The spring stretches from 10cm to 22cm when a force of 4N is applied.if it obeys Hooke's law ,its total length in cm when a force of 6N is applied is?
According to Hooke's law, the force applied is directly proportional to the extension of the spring. Mathematically, this can be represented as:
F = kx
where F is the force applied, k is the spring constant, and x is the extension of the spring.
To find the spring constant, we can use the given information that the spring stretches from 10cm to 22cm when a force of 4N is applied. The extension of the spring is:
x = 22cm - 10cm = 12cm = 0.12m
The force applied is 4N, so we can rearrange the equation to solve for k:
k = F/x = 4N / 0.12m = 33.33 N/m
Now, we can determine the extension of the spring when a force of 6N is applied. Rearranging the equation, we have:
x = F/k = 6N / 33.33 N/m = 0.18m
To find the total length of the spring, we add the original length to the extension:
Total length = Original length + Extension
Total length = 10cm + 18cm = 28cm
Therefore, when a force of 6N is applied, the total length of the spring is 28cm.
To find the total length of the spring when a force of 6N is applied, we can use Hooke's law. Hooke's law states that the force applied to a spring is directly proportional to its extension.
The formula for Hooke's law is:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant,
x is the extension of the spring.
We can rearrange the formula to solve for x:
x = F / k
First, let's calculate the spring constant k using the given information:
The initial length of the spring is 10 cm when no force is applied, and it stretches to 22 cm when a force of 4N is applied.
The extension of the spring is 22 cm - 10 cm = 12 cm.
Using Hooke's law, we can calculate k as follows:
4N = k * 12 cm
k = 4N / 12 cm = 1/3 N/cm
Now, let's use this value of k to find the extension of the spring when a force of 6N is applied:
x = 6N / (1/3 N/cm)
x = 6N * (3N/cm)
x = 18 cm
Finally, we can calculate the total length of the spring when a force of 6N is applied by adding the extension to the initial length of the spring:
Total length = initial length + extension
Total length = 10 cm + 18 cm
Total length = 28 cm
Therefore, the total length of the spring when a force of 6N is applied is 28 cm.
To find the total length of the spring when a force of 6N is applied, we need to understand Hooke's law and the relationship between the force applied and the stretch of the spring.
Hooke's law states that the force applied to a spring is proportional to the displacement or stretch of the spring from its equilibrium position. Mathematically, it can be represented as:
F = kx
Where:
F is the force applied to the spring,
k is the spring constant,
x is the displacement or stretch of the spring.
Given that the spring stretches from 10cm to 22cm when a force of 4N is applied, we can use this information to solve for the spring constant, k.
10cm represents the equilibrium position (no force applied), so we can set x = 0, and F = 0 in Hooke's law equation. This gives us:
0 = k(10)
k = 0
Therefore, k = 0 for this particular spring.
Now, we can use the spring constant (k = 0) to find the total length of the spring when a force of 6N is applied.
Let's denote the total length of the spring as L.
According to Hooke's law:
F1 / x1 = F2 / x2
Where:
F1 is the force of 4N,
x1 is the stretch from the equilibrium position (10cm),
F2 is the force of 6N,
x2 is the stretch (unknown).
Substituting the values we know into the equation:
4 / 12 = 6 / x2
Simplifying the equation:
4x2 = 6 * 12
4x2 = 72
x2 = 72 / 4
x2 = 18
Therefore, when a force of 6N is applied, the spring stretches to 18cm.
To find the total length of the spring, we need to add the equilibrium position and the stretch:
Total length = Equilibrium position + Stretch
Total length = 10cm + 18cm
Total length = 28cm
Therefore, when a force of 6N is applied, the total length of the spring is 28cm.