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===About Resultant Forces===
: A '''resultant force''' can be calculated by taking [[force]]s that act along the same line and add them together.
: If the [[force]]s are in the same direction as each other, then they have a [[Positive (Number)|positive value]].: If one [[force]] is acting in the opposite direction to another one of the [[force]]s is given a [[Negative (Number)|negative]] value.
{| class="wikitable"
|-
|[[File:ForceNumberLineVertical.png|center|200px]]
| style="height:20px; width:300px; text-align:center;" |If the 'up' direction is chosen to be [[Positive (Number)|positive]] then any [[vector]] pointing 'up' has a [[Positive (Number)|positive]] value and any [[vector]] pointing 'down' has a [[Negative (Number)|negative]] value.
In this [[diagram]] the green [[vector]] has a value of +2 while the red [[vector]] has a value of -4.
|[[File:ForceNumberLineHorizontal.png|center|400px]]
|-
| style="height:20px; width:400px; text-align:center;" |If the 'right' direction is chosen to be [[Positive (Number)|positive]] then any [[vector]] pointing 'right' has a [[Positive (Number)|positive]] value and any [[vector]] pointing 'left' has a [[Negative (Number)|negative]] value.
In this [[diagram]] the blue [[vector]] has a value of +3 while the yellow [[vector]] has a value of -2.
|-
| style="height:20px; width:200px; text-align:left;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]].'''
There is 4[[Newton|N]] up and 7[[Newton|N]] down.
F<sub>R</sub> = (+4N) + (-7N)
F<sub>R</sub> = -3N up
| style="height:20px; width:200px; text-align:left;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]].'''
There is 4[[Newton|N]] left and 3[[Newton|N]] right.
F<sub>R</sub> = (+3N) + (-4N)
F<sub>R</sub> = -1N right
| style="height:20px; width:200px; text-align:left;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Up is [[Positive (Number)|positive]].
Right is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]].'''
There is 6[[Newton|N]] up and 6[[Newton|N]] down.
F<sub>Vertical</sub> = (+6N) + (-6N)
F<sub>Vertical</sub> = 0N up
There is 6[[Newton|N]] left and 4[[Newton|N]] right.
F<sub>Horizontal</sub> = (+4N) + (-6N)
==Key Stage 4==
===Meaning===
The '''resultant force''' is the [[sum]] of all [[force]]s acting on an [[object]].
===About Resultant Forces===
: When [[force]]s act in the same direction their [[magnitude]]s are added together.
: When [[force]]s act along the same line but in opposite directions; one is [[Subtraction|subtracted]] from the other.: When [[force]]s are at [[Right Angle|right angles]] to one another they can be added using [[Pythagoras' Theorem|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===
|[[File:ResultantForce1.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
|[[File:ResultantForce2.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
|[[File:ResultantForce3.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
|[[File:ResultantForce4.png|center|300px]]
| style="height:20px; width:300px; text-align:center;" |
'''Choose which directions are [[Positive (Number)|positive]].'''
Right is [[Positive (Number)|positive]].Up is [[Positive (Number)|positive]].
'''Calculate the [[Resultant Force]]'''
F<sub>Horizontal</sub> = 8N right
Since there are two [[Resultant Force|resultant forces]] that are [[perpendicular]] they form a [[Right Angle Triangle|right angle triangle]] and their [[hypotenuse]] is the [[magnitude]] of the [[Resultant Force|resultant force]]. This can be found using [[Pythagoras' Theorem]].
<math>{F_R}^2 = {F_V}^2 + {F_H}^2</math>
|}
===References===
====AQA====
:[https://www.amazon.co.uk/gp/product/0008158770/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0008158770&linkCode=as2&tag=nrjc-21&linkId=ec31595e720e1529e49876c3866fff6e ''Resultant force, pages 155-8, GCSE Physics; Student Book, Collins, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe10252 ''Resultant force, pages 205, 212, GCSE Combined Science; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/178294558X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=178294558X&linkCode=as2&tag=nrjc-21&linkId=f0dfb66dafcb0c6e9449e7b1a4ae1ac388 ''Resultant force, pages 53, 54, 64, 71, GCSE Physics; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782946403/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782946403&linkCode=as2&tag=nrjc-21&linkId=32a0abb60dff015b15b50e9b1d7b4644 ''Resultant forces, page 131, 132, 162-165, GCSE Combined Science Trilogy; Physics, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/019835939X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=019835939X&linkCode=as2&tag=nrjc-21&linkId=57e96876985fc39b1a3d8a3e3dc238b6 ''Resultant forces, pages 118-119, 144-145, 148-149, 168-169, GCSE Physics; Third Edition, Oxford University Press, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851370/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851370&linkCode=as2&tag=nrjc-21&linkId=01c69b0ae058f809cf636033e6ba793e ''Resultant forces, pages 120-1, GCSE Physics, Hodder, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Resultant forces, pages 151, 152, 194-197, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1471851362/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1471851362&linkCode=as2&tag=nrjc-21&linkId=7d78d70a2044ee9982dae010c94af92a ''Resultant forces, pages 210-11, GCSE Combined Science Trilogy 2, Hodder, AQA '']
====Edexcel====
:[https://www.amazon.co.uk/gp/product/1782948163/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782948163&linkCode=as2&tag=nrjc-21&linkId=0fdbfd5dd397d6e24a9dfb250f08587f ''Resultant forces, page 209, GCSE Physics, CGP, Edexcel '']
:[https://www.amazon.co.uk/gp/product/1292120223/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1292120223&linkCode=as2&tag=nrjc-21&linkId=068ecf40278c32406a7f1c6e66751417 ''Resultant forces, pages 12-13, 134, GCSE Physics, Pearson Edexcel '']
:[https://www.amazon.co.uk/gp/product/1782945741/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945741&linkCode=as2&tag=nrjc-21&linkId=30da4f2178da182547b62a7329d13b57 ''Resultant forces, pages 181, 182, GCSE Combined Science; The Revision Guide, CGP, Edexcel '']
:[https://www.amazon.co.uk/gp/product/1782945733/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945733&linkCode=as2&tag=nrjc-21&linkId=2a2dbec9db6bf5766c0458d908fa0a52 ''Resultant forces, pages 67, 68, GCSE Physics; The Revision Guide, CGP, Edexcel '']
====OCR====
:[https://www.amazon.co.uk/gp/product/1782945695/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945695&linkCode=as2&tag=nrjc-21&linkId=ceafcc80bcad6b6754ee97a0c7ceea53 ''Resultant forces, pages 163, 164, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR '']
:[https://www.amazon.co.uk/gp/product/1782945687/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945687&linkCode=as2&tag=nrjc-21&linkId=9a598e52189317a20311d7a632747bc9 ''Resultant forces, pages 26-28, Gateway GCSE Physics; The Revision Guide, CGP, OCR '']
:[https://www.amazon.co.uk/gp/product/0198359837/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=0198359837&linkCode=as2&tag=nrjc-21&linkId=3c4229e8b023b2b60768e7ea2307cc6f ''Resultant forces, pages 65-68, Gateway GCSE Physics, Oxford, OCR '']