Vector Diagram – GCSE Physics

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Introduction

  • A Vector diagram is a graphical representation of vectors, which are quantities that have both magnitude and direction.
  • Vector diagrams are used to visualize and analyze physical quantities like force, velocity, acceleration, displacement, electric fields etc.

Real-life application:

Vector Diagram GCSE Examples: Illustration showing applications of vector diagrams in aviation, navigation, electrical engineering, and astronomy

What is Vector Diagram?

  • The forces in a free body diagram can be compared as vector arrows using a scale vector diagram.
  • Example: The object experiences a resultant force of 5N acting diagonally between the right and upward directions due to the combination of the two perpendicular forces.

Vector Diagram GCSE Examples: Vector diagram using scale drawing to find the resultant of two perpendicular forces, 4N and 3N

Key Points:

Vectors are depicted as arrows, where:

    • The length of the arrow represents the magnitude.
    • The direction of the arrow indicates the vector’s orientation.
  • A scale diagram is used within a vector diagram to make the representation accurate and measurable.
  • This allows large or complex quantities to be visualized accurately on a smaller or more manageable page.
  • The length of each arrow in the scale vector diagram should be proportional to the magnitude of the force it represents.
  • The resultant force is represented by the arrow joining the start of the first force to the end of the last force.

How to calculate magnitude and direction of the resultant force by using vector diagram?

  • A vector diagram is a scaled drawing that uses arrows (vectors) to represent forces, where:
    • Length = Magnitude (measured with scale)
    • Direction = Angle of the force (measured with a protractor).
  • By plotting vectors tip-to-tail and measuring the resultant, we find the net force’s size and direction without calculations.

Steps to calculate Resultant force:

  • Step#1: Choose a suitable scale for a scale vector diagram.
  • Step#2: Draw vectors to scale.
  • Step#3: Draw the resultant vector (from start to end point).
  • Step#4: Measure the Magnitude and Direction of the Resultant force using the scale.

certified Physics and Maths tutorSolved Example

Problem: An object is acted upon by two forces:

  • Force A = 6 N to the right
  • Force B = 8 N upward

Find the magnitude and direction of the resultant.

Solution: 

Step #1: Choose a suitable scale for a scale vector diagram

Let’s choose:

1 cm = 2 N So,

    • 6 N : 3 cm
    • 8 N : 4 cm

Step #2: Draw vectors to scale:

    • Draw a 3 cm arrow to the right for Force A.
    • From its head, draw a 4 cm arrow upward for Force B.

Vector Diagram GCSE Questions: Vector diagram showing two perpendicular forces, Force A at 6N and Force B at 8N

Step #3: Draw vectors to scale:

    • Draw a diagonal arrow from the tail of Force A to the head of Force B.

Vector diagram showing resultant of 6N and 8N perpendicular forces using triangle method

Step #4: Measure the Magnitude and Direction of the Resultant force using the scale.

    • Measure the length of the diagonal = 5 cm
    • Convert using scale:

Vector magnitude calculation using scale: 5 cm times 2 N/cm equals 10 N

    • Measure angle from horizontal using a protractor = 53°

So, the final answer is

    • Resultant Force = 10 N
    • Direction = 53°

Vector diagram showing 6N and 8N forces at right angles with resultant force of 10N

certified Physics and Maths tutorSolved Example

Problem: At a certain point in time, a football experiences a 6 N downward gravitational force and a 10 N horizontal drag force as it flies through the air. Find the magnitude of the resultant of these two forces.

(Vector Diagram GCSE Question)

Solution: 

Step #1: Choose a suitable scale for a scale vector diagram

Let’s choose:

1 cm = 2 N So,

      • 6 N : 3 cm
      • 10 N : 5 cm

Step #2: Draw vectors to scale:

    • Draw a 5 cm arrow to the left for 10 N drag force.
    • From its head, draw a 3 cm arrow downward for 6 N gravity.

Vector diagram showing 10N force to the left and 6N force downward at right angles

Step #3: Draw the resultant vector:

    • Connect the tail of the first vector to the head of the second vector.

Step #4: Measure the Magnitude by using the scale.

    • Resultant = 5.83 cm
    • Convert:

Vector magnitude calculated as 5.83 cm times 2 N/cm equals 11.66 N

So, the final answer is – resultant Force = 11.66 N

Vector diagram showing 10N and 6N forces at right angles with resultant force of 11.66N

  • The forces are balanced if their scale vector diagram forms a closed loop.

certified Physics and Maths tutorSolved Example

Problem: Three forces act on an object at a point:

  • Force A = 4 N
  • Force B = 3 N

If the object is in equilibrium, find Force C and show that the vector diagram forms a closed triangle.

(Vector Diagram GCSE Question)

Solution: 

Step #1: Choose a Scale

Let’s use:

    • 1 cm = 1 N

Step #2: Draw vectors to scale:

    • Draw a 4 cm arrow to the right and mark as force A.
    • From the head of Force A, draw a 3 cm arrow upward and mark as Force B.

Vector diagram showing Force A as 4N to the right and Force B as 3N upward at 90 degrees

Step #3: Draw the resultant vector:

    • To balance the other two, draw a vector from the head of Force B back to the tail of Force A. This completes the triangle the diagram is a closed loop

Vector diagram with Force A at 4N, Force B at 3N, and resultant Force C shown as diagonal

Step #4: Measure Force C

    • Use a ruler to measure the closing side:
    • It should be 5 cm
    • So, Force C = 5 N (using 1 cm = 1 N)

So, it forms a closed triangle and Resultant = 0 N, because forces are balanced,

Vector diagram showing 4N and 3N forces with a resultant of 15N using triangle method

Frequently Asked Questions

Solution:

A drawing that uses arrows (vectors) to represent forces or movements, where:

  • Length = Size of force (e.g., 1 cm = 10 N)
  • Direction = Where the force acts (measured with a protractor).

Solution:

To find resultant force, follow these steps:

  1. Draw vectors tip-to-tail to scale.
  2. Connect the start to the end — this is your resultant force.
  3. Measure its length (convert to force using your scale) and angle.

Solution:

If the vector diagram forms a closed loop (the last arrow ends where the first started), forces are balanced. If not, they’re unbalanced.

Solution:

Yes! Just keep adding them tip-to-tail in any order – the resultant will be the same.

Solution:

In equilibrium, vectors form a closed shape with no gap – the resultant is zero.

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