Question

Find the magnitude of F1 and F2 if F1 and F2 make angle 30 degree and 45 degree with F3 in which magnitude of F3 is 10N
(given F1vector + F2vector = F3vector)

Answer 1

Given that,

Angle between F₁ and F₂ = 30°

Angle between F₁ and F₃ = 45°

Magnitude of third force = 10 N

According to figure

The force along x- axis is

Using equilibrium equation

$\sum{F_{x}}=0$

$F_{3}\cos\theta+F_{1}\cos\theta=F_{2}$....(I)

The force along y- axis is

Using equilibrium equation

$\sum{F_{y}}=0$

$F_{1}\sin\theta+F_{3}\sin\theta=0$....(II)

We need to calculate the magnitude of F₁

Using equation (II)

$F_{1}\sin\theta+F_{3}\sin\theta=0$

Put the value into the formula

$F_{1}\sin\75+10\sin45=0$

$F_{1}=\dfrac{-10\sin45}{\sin 75}$

$F_{1}=-7.32\ N$

Negative sign shows the opposite direction .

We need to calculate the magnitude of F₂

Using equation (I)

$F_{3}\cos\theta+F_{1}\cos\theta=F_{2}$

Put the value in the equation

$10\cos45-7.32\cos75=F_{2}$

$F_{2}=5.17\ N$

Hence, The magnitude of F₁ and F₂ are 7.32 N and 5.17 N.