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Usually I have been dealing with equilibrium that shows 2 hinges pulling a cable with a pulley in between, meaning that the hinges are at the same height and there will be same tension for both sides of the cable.

However, if I were to move one of the hinge upwards, how will I then calculate the tension of the cable ( 2.5m cable) ? Imagine that the right side hinge is moved up by 0.3m, my pulley will slide to the left.

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  • $\begingroup$ Can you include a diagram? $\endgroup$
    – Protein
    Commented Aug 7, 2020 at 4:19
  • $\begingroup$ @Protein done. how do I get x and tension in the cable? $\endgroup$
    – matrices and shit
    Commented Aug 7, 2020 at 4:31
  • $\begingroup$ Draw a triangle of forces and a congruent triangle showing the geometry of the system noting that $A $\endgroup$
    – Farcher
    Commented Aug 7, 2020 at 6:22
  • $\begingroup$ As each length was initially equal so assume equal increase and decrease in lengths and apply pythagoras theorum to find x $\endgroup$
    – imposter
    Commented Aug 7, 2020 at 7:19

2 Answers 2

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The answer is very simple so my answer is short. Apply horizontal and vertical equilibrium

Now as the tension forces are different , take the vertical component of tension and balance it with mg. For horizontal equilibrium balance the horizontal component of tension and solve the equation

Use the dimensions to calculate angle that the strings make with vertical.

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Tension would be the same no matter wether it is levelled or at any height. Since the cable goes through and through, I suppose tension in the cable on both sides is same. Therefore the cables should be at equal angles to the horizontal in order for them to cancel out so that pulley is at equilibrium. Assume the angle to be @. Now let the length of cable on left and right sides are A and B. Then, Acos @ + B cos @= 1.5(distance between hinges) (A+B)cos @ =1.5 cos @= 1.5/2.5=3/5 sin@=4/5 Now balance the tension component in vertical direction with weight of pulley. 2Tsin@=25g T=125g/8

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  • $\begingroup$ Please note that this angle@ is independent of the height difference between the hinges and is characteristic of the length of cable and the horizontal separation between the hinges. Hence the tension too depends only on these two factors. $\endgroup$
    – Prakhar Pratap Mall
    Commented Aug 7, 2020 at 15:09
  • $\begingroup$ Please ignore my sloppy equation solving. $\endgroup$
    – Prakhar Pratap Mall
    Commented Aug 7, 2020 at 15:10
  • $\begingroup$ Please use MathJax , the angle @ really looks dirty infront of $\alpha$ $\endgroup$
    – Dorothea
    Commented Aug 14, 2020 at 16:35

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