# Resultant Force

## Contents

## Key Stage 3

### Meaning

The **Resultant Force** is the overall force on an object.

### About Resultant Forces

- A
**resultant force**can be calculated by taking forces that act along the same line and add them together. - If the forces are in the same direction as each other, then they have a positive value.
- If one force is acting in the opposite direction to another one of the forces is given a negative value.

If the 'up' direction is chosen to be positive then any vector pointing 'up' has a positive value and any vector pointing 'down' has a negative value.
In this diagram the green vector has a value of +2 while the red vector has a value of -4. If the number lines represent the number of Newtons force then the Resultant Force is the two values added together. F F |

If the 'right' direction is chosen to be positive then any vector pointing 'right' has a positive value and any vector pointing 'left' has a negative value.
In this diagram the blue vector has a value of +3 while the yellow vector has a value of -2. If the number lines represent the number of Newtons force then the Resultant Force is the two values added together. F F |

### Examples

Up is positive.
F F |
Right is positive.
There is 4N left and 3N right. F F |
Up is positive. Right is positive.
F F There is 6N left and 4N right. F F |

## Key Stage 4

### Meaning

The **resultant force** is the sum of all forces acting on an object.

### About Resultant Forces

- When forces act in the same direction their magnitudes are added together.
- When forces act along the same line but in opposite directions; one is subtracted from the other.
- When forces are at right angles to one another they can be added using Pythagoras' Theorem to find the magnitude of the
**resultant force**and then trigonometry can be used to find the direction of the**resultant force**.

### Examples

Up is positive.
There is 29N up and 37N down. F F |

Right is positive.
There is 114N right and 105N left. F F |

Right is positive. Up is positive.
There is 38N up and 38N down. F F
There is 50N right and 40N left. F F |

Right is positive. Up is positive.
There is 22N up and 16N down. F F
There is 26N right and 18N left. F F Since there are two resultant forces that are perpendicular they form a right angle triangle and their hypotenuse is the magnitude of the resultant force. This can be found using Pythagoras' Theorem. \({F_R}^2 = {F_V}^2 + {F_H}^2\) \(F_R = \sqrt{6^2 + 8^2}\) \(F_R = \sqrt{100}\) \(F_R = 10N\) The angle from the horizontal can be found using Trigonometry. \(\tan \theta = \frac{Opposite}{Adjacent}\) \(\tan \theta = \frac{6}{8}\) \(\theta = 36.9^\circ \) up from horizontal |

### References

#### AQA

*Resultant force, pages 155-8, GCSE Physics; Student Book, Collins, AQA**Resultant force, pages 205, 212, GCSE Combined Science; The Revision Guide, CGP, AQA**Resultant force, pages 53, 54, 64, 71, GCSE Physics; The Revision Guide, CGP, AQA**Resultant forces, page 131, 132, 162-165, GCSE Combined Science Trilogy; Physics, CGP, AQA**Resultant forces, pages 118-119, 144-145, 148-149, 168-169, GCSE Physics; Third Edition, Oxford University Press, AQA**Resultant forces, pages 120-1, GCSE Physics, Hodder, AQA**Resultant forces, pages 151, 152, 194-197, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA**Resultant forces, pages 210-11, GCSE Combined Science Trilogy 2, Hodder, AQA*

#### Edexcel

*Resultant forces, page 209, GCSE Physics, CGP, Edexcel**Resultant forces, pages 12-13, 134, GCSE Physics, Pearson Edexcel**Resultant forces, pages 181, 182, GCSE Combined Science; The Revision Guide, CGP, Edexcel**Resultant forces, pages 67, 68, GCSE Physics; The Revision Guide, CGP, Edexcel*