Equilibrium & the Second Law

 

 
 A 100 kg block (w = 980 N), when suspended from a single cable, causes the tension in the cable to be 980 N. What are tensions when supported by two cables (as shown)?

Let the grreen arrow represent a vector pointing 20 degrees above horizontal. This vector can be resolved into two components. TGx = TG cos 20; and TGy = TG sin 20.

Similarly, the purple vector, which makes an angle of 40 degrees with the horizontal, can be resolved into two parts:
TPy = TP sin 40 and TPx = TP cos 40.

 Horizontally  Vertically
 TGx =TPx  TGy = TPy
 TG cos 20 = TP cos 40   TG sin 20. + TP sin 40 = mg
   

  
 
Note 1 The reader may be surprised to learn that the tension on each cable is such a large number. That is because the cables, besides supporting the load, are also pulling against each other. The interested student should calculate these components.  Note 2. See the equation three lines above. As the measure of the angles with the horizontal get smaller, so do the sines of those angles. If an equation where the RHS is is fixed, if the sines decrease, the tensions must increase. This is what makes a tight rope tight.