Question:

A spring is stretched by a force of 20 N. When the spring is stretched by an additional 0.5 m, the force applied becomes 30 N. Using Hooke's law, determine the spring constant of the spring.

Answer:

We can use Hooke's law, which states that the force applied on a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, this can be expressed as:

F = -kx

where F is the force applied, k is the spring constant, and x is the displacement.

Given that when the force applied is 20 N, the displacement is 0 m, and when the force is increased to 30 N, the displacement becomes 0.5 m, we can set up two equations:

20 N = -k(0 m) (Equation 1) 30 N = -k(0.5 m) (Equation 2)

From Equation 1, we see that the displacement is zero, meaning the spring is in its equilibrium position. This implies that the force applied is equal to zero at this point. Therefore, we can conclude that the spring constant is also equal to zero.

Substituting the value of k as 0 into Equation 2, we get:

30 N = 0

This equation is not valid since it implies that 30 N is equal to 0, which is not possible. Therefore, we can conclude that the assumptions made in the given question are either incorrect or incomplete, as it is not possible to determine the spring constant using the provided information.

In a correct scenario, we would need additional data such as the original displacement when a specific force is applied or vice versa in order to calculate the spring constant.