The force required to stretch a Hooke’s-law

spring varies from 0 N to 63.5 N as we stretch
the spring by moving one end 5.31 cm from
its unstressed position.
Find the force constant of the spring.
Answer in units of N/m

K = 63.5N/0.0531m = 1196N/m.

To find the force constant of the spring, we can 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.

Hooke's Law can be written as:

F = k * x

Where F is the force, k is the force constant (also known as the spring constant), and x is the displacement.

Given that the force varies from 0 N to 63.5 N and the displacement is 5.31 cm (which we'll convert to meters), we can substitute these values into the equation and solve for k.

Using the formula F = k * x:

63.5 N = k * 0.0531 m

Dividing both sides of the equation by 0.0531 m gives:

k = 63.5 N / 0.0531 m

Calculating:

k ≈ 1196.03 N/m

Therefore, the force constant of the spring is approximately 1196.03 N/m.

To find the force constant of the spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law can be expressed as:

F = k * x

Where:
F is the force applied to the spring
k is the force constant of the spring
x is the displacement of the spring from its equilibrium position

In this case, we are given that the force required to stretch the spring varies from 0 N to 63.5 N as we move one end 5.31 cm from its unstressed position.

Let's calculate the force constant (k) using the given information:

F = 63.5 N (maximum force required)
x = 5.31 cm (displacement)

We need to convert the displacement from cm to meters since the force constant should be in units of N/m:

x = 5.31 cm = 5.31 * 0.01 m = 0.0531 m

Now we can solve for k:

F = k * x
63.5 N = k * 0.0531 m

To find k, we can rearrange the equation:

k = F / x
k = 63.5 N / 0.0531 m

Evaluating the expression:

k ≈ 1197.5 N/m

Therefore, the force constant of the spring is approximately 1197.5 N/m.