Scale Drawings (Edexcel GCSE Physics)

Higher Tier Only

• Resolving vectors into components allows for more accurate calculations of resultant forces
• By resolving all of the involved forces into their horizontal and vertical components and then adding or subtracting as required, a final resultant force vector can be constructed using a scale diagram
• Vector diagrams can also be used to illustrate net (or resultant) forces and equilibrium situations

Net Force

• Vector diagrams include arrows in a particular direction which represent the different forces on an object
• The size of the arrow corresponds to the size of the force
• Net, or resultant, forces can be calculated by adding or subtracting all of the forces acting on the object
  • Forces working in opposite directions are subtracted from each other
  • Forces working in the same direction are added together

• If the forces acting in opposite directions are equal in size, then there will be no resultant force – the forces are said to be balanced

Resultant forces on an object 

Resolution of Forces

• Two forces can be added together to find the resultant force
• When two vectors are not at right angles, the resultant vector can be calculated using a scale drawing
  • Step 1: Link the vectors head-to-tail if they aren’t already
  • Step 2: Draw the resultant vector using the triangle or parallelogram method
  • Step 3: Measure the length of the resultant vector using a ruler
  • Step 4: Measure the angle of the resultant vector (from North if it is a bearing) using a protractor

A scale drawing of two vector additions. The magnitude of resultant vector R is found using a rule and its direction is found using a protractor

• Note that with scale drawings, a scale may be given for the diagram such as 1 cm = 1 km since only limited lengths can be measured using a ruler
• The final answer is always converted back to the units needed in the diagram
  • Eg. For a scale of 1 cm = 2 km, a resultant vector with a length of 5 cm measured on your ruler is actually 10 km in the scenario

Equilibrium

• A system is in equilibrium when all the forces are balanced. This means:
  • There is no resultant force

• An object in equilibrium will therefore remain at rest, or at a constant velocity, and not rotate or move

An object is in equilibrium if the horizontal forces on it are equal and vertical forces on it are also equal

Step 1: Decide on a suitable scale

• • A scale of 1 cm to 1.0 kN is the most suitable for this scenario

Step 2: Use grid paper to draw the vectors top to tail and to scale

Step 3: Draw the resultant vector and measure its length

Step 4: Use the scale to convert the length to kN

• • The resultant force is 8.6 cm, meaning the resultant force is equal to 8.6 kN