Today we considered a spring pulling a mass along the table. There is no friction. The free-body diagram looks like:
Since the acceleration has no vertical component, then n = mg.
The spring force Fs has magnitude ks, where s is the stretch of the spring. From Newton's second law:
ks = ma
k = ma/s
Now we put in the numbers:
k = (0.5 kg) (1 m/s2) /(1 cm)
= 50 kg· m/s2
= 50 N/m
Notice that the units are consistent with Hooke's law: F = ks. Also notice that since we worked with force magnitudes, we did not need any minus signs.