, one on either side. Calculate the
magnitude of two forces.
Answers
Answer:
...........................
Given info : The resultant of two forces is 250 N and the same are inclined at 30° and 45° with resultant one on either side.
To find : let A and B are two forces resultant of which is 250 N and the same are inclined at 30° and 45° with resultant one on either side.
so, angle between two forces, θ = 30° + 45° = 75°
so, A² + B² + 2ABcos75° = 250
⇒A² + B² + 2AB(√3 - 1)/2√2 = 250
⇒A² + B² + 0.366AB = 250 ...(1)
if we assume resultant lies along y axis.
then, A = -Asin30° i + Acos30° j = -A/2 i + √3/2 A j
B = Bsin45 i + Bcos45° j = (B/√2 i + B/√2 j)
so, A + B = (-A/2 + B/√2)i + (√3A/2 + B/√2) j = 250 j
so, (-A/2 + B/√2) = 0 ⇒A/B = √2 ...(2)
and √3A/2 + B/√2 = 250
⇒√3√2B/2 + B/√2 = 250 [ from eq (2) ]
⇒(√3 + 1)B/√2 = 250
⇒B = 250√2/(√3 + 1) = 129.41 N
and A = √2B = √2 × 129.41 = 183 N
you can verify it by using equation (1).
Therefore the forces are 183 N and 129.41 N