Strategies for solving static equilibrium problems

[F|234K]

i have found that static equilibrium questions (which require the sum of all forces and torques to be zero) are the most challenging to me.

i don't know why, maybe there are a lot of different type of static equilibrium questions (they always ask the same questions but with different situations...).

hence, i would really appreciate it if you guys will tell me some of ur "strategies" when it comes to doing these questions, or some cautious things people need to pay close attention to when doing them, or just some mental notes you made to yourself when you were trying to learn how to do them.

thanks in advance

 

[Davorak]

Well it has more then likely been told to you before but I will say it again, draw a freed body diagram. Draw arrows where the forces are. Then break these force arrows up into their x and y directions. Practice is also important as in anything else. Some things will not be obvious on first glance, but will seem so on your third or fourth time on the same type of problem.

 

[F|234K]

thanks.

ok, but then sometimes, there are those weird situations (like ladders) which are hard to analyse.

 

[Davorak]

$$\begin{picture}(100,100)(0,0)<br /> <br /> \put(0,0){\line(1,0){100}}<br /> \put(0,0){\line(0,1){100}}<br /> \put(0,75){\line(1,-1){75}}<br /> \put(40,5){{\bf b}}<br /> \end{picture}$$

b is the angle between the ladder and the ground. If a weight is place on the ladder like so:
$$\begin{picture}(100,100)(0,0)<br /> <br /> \put(0,0){\line(1,0){100}}<br /> \put(0,0){\line(0,1){100}}<br /> \put(0,75){\line(1,-1){75}}<br /> \put(37.5,37.5){\circle{5}}<br /> <br /> \put(37.5,37.5){\line(0,-1){20}}<br /> \put(37.5,17.5){\line(1,1){10}}<br /> \put(37.5,17.5){\line(-1,1){10}}<br /> \put(07.5,17.5){{\bf Fa}}<br /> <br /> \put(40,5){{\bf b}}<br /> \end{picture}$$

The wall can not provide any upward force so the upward force must be provided by the part of the ladder touching the ground so:?

$$\begin{picture}(100,100)(0,0)<br /> <br /> \put(0,0){\line(1,0){100}}<br /> \put(0,0){\line(0,1){100}}<br /> \put(0,75){\line(1,-1){75}}<br /> \put(37.5,37.5){\circle{5}}<br /> <br /> \put(37.5,37.5){\line(0,-1){20}}<br /> \put(37.5,17.5){\line(1,1){10}}<br /> \put(37.5,17.5){\line(-1,1){10}}<br /> \put(07.5,17.5){{\bf Fa}}<br /> <br /> \put(75.5,0){\line(0,11){20}}<br /> \put(75,20){\line(-1,-1){10}}<br /> \put(75,20){\line(1,-1){10}}<br /> \put(95,20){{\bf Fb}}<br /> <br /> \put(40,5){{\bf b}}<br /> \end{picture}$$

Fa therefore must equal Fb


Now to find the force on the wall.

$$\begin{picture}(100,100)(50,0)<br /> <br /> \put(50,0){\line(1,0){100}}<br /> \put(50,0){\line(0,1){100}}<br /> \put(50,75){\line(1,-1){75}}<br /> \put(87.5,37.5){\circle{5}}<br /> <br /> \put(87.5,37.5){\line(0,-1){20}}<br /> \put(87.5,17.5){\line(1,1){10}}<br /> \put(87.5,17.5){\line(-1,1){10}}<br /> \put(57.5,17.5){{\bf Fa}}<br /> <br /> \put(125.5,0){\line(0,1){20}}<br /> \put(125,20){\line(-1,-1){10}}<br /> \put(125,20){\line(1,-1){10}}<br /> \put(145,20){{\bf Fb}}<br /> <br /> \put(50,75){\line(-1,0){20}}<br /> \put(30,75){\line(1,1){10}}<br /> \put(30,75){\line(1,-1){10}}<br /> \put(30,55){{\bf Fc}}<br /> <br /> <br /> \put(90,5){{\bf b}}<br /> \end{picture}$$

The angle between the ladder and the force Fb is 90-b.
Now we can use the triangle made by Fb and Fc
Fb Tan(90-b) = Fa

 

[F|234K]

ok. thanks a lot.