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This is an example question from the book that I dont understand. (I have attached a photo of the problem).

The question says this : "A light spring, of natural length 1.6m and modulus of elasticity 40N, is attached to a floor at point A. The other end of the spring is attached to a block, C, of mass 2kg. The same block is attached to a second light spring, of natural length 1.2m and modulus of elasticity 25N, which is then attached to a ceiling at point B. Both springs are vertical. A and C are vertically below B. Given that AB is 4.5m, find the distance AC."

The part I dont understand is that why in the diagram and their solution, do they have T2 pointing downwards. If the bottom spring is compressed, wouldn't the tension T2 point upwards to balance the weight of the mass?

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  • $\begingroup$ From the diagram you have posted the bottom spring is being extended and not being compressed. As you can see the natural length of the bottom spring is 1.6 m and the extended length is 1.6m + x as shown in the diagram. $\endgroup$
    – Somanna
    Commented Mar 8, 2020 at 15:02

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The part I dont understand is that why in the diagram and their solution, do they have T2 pointing downwards. If the bottom spring is compressed, wouldn't the tension T2 point upwards to balance the weight of the mass?

The question states that the natural length of the bottom spring is $1.6m$. Since it is longer than this in the diagram, $(1.6 + x)$m, it is being stretched not compressed. Therefore the force due to the spring on the block, $T2$, is downwards.

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