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| 183_notes:examples:statics [2016/03/18 16:36] – klinkos1 | 183_notes:examples:statics [2016/03/25 15:58] (current) – klinkos1 | ||
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| ====== Example: Statics====== | ====== Example: Statics====== | ||
| - | {{ 183_projects:screen_shot_2016-03-18_at_11.15.44_am.png | + | {{183_notes:examples: |
| - | + | If a sign were hung like the one above, what would be the tension forces acting on both of the ropes? | |
| - | If a sign were hung like the one above, what would the tension forces acting on both of the ropes? | + | |
| ==== Setup ==== | ==== Setup ==== | ||
| - | To solve for the force of tension in both rope 1 and 2, both forces have to broken down into their x and y components and then solve the resulting system of equations. | + | To solve for the force of tension in both rope 1 and 2, both forces have to broken down into their x and y components, and then solve the resulting system of equations. |
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| *Gravity works in the negative y direction, with $g=9.81m/ | *Gravity works in the negative y direction, with $g=9.81m/ | ||
| *There are two forces of tension, on for rope 1, and one for rope 2 | *There are two forces of tension, on for rope 1, and one for rope 2 | ||
| - | *Mass of the object? | + | |
| - | *Angles of the ropes? | + | |
| | | ||
| === Lacking === | === Lacking === | ||
| - | *Either | + | *The force of tension |
| + | *Mass of the object | ||
| + | *Angles of the ropes | ||
| === Approximations & Assumptions === | === Approximations & Assumptions === | ||
| *The lengths of the two ropes is irrelevant, only the angle matters to solve for the two forces | *The lengths of the two ropes is irrelevant, only the angle matters to solve for the two forces | ||
| - | *The net force is zero since the system is stationary | + | *The net force is zero, since the system is stationary |
| === Representations === | === Representations === | ||
| - | *I have a drawing but I'm having a hard time adding pictures | + | {{183_notes: |
| ==== Solution ==== | ==== Solution ==== | ||
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| For rope one, $$T_{1,y} = T_{1}\cos{\alpha}$$ | For rope one, $$T_{1,y} = T_{1}\cos{\alpha}$$ | ||
| For rope 2, $$T_{2,y} = T_{2}\cos{\beta}.$$ | For rope 2, $$T_{2,y} = T_{2}\cos{\beta}.$$ | ||
| - | When finding the net force in the y direction, we cannot forget our assumption that gravity also works in the dimension | + | When finding the net force in the y direction, we cannot forget our assumption that gravity also works in the y direction but in the opposite direction as our tension forces. The net force in the y direction is, |
| $$\sum F_{y} = T_{1}\cos{\alpha}+T_{2}\cos{\beta}-Mg = 0.$$ | $$\sum F_{y} = T_{1}\cos{\alpha}+T_{2}\cos{\beta}-Mg = 0.$$ | ||
| Now we have two unknowns (the tension of the two ropes) and two equations, so we can solve this as a system of equations. | Now we have two unknowns (the tension of the two ropes) and two equations, so we can solve this as a system of equations. | ||
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| Now we have solutions for both tension forces, $T_{1}$ and $T_{2}$ | Now we have solutions for both tension forces, $T_{1}$ and $T_{2}$ | ||
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