a force of 125N is required to extend a spring by 2.8cm. what force is required to stretch the same spring by 3.2cm

To solve this problem, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement of the spring from its equilibrium position. Mathematically, it can be expressed as:

F = -kx

Where:
F is the force applied to the spring,
k is the spring constant, and
x is the displacement of the spring.

In this case, we are given the force and displacement for the first scenario:

Force (F1) = 125 N, and
Displacement (x1) = 2.8 cm = 0.028 m.

We can rearrange the equation to solve for the spring constant (k):

k = -F1 / x1

k = -125 N / 0.028 m
k = -4464.29 N/m (approximately)

Now, we can use the spring constant (k) to find the force required for the second scenario:

Displacement (x2) = 3.2 cm = 0.032 m.

Using Hooke's Law:

F2 = -k * x2

F2 = -(-4464.29 N/m) * 0.032 m
F2 ≈ 142.85 N

Therefore, a force of approximately 142.85 N is required to stretch the same spring by 3.2 cm.

thgbv