A force of 3N stretches an elstics material by 40mm. What additional force will stretch the material 45mm? Assuming the elastic limit is not exceeded.
To find the additional force needed to stretch the material by 45mm, we can use the concept of proportionality between force and extension.
We can set up a proportion:
(Force1 / Extension1) = (Force2 / Extension2)
Using the given values, we have:
(3N / 40mm) = (Force2 / 45mm)
Cross-multiplying, we get:
3N * 45mm = Force2 * 40mm
Simplifying, we find:
Force2 = (3N * 45mm) / 40mm
Calculating, we get:
Force2 = 3.375N
Therefore, an additional force of 3.375N will stretch the material by 45mm.
To answer this question, we can use Hooke's Law, which states that the force needed to stretch or compress a spring or elastic material is directly proportional to the displacement.
The formula for Hooke's Law is:
F = k * x
F is the force applied, k is the spring constant, and x is the displacement.
Given that the force applied is 3N and the displacement is 40mm, we can calculate the spring constant using the formula:
k = F / x
k = 3N / 40mm
k = 0.075 N/mm
Now, we can use the spring constant to find the additional force required to stretch the material by 45mm:
F2 = k * x2
F2 = 0.075 N/mm * 45mm
F2 = 3.375 N
Therefore, an additional force of 3.375 N will stretch the elastic material by 45mm.