A10-cm-long spring is attached to theceiling. when a 2.0 kg mass is hung from it, the spring stretches to a length of 15 cm. a.what is the spring constant k? b. how long is the spring when a 3.0kg mass is suspended from it?

(a) 392 N/m

Hook's law states that:

(1)

where

F is the force exerted on the spring

k is the spring constant

is the stretching/compression of the spring

In this problem:

- The force exerted on the spring is equal to the weight of the block attached to the spring:

- The stretching of the spring is

Solving eq.(1) for k, we find the spring constant:

(b) 17.5 cm

If a block of m = 3.0 kg is attached to the spring, the new force applied is

And so, the stretch of the spring is

And since the initial lenght of the spring is

The final length will be

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explanation: