Question

the magnitude of resultant of two equal forces is 1000 n. find the magnitude of each force if they are perpendicular​

Answer 1

Answer:-

F = 707.10 N

Given :-

R = 1000 N

$\theta = 90^{\circ}$

To find:-

The magnitude of each forces.

Solution:-

Let the two forces be $F_1 and F_2$ and the angle between them is $\theta = 90^{\circ}$.

Since,

→$\mathsf{F_1 = F_2}$

• By using vector law of addition.

→$\mathsf{R = \sqrt{F_1^2 + F_2 ^2 + 2 F_1 \times F_2 Cos \theta}}$

→$\mathsf{R = \sqrt{F_1 ^2 + F_2^2 + 2F_1 \times F_2 Cos 90^{\circ}}}$

→$\mathsf{ R = \sqrt{F_1^2 + F_1 ^2 + 2F_1 ^2 \times 0 }}$

→$\mathsf{R = \sqrt{2F_1^2 }}$

• Put the given values,

→$\mathsf{1000= \sqrt{2 F_1^2 }}$

→$\mathsf{1000 = F_1 \sqrt{2}}$

→$\mathsf{ F_1 = \dfrac{1000}{\sqrt{2}}}$

→$\mathsf{ F_1 = \dfrac{1000}{1.414}}$

→$\mathsf{F_1 = 707.10 N}$

hence,

The magnitude of each force will be 707.10 N.