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Created page with "==Key Stage 4== ===Meaning=== A '''scale diagram''' is a method used to add vectors by drawing them as arrows whose length and direction are accurately drawn to represent..."
==Key Stage 4==
===Meaning===
A '''scale diagram''' is a method used to add [[vector]]s by drawing them as arrows whose length and direction are accurately drawn to represent the [[magnitude]] and direction of the [[vector]].
===About Scale Diagrams===
: '''Scale diagrams''' use a 'scale' to show how the units of the [[vector]] are represented by a single unit of length (cm or mm). For example 100N = 1cm, so an arrow of 5cm represents a [[force]] of 500N.
: '''Scale diagrams''' can be used to add [[force]]s, [[displacement]]s, [[velocity|velocities]] or [[acceleration]]s.
===Examples===
{| class="wikitable"
|-
|[[File:FreeBodyDiagram2.png|center|300px]]
|[[File:ScaleDiagram1.png|center|300px]]
|-
| style="height:100px; width:400px; text-align:left;" colspan= "2"|The two [[vector]] [[force]]s drawn to a 'scale' on a [[Scale Diagram]]. This scale is 1N = 1cm. The two [[force]]s can be added by placing the start of one [[vector]] [[force]] at the end of the other. This [[Scale Diagram]] shows that the two [[force]]s cancel one another out so the net [[force]] is zero.
|}
{| class="wikitable"
|-
|[[File:FreeBodyDiagram3.png|center|300px]]
|[[File:ScaleDiagram2.png|center|300px]]
|-
| style="height:100px; width:400px; text-align:left;" colspan= "2"|The two [[vector]] [[force]]s drawn to a 'scale' on a [[Scale Diagram]]. This scale is 1N = 1cm. The two [[force]]s can be added by placing the start of one [[vector]] [[force]] at the end of the other. This [[Scale Diagram]] shows that the two arrows add to make a length of 6.1cm, which represents 6.1N, in a direction of 35° down from the [[horizontal]].
|}
{| class="wikitable"
|-
|[[File:ResolvingVectors1.png|center|200px]]
|[[File:ResolvingVectors2.png|center|200px]]
|[[File:ResolvingVectors3.png|center|200px]]
|-
| style="height:100px; width:200px; text-align:left;"|A [[boat]] is being pulled by two separate tug boats attached by a cable. The tension in each cable is 5000N.
| style="height:100px; width:200px; text-align:left;"|The tug boats and cables are replaced by [[vector]] [[force]]s from the [[boat]].
| style="height:100px; width:200px; text-align:left;"|The two [[force]]s are redrawn in a a [[Scale Diagram]] with scale is 1000N = 1cm placing the start of one [[vector]] [[force]] at the end of the other.
|-
| style="height:100px; width:400px; text-align:left;" colspan= "3"|This [[Scale Diagram]] shows that the two arrows add to make a length of 9.4cm, which represents 9400N, in a direction of 90° from the [[North]] which is an [[East]]erly direction.
|}
===Meaning===
A '''scale diagram''' is a method used to add [[vector]]s by drawing them as arrows whose length and direction are accurately drawn to represent the [[magnitude]] and direction of the [[vector]].
===About Scale Diagrams===
: '''Scale diagrams''' use a 'scale' to show how the units of the [[vector]] are represented by a single unit of length (cm or mm). For example 100N = 1cm, so an arrow of 5cm represents a [[force]] of 500N.
: '''Scale diagrams''' can be used to add [[force]]s, [[displacement]]s, [[velocity|velocities]] or [[acceleration]]s.
===Examples===
{| class="wikitable"
|-
|[[File:FreeBodyDiagram2.png|center|300px]]
|[[File:ScaleDiagram1.png|center|300px]]
|-
| style="height:100px; width:400px; text-align:left;" colspan= "2"|The two [[vector]] [[force]]s drawn to a 'scale' on a [[Scale Diagram]]. This scale is 1N = 1cm. The two [[force]]s can be added by placing the start of one [[vector]] [[force]] at the end of the other. This [[Scale Diagram]] shows that the two [[force]]s cancel one another out so the net [[force]] is zero.
|}
{| class="wikitable"
|-
|[[File:FreeBodyDiagram3.png|center|300px]]
|[[File:ScaleDiagram2.png|center|300px]]
|-
| style="height:100px; width:400px; text-align:left;" colspan= "2"|The two [[vector]] [[force]]s drawn to a 'scale' on a [[Scale Diagram]]. This scale is 1N = 1cm. The two [[force]]s can be added by placing the start of one [[vector]] [[force]] at the end of the other. This [[Scale Diagram]] shows that the two arrows add to make a length of 6.1cm, which represents 6.1N, in a direction of 35° down from the [[horizontal]].
|}
{| class="wikitable"
|-
|[[File:ResolvingVectors1.png|center|200px]]
|[[File:ResolvingVectors2.png|center|200px]]
|[[File:ResolvingVectors3.png|center|200px]]
|-
| style="height:100px; width:200px; text-align:left;"|A [[boat]] is being pulled by two separate tug boats attached by a cable. The tension in each cable is 5000N.
| style="height:100px; width:200px; text-align:left;"|The tug boats and cables are replaced by [[vector]] [[force]]s from the [[boat]].
| style="height:100px; width:200px; text-align:left;"|The two [[force]]s are redrawn in a a [[Scale Diagram]] with scale is 1000N = 1cm placing the start of one [[vector]] [[force]] at the end of the other.
|-
| style="height:100px; width:400px; text-align:left;" colspan= "3"|This [[Scale Diagram]] shows that the two arrows add to make a length of 9.4cm, which represents 9400N, in a direction of 90° from the [[North]] which is an [[East]]erly direction.
|}