(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