Question

the resultant of two forces one double the other magnitude is perpendicular to the smaller of the two forces find the angle between the forces

Answer 1

Answer:

Let two forces F₁ and F₂ are given

A/C to question,

|F₁| = 2|F₂|

Resultant of two forces F₁ and F₂ are given by

R = F₁ + F₂

A/C to question,

R is perpendicular upon smaller force.

Here smaller force is F₂.

So, R.F₂ = 0

⇒(F₁ + F₂).F₂ = 0

⇒F₁.F₂ + F₂² = 0

⇒|F₁||F₂|cosФ + |F₂|² = 0

Now, put |F₁| = 2|F₂|

⇒2|F₂|.|F₂|cosФ + |F₂|² = 0

⇒2cosФ + 1 = 0

⇒cosФ = -1/2 = cos120°

Hence, angle between two forces is 120°

Explanation: