Question

If the resultant of two forces 3 N and 4N is 5N, then
what is the mgle between the two forces 3 (1M)
C​

Answer 1

Answer:

• Force (F₁) = 3 N
• Force (F₂) = 4 N
• Resultant (R) = 5 N

By applying parallelogram law we have :

$\longrightarrow\tt \overrightarrow{R} = \sqrt{A^2 + B^2 + 2AB \cos (\theta)}$

• A = 3 N
• B = 4 N

$\longrightarrow\tt 5= \sqrt{(3)^2 + {(4)}^{2} + 2 \times 3 \times 4 \times \cos (\theta)}$

$\longrightarrow\tt 5= \sqrt{9 + 16 + 2 4\times \cos (\theta)}$

Squaring both the sides we have:

$\longrightarrow\tt 25= 9 + 16 + 2 4\times \cos (\theta)$

$\longrightarrow\tt 25 - 9= 16 + 2 4\times \cos (\theta)$

$\longrightarrow\tt 16= 16 + 2 4\times \cos (\theta)$

$\longrightarrow\tt 16 - 16= 2 4\times \cos (\theta)$

$\longrightarrow\tt 0= 2 4\times \cos (\theta)$

$\longrightarrow\tt\cos (\theta) = \dfrac{0}{24}$

$\longrightarrow\tt\cos (\theta) = 0$

$\longrightarrow\tt(\theta) = \cos^{ - 1} 0$

$\longrightarrow \underline{ \boxed{\bold{(\theta) = {90}^{ \circ} }}}$