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===About Resultant Forces===
 
===About Resultant Forces===
 
: A '''resultant force''' can be calculated by taking [[force]]s that act along the same line and add them together.
 
: 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)|value]].
+
: 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 (Number)|negative]] value.
+
: If one [[force]] is acting in the opposite direction to another one of the [[force]]s is given a negative value.
  
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
 
|[[File:ForceNumberLineVertical.png|center|200px]]
 
|[[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.
+
| 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.
 
In this [[diagram]] the green [[vector]] has a value of +2 while the red [[vector]] has a value of -4.
Line 26: Line 26:
 
|[[File:ForceNumberLineHorizontal.png|center|400px]]
 
|[[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.
+
| 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.
 
In this [[diagram]] the blue [[vector]] has a value of +3 while the yellow [[vector]] has a value of -2.
Line 46: Line 46:
 
|-
 
|-
 
| style="height:20px; width:200px; text-align:left;" |
 
| style="height:20px; width:200px; text-align:left;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Up is [[Positive (Number)|positive]].
+
Up is positive.
  
 
'''Calculate the [[Resultant Force]].'''
 
'''Calculate the [[Resultant Force]].'''
  
−
There is 4[[N]] up and 7[[N]] down.
+
There is 4[[Newton|N]] up and 7[[Newton|N]] down.
  
 
F<sub>R</sub> = (+4N) + (-7N)
 
F<sub>R</sub> = (+4N) + (-7N)
Line 58: Line 58:
 
F<sub>R</sub> = -3N up
 
F<sub>R</sub> = -3N up
 
| style="height:20px; width:200px; text-align:left;" |
 
| style="height:20px; width:200px; text-align:left;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Right is [[Positive (Number)|positive]].
+
Right is positive.
  
 
'''Calculate the [[Resultant Force]].'''
 
'''Calculate the [[Resultant Force]].'''
  
−
There is 4[[N]] left and 3[[N]] right.
+
There is 4[[Newton|N]] left and 3[[Newton|N]] right.
  
 
F<sub>R</sub> = (+3N) + (-4N)
 
F<sub>R</sub> = (+3N) + (-4N)
Line 70: Line 70:
 
F<sub>R</sub> = -1N right
 
F<sub>R</sub> = -1N right
 
| style="height:20px; width:200px; text-align:left;" |
 
| style="height:20px; width:200px; text-align:left;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Up is [[Positive (Number)|positive]].
+
Up is positive.
  
−
Right is [[Positive (Number)|positive]].
+
Right is positive.
  
 
'''Calculate the [[Resultant Force]].'''
 
'''Calculate the [[Resultant Force]].'''
  
−
There is 6[[N]] up and 6[[N]] down.
+
There is 6[[Newton|N]] up and 6[[Newton|N]] down.
  
 
F<sub>Vertical</sub> = (+6N) + (-6N)
 
F<sub>Vertical</sub> = (+6N) + (-6N)
Line 84: Line 84:
 
F<sub>Vertical</sub> = 0N up
 
F<sub>Vertical</sub> = 0N up
  
−
There is 6[[N]] left and 4[[N]] right.
+
There is 6[[Newton|N]] left and 4[[Newton|N]] right.
  
 
F<sub>Horizontal</sub> = (+4N) + (-6N)
 
F<sub>Horizontal</sub> = (+4N) + (-6N)
Line 93: Line 93:
 
==Key Stage 4==
 
==Key Stage 4==
 
===Meaning===
 
===Meaning===
−
The '''resultant force''' is the [[sum]] of all [[force]]s acting on an [[object]].
+
The '''resultant force''' is the sum of all [[force]]s acting on an [[object]].
  
 
===About Resultant Forces===
 
===About Resultant Forces===
 
: When [[force]]s act in the same direction their [[magnitude]]s are added together.
 
: 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 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|Pythagoras' theorem]] to find the [[magnitude]] of the '''resultant force''' and then trigonometry can be used to find the direction of the '''resultant force'''.
+
: 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===
 
===Examples===
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|[[File:ResultantForce1.png|center|300px]]
 
|[[File:ResultantForce1.png|center|300px]]
 
| style="height:20px; width:300px; text-align:center;" |
 
| style="height:20px; width:300px; text-align:center;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Up is [[Positive (Number)|positive]].
+
Up is positive.
  
