Scale Drawings (Edexcel GCSE Physics)
Revision Note
Author
Katie MExpertise
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
Worked example
The diagram below shows two rhinos pushing against a vehicle. The two forces are at right angles to each other.Draw a scale vector diagram to determine the magnitude of the resultant force. Label the two forces applied and the resultant, and clearly state the scale used.
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
Exam Tip
When constructing scale drawings, always use a ruler and a sharp pencil and double check the scale (e.g. is 1 square = 1 cm)
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