Question

Add a force of 8N directed northwards to a force of 6N directed westwards. Calculate the magnitude and direction of resultant with north.

Answer 1

The net force resultant will be 2 newtons northward

Answer 2

Answer:The magnitude of resultant is 10 N and direction of resultant with north is 53.12°

Explanation:

Given:Force directed towards north $= 8N$

          Force directed towards west $= 6N$

To find: We have find the resultant of the forces and direction with north.

The resultant of the forces can be given by

$R=\sqrt{A^{2}+B^{2}+2ABcos }$θ

$R=\sqrt{8^{2}+6^{2}+2(8)(6)cos90 }$°

$R=\sqrt{64+35+2(8)(6)(0)}$

$R=\sqrt{64+36}$

$R=\sqrt{100}$

$R=10N$

∴ The magnitude of resultant is 10 N.

The direction of resultant force with north can be given by,

tanθ $= \frac{8}{6}$    

tanθ $= 1.3333$

    θ $= tan^{-1} (1.3333)$  

    θ $= 53.12$°

∴ The direction of resultant with north is 53.12°

Concept:Vectors are geometrical entities that have magnitude and direction. A vector can be represented by a line with an arrow pointing towards its direction and its length represents the magnitude of the vector. Therefore, vectors are represented by arrows, they have initial points and terminal points.Vectors play an important role in physics. For example, velocity, displacement, acceleration, force are all vector quantities that have a magnitude as well as a direction.

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