If a force of 20N stretches a spring 15 cm, by what amount will the spring stretch is if a force of 80 N is applied?

60

To determine the amount by which the spring will stretch when a force of 80N is applied, we can use Hooke's Law, which states that the force exerted on a spring is proportional to the amount of stretch or compression.

Hooke's Law equation can be written as:

F = k ∆x

Where:
F is the force applied to the spring (in Newtons),
k is the spring constant (in N/m), and
∆x is the displacement or stretch of the spring (in meters).

We are given that a force of 20N stretches the spring 15 cm. To find the spring constant (k), we can rearrange the equation as follows:

k = F / ∆x

k = 20N / 0.15m (since 15 cm is equal to 0.15m)

k = 133.33 N/m

Now, we can use this spring constant to find the amount by which the spring will stretch when a force of 80N is applied.

∆x = F / k

∆x = 80N / 133.33 N/m

∆x ≈ 0.6 m

Therefore, the spring will stretch by approximately 0.6 meters when a force of 80N is applied.

To determine the amount by which the spring will stretch when a force of 80N is applied, 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.

Hooke's Law can be represented by the equation F = kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring.

First, we need to find the spring constant, which is a measure of the stiffness of the spring. The formula to find the spring constant is k = F / x, where F is the force applied and x is the corresponding displacement of the spring.

Given that a force of 20N stretches the spring by 15 cm, we can substitute these values into the formula:

k = 20 N / 0.15 m

Simplifying this calculation, we find that the spring constant is 133.33 N/m.

Now that we have the spring constant, we can use it to determine the displacement of the spring when a force of 80 N is applied. Rearranging the formula F = kx, we have x = F / k.

Substituting the values into the formula:

x = 80 N / 133.33 N/m

Calculating this, we find that the spring will stretch by approximately 0.6 meters (or 60 cm) when a force of 80N is applied.