The resultant of two forces at right angle is 5N. When the angle between them is 120 degrees the resultant is root 13, then find the magnitudes of two forces.
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Forces vectors P and Q. Resultant R.
R² = P² + Q² + 2 P Q Cos θ
5² = P² + Q² --- 1 as θ= 90 ⁰
(√13² = P² + Q² + 2 P Q Cos 120⁰
13 = P² + Q² - PQ ---- 2
solving these equations, P Q = 12
Now P² + Q² + 2 P Q = 49
=> P + Q = 7 N taking only positive values. ---- 3
Also P² + Q² - 2 P Q = 1
=> P - Q = 1 N ----- 4
thus from eq 4 and 3, we get
P = 4 N and Q = 3 N
R² = P² + Q² + 2 P Q Cos θ
5² = P² + Q² --- 1 as θ= 90 ⁰
(√13² = P² + Q² + 2 P Q Cos 120⁰
13 = P² + Q² - PQ ---- 2
solving these equations, P Q = 12
Now P² + Q² + 2 P Q = 49
=> P + Q = 7 N taking only positive values. ---- 3
Also P² + Q² - 2 P Q = 1
=> P - Q = 1 N ----- 4
thus from eq 4 and 3, we get
P = 4 N and Q = 3 N
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