13. Moments

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Solution
Solution
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Force Moment
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{| width="100%" cellspacing="10px" align="center"
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5N at O
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|align="left"| Force
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<math>5\times 0=0</math>
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| valign="top"|Moment
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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 1.2=-9.6</math>
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|-
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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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|7 N
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<math>-6\times 0.5=-3</math>
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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 0.5=-3</math>
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|-
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|5 N
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| valign="top"| <math>5\times 1.2=6</math>
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|-
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|4 N
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| valign="top"| <math>4\times 0.5=2</math>
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|-
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|Total Moment
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| valign="top"| <math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math>
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5 N
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|}
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<math>5\times 1.2=6</math>
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4 N
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<math>4\times 0.5=2</math>
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-
 
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Total Moment
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<math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math>
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Revision as of 11:09, 18 September 2009

       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
5N at O \displaystyle 5\times 0=0
8 N \displaystyle -8\times 1.2=-9.6
7 N \displaystyle 7\times 0=0
6 N \displaystyle -6\times 0.5=-3
5 N \displaystyle 5\times 1.2=6
4 N \displaystyle 4\times 0.5=2
Total Moment \displaystyle 0-9.6+0-3+6+2=-4.6\text{ Nm}
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