 
'''Calculate the [[Resultant Force]]'''
 
'''Calculate the [[Resultant Force]]'''
Line 124: Line 124:
 
|[[File:ResultantForce2.png|center|300px]]
 
|[[File:ResultantForce2.png|center|300px]]
 
| style="height:20px; width:300px; text-align:center;" |
 
| style="height:20px; width:300px; text-align:center;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Right is [[Positive (Number)|positive]].
+
Right is positive.
  
 
'''Calculate the [[Resultant Force]]'''
 
'''Calculate the [[Resultant Force]]'''
Line 141: Line 141:
 
|[[File:ResultantForce3.png|center|300px]]
 
|[[File:ResultantForce3.png|center|300px]]
 
| style="height:20px; width:300px; text-align:center;" |
 
| style="height:20px; width:300px; text-align:center;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Right is [[Positive (Number)|positive]].
+
Right is positive.
−
Up is [[Positive (Number)|positive]].
+
Up is positive.
  
 
'''Calculate the [[Resultant Force]]'''
 
'''Calculate the [[Resultant Force]]'''
Line 167: Line 167:
 
|[[File:ResultantForce4.png|center|300px]]
 
|[[File:ResultantForce4.png|center|300px]]
 
| style="height:20px; width:300px; text-align:center;" |
 
| style="height:20px; width:300px; text-align:center;" |
−
'''Choose which directions are [[Positive (Number)|positive]].'''
+
'''Choose which directions are positive.'''
  
−
Right is [[Positive (Number)|positive]].
+
Right is positive.
−
Up is [[Positive (Number)|positive]].
+
Up is positive.
  
 
'''Calculate the [[Resultant Force]]'''
 
'''Calculate the [[Resultant Force]]'''
Line 188: Line 188:
 
F<sub>Horizontal</sub> = 8N right
 
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]].
+
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}^2 = {F_V}^2 + {F_H}^2</math>
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|}
 
|}
 +
 +
===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 '']

Latest revision as of 18:23, 18 December 2019

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.
ForceNumberLineVertical.png
 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.

FR = (+2N) + (-4N)

FR = -2N upwards

ForceNumberLineHorizontal.png
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.

FR = (+3N) + (-2N)

FR = 1N to the right

Examples

UnbalancedForces1.png
UnbalancedForces2.png
UnbalancedForces3.png

Choose which directions are positive.

Up is positive.

Calculate the Resultant Force.

There is 4N up and 7N down.

FR = (+4N) + (-7N)

FR = -3N up

Choose which directions are positive.

Right is positive.

Calculate the Resultant Force.

There is 4N left and 3N right.

FR = (+3N) + (-4N)

FR = -1N right

Choose which directions are positive.

Up is positive.

Right is positive.

Calculate the Resultant Force.

There is 6N up and 6N down.

FVertical = (+6N) + (-6N)

FVertical = 0N up

There is 6N left and 4N right.

FHorizontal = (+4N) + (-6N)

FHorizontal = -2N right

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

ResultantForce1.png

Choose which directions are positive.

Up is positive.

Calculate the Resultant Force

There is 29N up and 37N down.

FR = (+29N) + (-37N)

FR = -8N upwards


ResultantForce2.png

Choose which directions are positive.

Right is positive.

Calculate the Resultant Force

There is 114N right and 105N left.

FR = (+114N) + (-105N)

FR = 9N right

ResultantForce3.png

Choose which directions are positive.

Right is positive. Up is positive.

Calculate the Resultant Force

There is 38N up and 38N down.

FR = (+38N) + (-38N)

FR = 0N upwards

Calculate the Resultant Force

There is 50N right and 40N left.

FR = (+50N) + (-40N)

FR = 10N right

ResultantForce4.png

Choose which directions are positive.

Right is positive. Up is positive.

Calculate the Resultant Force

There is 22N up and 16N down.

FVertical = (+22N) + (-16N)

FVertical = 6N upwards

Calculate the Resultant Force

There is 26N right and 18N left.

FHorizontal = (+26N) + (-18N)

FHorizontal = 8N right

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

OCR

Resultant forces, pages 163, 164, Gateway GCSE Combined Science; The Revision Guide, CGP, OCR
Resultant forces, pages 26-28, Gateway GCSE Physics; The Revision Guide, CGP, OCR
Resultant forces, pages 65-68, Gateway GCSE Physics, Oxford, OCR
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