Question

The force applied to a spring varies directly with the distance that the spring is stretched. When 30N of force is applied, the spring stretches 3m.

a) Write a variation model using k as the constant of variation.
b) Find the value of k.
c) How many meters will the spring stretch when a 5N force is applied?

Answer 1

The force applied to a spring varies directly with its extension, and the constant of variation k, or spring constant, can be calculated using the formula k = F / x. Given a force of 30N causing 3m extension, k is found to be 10 N/m. Subsequently, applying a 5N force will result in 0.5 meters of extension.

Step-by-step explanation:

The force applied to a spring is directly proportional to the distance it is stretched, according to Hooke's Law. This relationship can be described by the equation F = kx, where F is the force applied, x is the distance the spring is stretched, and k is the spring constant.

a) A variation model for the relationship between the force and the stretching of the spring can be written as F = kx.

b) Given that when 30N of force is applied the spring stretches 3m, we can find the spring constant (k) as follows:

k = F / x = 30N / 3m = 10 N/m.

c) To find out how much the spring will stretch when a 5N force is applied, we use the same equation:

x = F / k = 5N / 10 N/m = 0.5 m.

Therefore, when a 5N force is applied to the spring, it will stretch by 0.5 meters.