Förberedande Mekanik

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Rad 15:		Rad 15:
-	[[Image:T13.GIF]]	+	[[Image:T13.1.GIF]]
-	<math>\text{Moment }=Fd</math> <math>\ \ \ \ \ \ \ \ \ \text{Moment }=Fd\sin \theta </math>	+	<math>\text{Moment }=Fd</math>
-	Clockwise moments are negative.	+	[[Image:T13.2.GIF]]
-	Anti-clockwise moments are positive.	+
		+	<math>\text{Moment }=Fd\sin \theta </math>
-	Example 11.1
-	Find the moment of each force shown below about the point O.
-
-	(a) (b)
		+	Clockwise moments are negative.
		+	Anti-clockwise moments are positive.
		+	Example 13.1
		+	[[Image:ex13.1whole.GIF]]
		+	Find the moment of each force shown below about the point O.
		+	[[Image:ex13.1.GIF]]
	Solution		Solution
-	(a) (b)	+
		+	(a)
	<math>20\times 0.8=16</math>		<math>20\times 0.8=16</math>
-
-	<math>12\times 1.2=14.4</math>
		+	Moment is -16 Nm
-	Moment is -16 Nm Moment is 14.4 Nm	+
		+	(b)
		+
		+	<math>12\times 1.2=14.4</math>
		+
		+	Moment is 14.4 Nm
		+
		+
	Example 13.2		Example 13.2
		+
		+	[[Image:ex13.2.GIF]]
		+
	Find the moment of each force shown below about the point O.		Find the moment of each force shown below about the point O.
	(a) (b)		(a) (b)

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Versionen från 17 september 2009 kl. 19.09

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 13.1

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

Solution

(a)

\displaystyle 20\times 0.8=16

Moment is -16 Nm

(b)

\displaystyle 12\times 1.2=14.4

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}