A train car is being pulled by two cables attached to the front of the car. Imagine it is being pulled straight east.

Cable 1 is acting at an angle of 11° north of east and cable 2 is acting at an angle of 14° South of east. (That is, cables 1 and 2 are 11° + 14° = 25° apart from each other ) .

The resultant of the tensile forces has a magnitude of 34 kN.

Find the magnitudes of the tensions in cables 1 and 2.  (Assume no side forces / loads from the rails, and other typical assumptions for this type of problem.)

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Solution:

Diagrammatically, we have the following problem to determine T₁ and T₂:

Since the resultant force is horizontal (i.e. to the East), both vector tensions T₁ and T₂ must add to give the resultant of 34 kN.  Hence we have;

Further, we can mark in the unknown angles of the triangle.

From this point we use the law of sines and set the slide rule for a simple solution.

Now sin155° does not appear on the rule, but it has the same numeric value as sin25° hence:

• Align C34 with S25
• Move the cursor to S11 and read C15.4
• Move the cursor to S14 and read C19.5

Hence the tension, T₁ in cable 1 is approximately 19.5 kN and the tension, T₂ in cable 2 is approximately 15.4 kN.