Balanced & Unbalanced Forces (OCR GCSE Physics A (Gateway))

Resolving Forces

Higher Tier Only

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

Forces in Equilibrium

Higher Tier Only

• 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