Scalar and vector quantities and resolving of forces

Scalar and vector quantities

Scalar quantities are physical quantities which have only magnitude; for, example speed, mass, volume, energy, time and temperature.

Vector quantities are physical quantities which have both magnitude and direction, for, example acceleration, momentum, weight, velocity, magnetic flux, force, pressure and displacement.

Resultant and composition of vectors or resolving vectors

Consider a force R acting of particle O at an angle θ  to the horizontal shown the figure below

The horizontal component, x, of the vector = Rcos θ.

The vertical component, y, of the vector R = Rsin θ

It Implies that

Example 1

Three forces of 3.5N, 4.0N and 2N, act on point O as shown in the figure below. Find the resultant force.

Solution

Magnitude of force

Fx = 2.0cos 90 + 3.5cos 60 – 4.0cos 60 = -0.25N

Fy = 2.0sin 90 + 3.5sin 30 – 4.0sin 60 = 1.567N

The resultant force is 1.5868N acting in the direction of 80.940 to the horizontal.

Example 2

(i) Define vector and scalar quantities and give an example each.

(ii) A body M of mass 6k is acted on by the forces of 5N, 20N, 25N and 30N as shown in the figure below. Find the acceleration of M

            Solution

Exercise

  1. Find the resultant force  in the figure below

[Ans. 6.85N at angle θ =40.60 to the horizontal]

2. Three forces as shown below act on a body of 5.0kg. Find the acceleration of the body.

            [Ans. 13.33ms-2]

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