If a force of 80N extends a spring of natural length 8m by 0.4m what will be the length of the spring when the applied force is 100N
F₁=kx₁
F₂=kx₂
F₁/F₂=x₁/x₂
x₂=x₁F₂/F₁=….
New length is L+ x₂=…
In order to determine the length of the spring when the applied force is 100N, you need to make use of Hooke's Law, which states that the extension of a spring is proportional to the applied force.
Hooke's Law equation is:
F = k * x
Where:
F is the applied force (in Newtons)
k is the spring constant (a measure of the stiffness of the spring)
x is the extension or compression of the spring (in meters)
To solve the problem, we first need to find the spring constant.
The spring constant can be calculated using the formula:
k = F / x
Given that the force is 80N and the extension is 0.4m, we can calculate the spring constant:
k = 80N / 0.4m = 200 N/m
Now, with the spring constant determined, we can use it to find the length of the spring when the applied force is 100N.
To find the extension when the force is 100N, we rearrange the equation:
F = k * x
Rearranging for x:
x = F / k
Substituting the values:
x = 100N / 200 N/m = 0.5m
The extension of the spring when the applied force is 100N is 0.5m.
To find the length of the spring, we add the extension to the natural length of the spring:
Length of the spring = Natural length + Extension
Length of the spring = 8m + 0.5m = 8.5m
Therefore, the length of the spring when the applied force is 100N will be 8.5m.