Understanding Spring Constant: 8.0kg Stone Compression

[JFlash]

The first part of this problem says that a 8.0kg stone rests on top of a spring, and compresses it by 10.0cm. It then asks what the spring constant is. This is the work I did (assuming g = 10m/s^2, not 9.8m/s^2):

(8.0kg)(10m/s^2) = 1/2k(10cm)^2; 80N = 50cm; k = 1.6

But, the textbook says the answer is .8. I don't understand why it's half my answer. Any help would be greatly appreciated.

 

[CompuChip]

On the left hand side, you have the gravitational force,
$$F_g = m g$$
On the left hand side, you have the spring potential energy,
$$W_s = \frac12 k x^2$$
Try taking the force exerted by the spring as well
$$F_s = k x$$

Actually, you could have noticed this mistake by looking at the units... you wrote down 80N = 50cm. Even if you meant
80 N = 50 cm^2 * k (N/cm)
you would have equated N to N cm.
Try to train yourself in spotting these mistakes: unless you know how to convert Newtons into Newtons times centimeters, an alarm bell should go off automatically.