13. Moment
Förberedande Mekanik
(Skillnad mellan versioner)
(New page: __NOTOC__ {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | style="border-bottom:1px solid #797979" width="5px" | {{Selected tab|Theory}} {{No...) |
m (flyttade 13. Moments till 13. Moment) |
||
| (8 mellanliggande versioner visas inte.) | |||
| Rad 5: | Rad 5: | ||
{{Not selected tab|[[13. Exercises|Exercises]]}} | {{Not selected tab|[[13. Exercises|Exercises]]}} | ||
| style="border-bottom:1px solid #797979" width="100%"| | | style="border-bottom:1px solid #797979" width="100%"| | ||
| + | |} | ||
| + | |||
| + | |||
| + | |||
| + | == '''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]] | ||
| + | |||
| + | <math>\text{Moment }=Fd</math> | ||
| + | |||
| + | [[Image:T13.2.GIF]] | ||
| + | |||
| + | <math>\text{Moment }=Fd\sin \theta </math> | ||
| + | |||
| + | 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''' | ||
| + | |||
| + | {| width="100%" cellspacing="10px" align="center" | ||
| + | |align="left"| Force | ||
| + | | valign="top"|Moment (Nm) | ||
| + | |- | ||
| + | |5N at O | ||
| + | | valign="top"| <math>5\times 0=0</math> | ||
| + | |- | ||
| + | |8 N | ||
| + | |valign="top"| <math>-8\times 1\textrm{.}2=-9\textrm{.}6</math> | ||
| + | |- | ||
| + | |7 N | ||
| + | | valign="top"| <math>7\times 0=0</math> | ||
| + | |- | ||
| + | |6 N | ||
| + | | valign="top"| <math>-6\times 0\textrm{.}5=-3</math> | ||
| + | |- | ||
| + | |5 N | ||
| + | | valign="top"| <math>5\times 1\textrm{.}2=6</math> | ||
| + | |- | ||
| + | |4 N | ||
| + | | valign="top"| <math>4\times 0\textrm{.}5=2</math> | ||
| + | |- | ||
| + | |Total Moment | ||
| + | | valign="top"| <math>0-9\textrm{.}6+0-3+6+2=-4\textrm{.}6\text{ Nm}</math> | ||
| + | |||
|} | |} | ||
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.
\displaystyle \text{Moment }=Fd
\displaystyle \text{Moment }=Fd\sin \theta
Clockwise moments are negative.
Anti-clockwise moments are positive.
For the rectangular lamina shown below, find the total moment of the forces acting, about the corner marked O.
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} |
