13. Moments

From Mechanics

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Key Points
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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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<math>\text{Moment }=Fd</math>
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<math>\text{Moment }=Fd\sin \theta </math>
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Clockwise moments are negative.
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Anti-clockwise moments are positive.
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Example 11.1
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Find the moment of each force shown below about the point O.
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(a) (b)
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Solution
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(a) (b)
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<math>20\times 0.8=16</math>
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<math>12\times 1.2=14.4</math>
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Moment is -16 Nm Moment is 14.4 Nm
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Example 13.2
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Find the moment of each force shown below about the point O.
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(a) (b)
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Solution
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(a) (b)
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<math>40\times 3\sin 60{}^\circ =104</math>
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<math>100\times 2\sin 20{}^\circ =68.4</math>
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Moment is 104 Nm (to 3 sf) Moment is 68.4 Nm (to 3 sf)
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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.
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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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<math>4\times 0.5=2</math>
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Total Moment
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<math>0-9.6+0-3+6+2=-4.6\text{ Nm}</math>

Revision as of 16:04, 17 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.






\displaystyle \text{Moment }=Fd

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


Clockwise moments are negative. Anti-clockwise moments are positive.


Example 11.1 Find the moment of each force shown below about the point O.

(a) (b)





Solution (a) (b)

\displaystyle 20\times 0.8=16

\displaystyle 12\times 1.2=14.4


Moment is -16 Nm Moment is 14.4 Nm

Example 13.2 Find the moment of each force shown below about the point O. (a) (b)




Solution (a) (b)






\displaystyle 40\times 3\sin 60{}^\circ =104

\displaystyle 100\times 2\sin 20{}^\circ =68.4


Moment is 104 Nm (to 3 sf) Moment is 68.4 Nm (to 3 sf)

Example 13.3 For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.






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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