Hi how do I explain the ans is 4)?

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# Answer

The answer is 4. To make sense of this question, you can draw out free-body diagrams.

Keep in mind that when compressed, each spring exerts a force of F = kx outwards, where k is some constant. This outwards force is what keeps the weight on top from dropping down. Hence, kx = mg. But if the spring above is exerting a force equalled to the weight to the object above upwards, it is also exerting a force equalled to the weight of the object downwards. Hence, the weight below experiences the force of gravity as well as the force of the spring (equalling to the weight of the mass above), totally to double the weight of one of those masses.

Now consider 2 facts:

1. the compression of the spring is proportional to how much force it has to generate.

2. If there are two springs in place instead of one, the force on each spring will be halved, so the compression will also be halved.

Putting everything together, we see that only in (4), the force on the bottom two springs is double of the force on the spring above, but because they split the force into half, the compression on all the springs are the same.

To ensure that you have properly made sense of this question, draw the free body diagram for each scenario, and apply Newton’s laws to explain why the other 3 cases are wrong.

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