Balanced & Unbalanced Forces (AQA GCSE Physics: Combined Science)

• 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

• 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

• There are two methods that can be used to combine vectors using a scale diagram: the triangle method and the parallelogram method

• To combine vectors using the parallelogram method:

  • Step 1: link the vectors tail-to-tail

  • Step 2: complete the resulting parallelogram

  • Step 3: the resultant vector is the diagonal of the parallelogram

  • Step 4: The magnitude of the resultant vector can be found by measuring the length of the arrow

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