Talking about the relationship between spring elongation and pulling force

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 hanging an object. The relationship between the length of a spring (cm) and the weight (kg) of the hanging object is known as the following table:

(1) The above table reflects the relationship between which variables, which is the independent variable and which is the dependent variable?

(2) When the weight of the object is 2kg, how does the length of the spring change?

(3) When the weight of an object gradually increases, how does the length of the spring change?

(4) If the weight of the object is xkg and the length of the spring is ycm, write the relationship between y and x according to the above table;

(5) When the weight of the object is 2.5kg, according to the relationship, there is no legend of heroes in the middle to find the length of the spring.

(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 quality 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 tension 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) Let x=2.5, substitute in the analytic formula of the function, and it can be solved. Spring manufacturer

Solution: (1) It reflects the relationship between the mass of Foshan ceramics and the length of the spring. The mass of the object is the independent variable; the length of the spring is the dependent variable;

(2) When the mass of the object is 2kg, the length of the spring is 13cm;

(3) When the mass of the object gradually increases, the length of the spring increases;

(4) According to the above table, the relationship between y and x is: y=12+0.5x;

(5) When x=2.5, y=12+0.5×2.5=13.75cm