A force of 2N stretches an elastic material by 0.03m. What additional force will stretch the material by 0.03. Assume that the elastic limit is not exceeded.
F = k x
twice as far requires twice the force
2/0.03 = x/(0.03+0.03)
X = 4N.
4-2 = 2N. added.
To find the additional force required to stretch the material by 0.03m, we need to understand Hooke's Law, which states that the force required to stretch or compress a material is directly proportional to the extension or compression produced.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force applied to the material
k is the spring constant (a measure of the material's elasticity)
x is the extension or compression produced
In this case, we are given that a force of 2N stretches the material by 0.03m. So, we can set up the following equation using Hooke's Law:
2N = k * 0.03m
To find the value of k (spring constant), we can rearrange the equation:
k = 2N / 0.03m
k = 66.67 N/m (rounded to two decimal places)
Now, we can use Hooke's Law to find the additional force required to stretch the material by 0.03m:
F = k * x
F = 66.67 N/m * 0.03m
F ≈ 2 N
Therefore, the additional force required to stretch the material by 0.03m is approximately 2N.