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: 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 value.: If one [[force]] is acting in the opposite direction to another one of the [[force]]s is given a 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 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 [[Newton]]s [[force]] then the [[Resultant Force]] is the two values added together. F_R = (+2N) + (-4N) F_R = -2N upwards|} {| class="wikitable"|-|[[File:ForceNumberLineHorizontal.png|center|400px]]|-| style="height:20px; width:400px; text-align:center;" |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 [[Newton]]s [[force]] then the [[Resultant Force]] is the two values added together. F_R = (+3N) + (-2N) F_R = 1N to the right|} ===Examples=== {| class="wikitable"|-|[[File:UnbalancedForces1.png|center|150px]]|[[File:UnbalancedForces2.png|center|200px]]|[[File:UnbalancedForces3.png|center|200px]]|-| style="height:20px; width:200px; text-align:left;" |'''Choose which directions are positive.''' Up is positive. '''Calculate the [[Resultant Force]].''' There is 4[[Newton|N]] up and subtracting 7[[Newton|N]] down. F_R = (+4N) + (-7N) F_R = -3N up| style="height:20px; width:200px; text-align:left;" |'''Choose which directions are positive.''' Right is positive. '''Calculate the [[Resultant Force]].''' There is 4[[Newton|N]] left and 3[[Newton|N]] right. F_R = (+3N) + (-4N) F_R = -1N right| style="height:20px; width:200px; text-align:left;" |'''Choose which directions are positive.''' Up is positive. Right is positive. '''Calculate the [[Resultant Force]].''' There is 6[[Newton|N]] up and 6[[Newton|N]] down. F_Vertical = (+6N) + (-6N) F_Vertical = 0N up There is 6[[Newton|N]] left and 4[[Newton|N]] right. F_Horizontal = (+4N) + (-6N) F_Horizontal = -2N right|} ==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 subtracted from the other.: When [[force]]s are at [[Right Angle|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=== {| class="wikitable"|-|[[File:ResultantForce1.png|center|300px]]| style="height:20px; width:300px; text-align:center;" |'''Choose which directions are positive.''' Up is positive. '''Calculate the [[Resultant Force]]''' There is 29N up and 37N down. F_R = (+29N) + (-37N) F_R = -8N upwards|}  {| class="wikitable"|-|[[File:ResultantForce2.png|center|300px]]| style="height:20px; width:300px; text-align:center;" |'''Choose which directions are positive.''' Right is positive. '''Calculate the [[Resultant Force]]''' There is 114N right and 105N left. F_R = (+114N) + (-105N) F_R = 9N right|} {| class="wikitable"|-|[[File:ResultantForce3.png|center|300px]]| style="height:20px; width:300px; text-align:center;" |'''Choose which directions are positive.''' Right is positive.Up is positive. '''Calculate the [[Resultant Force]]''' There is 38N up and 38N down. F_R = (+38N) + (-38N) F_R = 0N upwards '''Calculate the [[Resultant Force]]''' There is 50N right and 40N left. F_R = (+50N) + (-40N) F_R = 10N right|} {| class="wikitable"|-|[[File:ResultantForce4.png|center|300px]]| style="height:20px; width:300px; text-align:center;" |'''Choose which directions are positive.''' Right is positive.Up is positive. '''Calculate the [[Resultant Force]]''' There is 22N up and 16N down. F_Vertical = (+22N) + (-16N) F_Vertical = 6N upwards '''Calculate the [[Resultant Force]]''' There is 26N right and 18N left. F_Horizontal = (+26N) + (-18N) F_Horizontal = 8N right Since there are two [[Resultant Force|resultant forces]] that are [[perpendicular]] they form a 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> <math>F_R = \sqrt{6^2 + 8^2}</math> <math>F_R = \sqrt{100}</math> <math>F_R = 10N</math> The [[angle]] from the [[horizontal]] can be found using Trigonometry. <math>\tan \theta = \frac{Opposite}{Adjacent}</math> <math>\tan \theta = \frac{6}{8}</math> <math>\theta = 36.9^\circ </math> up from horizontal |} ===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 '']