Suppose you have two forces \(\vec F\) and \(\vec F\). How would y

1.	Suppose you have two forces \(\vec F\) and \(\vec F\). How would you combine them in order to have resultant forces of magnitudes1. zero2. 2 \(\vec F\), and3. \(\vec F\)
Answer» 1. If the forces act in opposite directions, the resultant is zero. 2. If the forces act in the same direction, resultant \(\vec R = 2 \vec F.\) 3. For \(\vec R = 2 \vec F\) \(\sqrt {F^2 +F^2 +2F.F.cos\theta} = F\) ⇒ 2F² (1 + cosθ) = F² ⇒ 1 + cosθ =\(\frac {1}{2}\) ⇒ θ = 120°

Suppose you have two forces \(\vec F\) and \(\vec F\). How would you combine them in order to have resultant forces of magnitudes1. zero2. 2 \(\vec F\), and3. \(\vec F\)

Answer»

1. If the forces act in opposite directions, the resultant is zero.

2. If the forces act in the same direction, resultant \(\vec R = 2 \vec F.\)

3. For \(\vec R = 2 \vec F\)

\(\sqrt {F^2 +F^2 +2F.F.cos\theta} = F\)

⇒ 2F² (1 + cosθ) = F²

⇒ 1 + cosθ =\(\frac {1}{2}\)

⇒ θ = 120°