Balanced & Unbalanced Forces (OCR Gateway GCSE Physics)

Resolution of Forces

• Any force vector can be split into two components
  • This is called "resolving" a force

Any force vector can be expressed in terms of a horizontal and vertical component. They are always at right-angles to each other 

• Two force vectors can also 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

• When three forces act on a body in equilibrium, they can be added together to form a closed vector triangle
  • This indicates that the resultant force on the body is zero

• This is illustrated in the example given below:

Three forces on an object in equilibrium form a closed vector triangle

• In general, any number of forces acting on a body in equilibrium can be added together
  • The force vectors will always form a closed shape (i.e., added head-to-tail, they will return to the starting position)
  • This always indicates that the resultant force is zero