Scale Drawings (Edexcel GCSE Physics)

Using Scale Drawings

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