13. Moment

Förberedande Mekanik

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Nuvarande version (1 mars 2010 kl. 14.10) (redigera) (ogör)
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Rad 9: Rad 9:
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Key Points
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== '''Key Points''' ==
The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.
The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.
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[[Image:T13.1.GIF]]
[[Image:T13.1.GIF]]
<math>\text{Moment }=Fd</math>
<math>\text{Moment }=Fd</math>
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[[Image:T13.2.GIF]]
[[Image:T13.2.GIF]]
Rad 24: Rad 21:
<math>\text{Moment }=Fd\sin \theta </math>
<math>\text{Moment }=Fd\sin \theta </math>
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Clockwise moments are negative.
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Clockwise moments are negative.
 
Anti-clockwise moments are positive.
Anti-clockwise moments are positive.
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Example 13.1
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'''[[Example 13.1]]'''
[[Image:ex13.1whole.GIF]]
[[Image:ex13.1whole.GIF]]
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'''[[Example 13.2]]'''
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[[Image:ex13.2.GIF]]
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Example 13.2
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'''[[Example 13.3]]'''
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[[Image:ex13.2.GIF]]
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Example 13.3
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For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.
For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.
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[[Image:ex13.3.GIF]]
[[Image:ex13.3.GIF]]
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Solution
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'''Solution'''
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Force Moment
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5N at O
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<math>5\times 0=0</math>
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8 N
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<math>-8\times 1.2=-9.6</math>
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7 N
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<math>7\times 0=0</math>
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6 N
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<math>-6\times 0.5=-3</math>
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5 N
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<math>5\times 1.2=6</math>
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4 N
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{| width="100%" cellspacing="10px" align="center"
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<math>4\times 0.5=2</math>
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|align="left"| Force
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| valign="top"|Moment (Nm)
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|-
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|5N at O
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| valign="top"| <math>5\times 0=0</math>
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|-
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|8 N
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|valign="top"| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math>
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|-
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|7 N
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| valign="top"| <math>7\times 0=0</math>
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|-
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|6 N
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| valign="top"| <math>-6\times 0\textrm{.}5=-3</math>
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|-
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|5 N
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| valign="top"| <math>5\times 1\textrm{.}2=6</math>
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|-
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|4 N
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| valign="top"| <math>4\times 0\textrm{.}5=2</math>
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|-
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|Total Moment
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| valign="top"| <math>0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm}</math>
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Total Moment
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|}
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<math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math>
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Nuvarande version

       Theory          Exercises      


Key Points

The moment of the force about the point O is the product of the force and the perpendicular distance to the line of action of the force from O.

Image:T13.1.GIF

\displaystyle \text{Moment }=Fd

Image:T13.2.GIF

\displaystyle \text{Moment }=Fd\sin \theta

Clockwise moments are negative.

Anti-clockwise moments are positive.


Example 13.1

Image:ex13.1whole.GIF


Example 13.2

Image:ex13.2.GIF


Example 13.3

For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.

Image:ex13.3.GIF

Solution

Force Moment (Nm)
5N at O \displaystyle 5\times 0=0
8 N \displaystyle -8\times 1\textrm{.}2=-9\textrm{.}6
7 N \displaystyle 7\times 0=0
6 N \displaystyle -6\times 0\textrm{.}5=-3
5 N \displaystyle 5\times 1\textrm{.}2=6
4 N \displaystyle 4\times 0\textrm{.}5=2
Total Moment \displaystyle 0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm}
Den här artikeln är hämtad från http://wiki.sommarmatte.se/wikis/2010/forberedandemekanik/index.php/13._Moment