A force of 15 N acts on the spring, under the action of which it is lengthened by 3 cm.

A force of 15 N acts on the spring, under the action of which it is lengthened by 3 cm. How much will the spring lengthen if a force of 25 N acts on it? What is the force acting on the spring if it is lengthened by 4 cm?

The solution of the problem:
1. Let’s find the stiffness of the spring by the formula
k = F / x, where F is the force acting on the spring, x is the elongation of the spring.
k = 15 H / 0.03 m = 500 H / m.
2. The stiffness of the spring remains unchanged. From the formula of paragraph 1, we express the elongation:
x = F / k;
x = 25 H / 500 H / m = 0.05 m = 5 cm.
3. Let us express the effective force:
F = k * x;
F = 500 H / m * 0.04 m = 20 H.
Answer: 1. Under the action of a force of 25 N, the spring will lengthen by 5 cm.
2. The spring will lengthen by 4 cm with a force of 20 N.