- Combining more than one force vector can result in
- Balanced forces – where there is no resultant force
- Unbalanced forces – where there is a resultant force
- If a force acts at an angle, the force may be broken down or resolved
- A single force can be resolved into two parts (components)
- A horizontal component
- A vertical component
The force (shown in red) may be broken into two components (shown in blue): a vertical one and a horizontal one
- When several forces act on an object in different directions, the resultant force can be found by adding the arrows together
- The two component arrows are placed head to tail with the single force starting at the tail of the first vector and ending at the head of the second
The resultant force can be found by adding the arrows together in a “head to tail” manner
- If the force arrows from a closed loop, then the forces are balanced, in other words, there is no resultant force
The forces in the above diagram form a closed loop – they are balanced
The resultant force is sometimes also known as the net force or the unbalanced force, so if you see any of these phrases used in an exam – don’t panic, they all mean the same thing!
- 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
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