A 6 cm long spring extends to 9 cm when a 1 kg load is suspended from it. What would be its length if a 2 kg load were suspended from it?

Respuesta :

Answer:

12 cm

Step-by-step explanation:

To calculate the length of a spring with a 2 kg load, compare the displacement of a 1 kg load and adjust accordingly.

When a 1 kg load is suspended from the spring, the spring which is 6 cm stretches to 9 cm. This is 3 cm longer due to the weight. If you attach a weight which is twice as much then the displacement will be twice as much. Instead of stretching an additional 3 cm, it will stretch 2*3 = 6 cm. Add this to the length of the spring and it stretches in total 6 + 6 = 12 cm.

When we use a mass of 2 kg, the length of the spring will be 12 cm.

What would be the spring length if we use a 2kg load?

The extension of the spring is proportional to the mass we attach to it, so if when we attach a mass of 1kg, the spring extends from 6 cm to 9 cm, so it extends:

9cm - 6cm = 3cm

This means that for each kilogram that we add, the spring will extend 3cm.

Then if we add a mass of 2 kg, the spring will extend 2 times 3 cm, or:

2*3cm = 6cm.

And the natural length of the spring is 6cm, then after the extension, the length will be:

6cm + 6cm = 12cm.

If you want to learn more about springs, you can read:

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