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Converted document STATIC EQUILIBRIUM EXAMPLES

STATIC EQUILIBRIUM EXAMPLES

Below there is a box that is hanging from two cables. From the picture, it can be inferred that this problem is in static equilibrium because it is not moving or rotating. In order for this to happen, the net forces and moments must equal zero. For simplification, this problem has no moments. Notice that T1 + T2 = mg; this is only true if this object is in static equilibrium. Now it has determined that the system is in static equilibrium, the tension of the two cables holding the box in equilibrium can be calculated.
figure images/1.png
Step 1: Break ALL forces into their x and y components as shown below
figure images/2.png
Step 2: Write down the equations of equilibrium
ΣFx = 0
 − T1sina + T2sinb
ΣFy = 0
T1cosa + T2cosb − mg = 0
Note that this gives two equations for the two unknowns, thus, this problem is ready to be solved.

Step 3: Solve for T1 or T2 from ΣFx = 0
T1 = (T2sinb)/(sina)

Step 4: Replace T1 found in step 3 and plug into ΣFy = 0
T1cosa + T2cosb − mg = 0
(T2sinb)/(sina)cosa + T2cosb = mg
T2 = (mg)/(X)

Step 5: Plug in T2 into the previously found T1.
Hint: Be sure to check the work and make sure nothing was left behind.