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Physics · Forces

Resultant forces

Calculate the resultant of forces acting in a straight line, and (Higher tier) use free body diagrams and vector diagrams to find resultants and resolve forces.

  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is a force measured in?

    Show answerHide answer

    Newtons

  2. 2

    What does balanced mean?

    Show answerHide answer

    Equal and opposite

  3. 3

    Is force a vector?

    Show answerHide answer

    Yes

  4. 4

    What does a resultant force of zero mean for motion?

    Show answerHide answer

    No change in velocity

  5. 5

    Add 40 N and 15 N.

    Show answerHide answer

    55 N

Learning Objectives

  1. 1Define a resultant force.
  2. 2Calculate the resultant of two forces acting in a straight line.
  3. 3Describe the forces on an isolated object using a free body diagram (Higher tier).
  4. 4Use scale drawings to find the resultant of two forces, and resolve a force into components (Higher tier).

RESULTANT FORCE

A number of forces acting on an object may be replaced by a single force that has the same effect: the resultant force.

Forces in the same direction are added. Forces in opposite directions are subtracted. If the resultant is zero the forces are balanced.

Forces in a Straight Line

A car's engine produces a driving force of 1800 N. Friction and air resistance give 1200 N in the opposite direction. Find the resultant force.

Show the solutionHide the solution
  1. 1 Opposite directions Subtract
  2. 2 Calculate \(1800 - 1200 = 600\) N

Answer600 N in the direction of the driving force.

Free Body Diagram (Higher)

Draw a free body diagram for a book at rest on a table.

Show the solutionHide the solution
  1. 1 Isolate the book Draw the book as a box on its own
  2. 2 Weight An arrow down from the centre of the box
  3. 3 Normal contact force An arrow up of equal length
  4. 4 Resultant Zero, so the forces are balanced

AnswerEqual arrows up and down: the resultant force is zero, so the book stays at rest.

Scale Drawing (Higher)

Two forces of 3.0 N (east) and 4.0 N (north) act on an object. Find the resultant using a scale drawing.

Show the solutionHide the solution
  1. 1 Scale 1 cm = 1 N
  2. 2 Draw 3 cm east, then 4 cm north from the end of the first arrow
  3. 3 Join start to finish The arrow is 5.0 cm
  4. 4 Direction Measure the angle: about \(53^\circ\) north of east

AnswerResultant 5.0 N at about 53° north of east.

Resolving a Force (Higher)

A force of 10 N acts at 30° above the horizontal. Find the horizontal and vertical components using a scale drawing.

Show the solutionHide the solution
  1. 1 Scale 1 cm = 1 N
  2. 2 Draw A 10 cm line at 30° to a horizontal line
  3. 3 Drop a perpendicular Make a right-angled triangle
  4. 4 Measure Horizontal about 8.7 cm and vertical 5.0 cm

AnswerComponents: about 8.7 N horizontally and 5.0 N vertically.

Key Points

Remember in an exam.

  • Direction

    Give the direction of the resultant.

  • Balanced

    Zero resultant means constant velocity (Newton's first law).

  • Free body diagram

    Show only the forces on the object, as arrows from its centre.

  • Units

    Forces in newtons.

Find the Resultant

Find the resultant force: (a) 50 N right and 20 N left (b) 30 N up and 30 N down (c) 12 N right and 8 N right.

1. Same direction: add.

2. Opposite: subtract.

A good answer shows: (a) 30 N right (b) 0 N (c) 20 N right.

Can I...?

  1. 1Define a resultant.
  2. 2Add forces in the same direction.
  3. 3Subtract opposite forces.
  4. 4Recognise balanced forces.
  5. 5Draw a free body diagram.
  6. 6Use a scale drawing.
  7. 7Resolve a force.
  8. 8Give direction.

Summary & Exam Focus

  • Resultant: same direction add, opposite subtract.
  • Zero resultant: balanced.
  • Higher: free body diagrams and scale drawings.
  • Resolve into perpendicular components.

Exam focus

A driving force of 1800 N and a resistive force of 1200 N act on a car. Calculate the resultant force. (2 marks) (2 marks)

Subtract the smaller from the larger and give the direction.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Resultant force
A single force with the same effect as all the forces on an object.
Balanced forces
Forces that are equal and opposite.
Free body diagram
A diagram showing all forces acting on an isolated object.
Component
One of two perpendicular forces that together have the same effect as one force.
Resolve
Split a force into two components at right angles.
Equilibrium
When the forces on an object are balanced.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 2 marks

    A car engine produces a driving force of 1800 N. The total resistive force is 1200 N. Calculate the resultant force on the car and state its direction.

    Show answerHide answer

    Model answer

    \(1800 - 1200 = 600\) N in the direction of the driving force (forwards).

    Mark scheme

    • 600 N — 1 mark
    • In the direction of the driving force — 1 mark
  2. Question 2 Use the diagram 2 marks

    The diagram shows the forces acting on a box. Calculate the resultant force.

    A box with a 40 N force to the right and a 15 N force to the left.
    Show answerHide answer

    Model answer

    \(40 - 15 = 25\) N to the right.

    Mark scheme

    • Subtracts 15 from 40 — 1 mark
    • 25 N to the right — 1 mark
  3. Question 3 Explain 2 marks

    A skydiver has a weight of 800 N and air resistance of 500 N. Calculate the resultant force and state its direction.

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    Model answer

    \(800 - 500 = 300\) N downwards.

    Mark scheme

    • 300 N — 1 mark
    • Downwards — 1 mark
  4. Question 4 Draw 3 marks

    Draw a free body diagram for a stationary book on a table. Label the forces.

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    Model answer

    A box with a downward arrow labelled weight and an upward arrow labelled normal contact force, of equal length.

    Mark scheme

    • Downward arrow labelled weight — 1 mark
    • Upward arrow labelled normal contact force — 1 mark
    • Arrows equal in length — 1 mark
  5. Question 5 Determine 4 marks

    Two forces act on an object at right angles to each other: 3.0 N east and 4.0 N north. Use a scale drawing to find the magnitude and direction of the resultant force.

    Show answerHide answer

    Model answer

    A scale drawing (for example 1 cm = 1 N) gives a resultant of 5.0 N at about 53° north of east (accept 51° to 55°).

    Mark scheme

    • Correct scale chosen — 1 mark
    • Right-angled triangle drawn accurately — 1 mark
    • 5.0 N — 1 mark
    • Direction about 53° north of east — 1 mark

Quick check

  1. Forces of 10 N and 6 N in opposite directions give a resultant of...

    1. A16 N
    2. B60 N
    3. C0 N
    4. D4 N
    Show answerHide answer

    D: 4 N

    Subtract.

  2. Balanced forces have a resultant of...

    1. Azero
    2. Bthe largest force
    3. Cthe sum of forces
    4. D10 N
    Show answerHide answer

    A: zero

    Equal and opposite.

  3. Two forces of 5 N in the same direction give...

    1. A0 N
    2. B10 N
    3. C25 N
    4. D5 N
    Show answerHide answer

    B: 10 N

    Add.

  4. A free body diagram shows...

    1. Aonly the weight
    2. Bvelocity only
    3. Call forces on one object
    4. Denergy changes
    Show answerHide answer

    C: all forces on one object

    It isolates the object.

  5. Resolving a force means...

    1. Adoubling it
    2. Bremoving it
    3. Cmaking it a scalar
    4. Dsplitting it into two perpendicular components
    Show answerHide answer

    D: splitting it into two perpendicular components

    The components have the same effect.

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