The stretch of the spring is proportional to the weight of the mass hung from it. Since the spring stretches by 5.9 cm when a 1.6 kg mass is hung from it, we can use this information to find the stretch when a 2.1 kg mass is hung from it.
The stretch of the spring is given by:
stretch = (mass x gravity x length) / (spring constant)
where mass is the mass hung from the spring, gravity is the acceleration due to gravity (9.81 m/s^2), length is the stretch of the spring, and the spring constant is a measure of the stiffness of the spring (measured in N/m).
We can rearrange this equation to solve for the stretch of the spring:
stretch = (mass x gravity x length) / (spring constant)
length = (spring constant x stretch) / (mass x gravity)
Substituting the given values, we get:
length = (spring constant x 0.059 m) / (1.6 kg x 9.81 m/s^2)
Simplifying, we get:
length = 0.236 m
Therefore, the stretch of the spring when a 2.1 kg mass is hung from it is 0.236 m.