# Forces in Equilibrium

Card 1: Vector and Scalar Quantity

## Vector and Scalar Quantity

A scalar quantity is a quantity which can be fully described by magnitude only.

A vector quantity is a quantity which is fully described by both magnitude and direction.

Card 1a: Vector Diagram

## Vector Diagram

The arrow shows the direction of the vector.

The length representing the magnitude of the vector.

Card 2: Equal Vector

## Equal Vector

Two vectors A and B may be defined to be equal if they have the same magnitude and point in the same direction.

Card 3: Vector Addition - Triangle Method

## Vector Addition - Triangle Method

Join the tail of the 2nd vector to the head of the 1st vector. Normally the resultant vector is marked with double arrow.

Card 4: Vector Addition - Parallelogram Method

## Vector Addition - Parallelogram Method

Join the tail of the 2nd vector to the tail of the 1st vector. Normally the resultant vector is marked with double arrow.

Card 5: Addition of 2 perpendicular vectors

## Addition of 2 Perpendicular Vectors

If 2 vectors (a and b) are perpendicular to each others, the magnitude and direction of the resultant vector can be determined by the following equation.

Example 1
Two forces, P and Q of magnitude 10N and 12N are perpendicular to each others. What is the magnitude of the resultant force if P and Q are acting on an object?

            \begin{gathered}
{\text{Magnitude of the resultant force,}} \hfill \\
|F| = \sqrt {10^2  + 12^2 }  = \sqrt {244}  = 15.62N \hfill \\
\end{gathered}

Example 2

Diagram above shows that four forces of magnitude 2N, 4N, 5N and 8N are acting on point O. All the forces are perpendicular to each others. What is the magnitude of the resulatant force that acts on point O?

The resultant force of the horizntal component = 5 - 2 = 3N to the right
The resultant force of the vertical component = 8 - 4 = 4N acting downward.

Therefore, the magtitude of these 2 force components,

            |F| = \sqrt {3^2  + 4^2 }  = \sqrt {25}  = 5


Card 6: Vector Resolution

## Vector Resolution

A vector can be resolve into 2 component which is perpendicular to each others.

Example 3

Diagram above shows a lorry pulling a log with an iron cable. If the tension of the cable is 3000N and the friction between the log and the ground is 500N, find the horizontal force that acting on the log.

Horizontal component of the tension = 3000 cos30o =2598N
Friction = 500N

Resultant horizontal force = 2598N - 500N =2098N

Example 4

Diagram above shows two forces of magnitude 25N are acting on an object of mass 2kg. Find the acceleration of object P, in ms-2.

Horizontal component of the forces = 25cos45o + 25cos45o = 35.36N

Vertical component of the forces = 25sin45o - 25sin45o = 0N

The acceleration of the object can be determined by the equation

F = ma
(35.36) = (2)a
a = 17.68 ms-2

Card 7: Inclined Plane

## Inclined Plane

Weight component along the plane = Wsinθ.
Weight component perpendicular to the plane = Wcosθ.

Example 5

A block of mass 2 kg is pulling along a plane by a 20N force as shown in diagram above. Given that the fiction between block and the plane is 2N, find the magnitude of the resultant force parallel to the plane.

First of all, let's examine all the forces or component of forces acting along the plane.

The force pulling the block, F = 20N
The frictional force Ffric = 2N
The weight component along the plane = 20sin30o = 10N

The resultant force along the plane = 20 - 2 - 10 = 8N

Card 8: What does the phrase “Force in Equilibrium” means?

## Vectors in Equilibrium

When 3 vectors are in equilibrium, the resultant vector = 0. After joining all the vectors tail to head, the head of the last vector will join to the tail of the first vector.

Card 9: What does the phrase “Force in Equilibrium” means?

## Forces in equilibrium

Forces are in equilibrium means the resultant force in all directions are zero.

Example 6

Diagram above shows a load of mass 500g is hung on a string C, which is tied to 2 other strings A and B. Find the tension of string A.

Tension of string C, TC = weight of the load = 5N
All forces in the system are in equilibrium, hence

Vertical component of tension A (TA) = TC
TAcos60o = TC
TA = TC/cos60o
TA = 5/cos60o = 10N

Card 10: Empty Card

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