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Two forces 5 and 10 kg wt are acting with an inclination of 120o between them. What is the angle which the resultant makes with 10kg wt?

CLASS - XI PHYSICS (Kinematics)

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CLASS - XI PHYSICS (Kinematics)

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Let P = 5 kg weight = 5 g Newtons

Q = 10 g Newtons

Using the parallelogram law of addition of vectors :

Resultant force magnitude = R

R² = P² + Q² + 2 P Q Cos Ф = 5² + 10² + 2 * 5 * 10 * Cos 120

= 125 - 50 = 75

R = 5√3 newtons

Angle made by R with Q = 10 kg weight = α

tan α = P Sin Ф / ( P + Q Cos Ф)

= 5 Sin 120 / (10 + 5 Cos 120) = 2.5 √3 / 7.5 = 1/√3

α = 30°

Q = 10 g Newtons

Using the parallelogram law of addition of vectors :

Resultant force magnitude = R

R² = P² + Q² + 2 P Q Cos Ф = 5² + 10² + 2 * 5 * 10 * Cos 120

= 125 - 50 = 75

R = 5√3 newtons

Angle made by R with Q = 10 kg weight = α

tan α = P Sin Ф / ( P + Q Cos Ф)

= 5 Sin 120 / (10 + 5 Cos 120) = 2.5 √3 / 7.5 = 1/√3

α = 30°