Question

A force of 60 N is used to stretch two springs that are initially the same length. Spring A has a spring constant of 4 N/m, and spring B has a spring constant of 5 N/m. How do the lengths of the springs compare?

Answer 1

In order to compare the lengths of two springs with different spring constants, we can use Hooke's Law to find the displacements for each spring. By dividing the force by the spring constant, we can calculate the displacement and determine the length of each spring. Spring A is longer than spring B.

Step-by-step explanation:

In order to compare the lengths of the two springs A and B, we need to use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position. The equation for Hooke's Law is F = kx, where F is the force, k is the spring constant, and x is the displacement.

Using this equation, we can find the displacement for each spring by rearranging the equation to solve for x: x = F/k.

For spring A, with a force of 60 N and a spring constant of 4 N/m, the displacement is x = 60/4 = 15 m.

For spring B, with a force of 60 N and a spring constant of 5 N/m, the displacement is x = 60/5 = 12 m.

Therefore, the length of spring A is 15 m and the length of spring B is 12 m. Spring A is longer than spring B.

Answer 2

The length(extension in spring, x), force applied (F) and the spring constant(k) are related by the following equation:

F = kx

For spring 1:
60 = 4x
so,
x = 15 m

For spring 2:
50 = 5x
so,
x = 10m

Thus the extension in length of second spring will be 5 meters more than the first spring