Studying the elongation of the spring: the elongation of the spring is related to the weight of the object hanging by the spring dynamometer, and the length of the spring is related to the hanging object. A spring dynamometer is used to hang a heavy object and a spring does not hang a heavy object. The length is different, and it is in a free state without hanging heavy objects.

The spring will stretch after being hung on an object. The relationship between the length of a spring (cm) and the weight of the hung object (kg) is as follows:

(1) Because the data in the table mainly relates to the length of the spring and the weight of the hanging object, it reflects the relationship between the mass of the hanging object and the length of the spring. The mass of the hanging object is the independent variable; the length of the spring Is the dependent variable;

(2) It can be seen from the table that when the mass of the object is 2kg, the length of the extension spring is 13cm;

(3) According to the data in the table, the length of the spring increases with the weight of the hanging object;

(4) According to the data in the table, when x=0, y=12, and every additional kilogram of weight increases the length by 0.5cm, so y=0.5x+12;

(5) If the mass of the object x=2.5, substituting into the functional analytical formula, it can be solved when x=2.5, y=12+0.5×2.5=13.75cm.

From the above analysis, the spring elongation has a linear relationship with the weight of the object suspended by the spring dynamometer.