pls solve this problem using integration.. A Force of 25N is required to stretch a string from natural length of 12cm to 13cm. Find the Work done in stretching it from 13cn to 14cn. Thanks a lot :)
is it 0.375J? Am I correct.. pls correct me If Im wrong..
I don't get that. I will be happy to examine your work.
just go to this site below and compare it to my answer. Sorry I don't have time to show my solution because I am in a hurry. I will have an Exam tomorrow morning and I have a lot of topics that I need to study. just correct me if I'm wrong.. thanks
tutorial.math.
To solve this problem using integration, we first need to establish the relationship between force and displacement for stretching the string.
We know that work is defined as the product of force and displacement. Mathematically, it can be represented as:
Work (W) = ∫ F dx
Where F represents the force applied and dx represents the displacement.
Given that a force of 25N is needed to stretch the string from its natural length of 12cm to 13cm, we can calculate the work done. To do this, we need to integrate the force function over the displacement range from 12cm to 13cm. Let's denote the displacement as x.
∫ F dx = ∫ (25N) dx
To determine the limits of integration, we need to convert the units of displacement into the same unit as the limits. Since the force is given for a change in length of the string, we consider the displacement difference as:
Δx = (13cm) - (12cm) = 1cm
Now, we can rewrite the integral as:
W = ∫ (25N) dx
= ∫ 25 dx
To evaluate this integral, we integrate with respect to x using the constant of integration (C):
W = 25x + C
Since C is a constant and the limits of integration are from 12cm to 13cm, we can substitute these values into the expression for work done to find the specific value:
W = (25(13) + C) - (25(12) + C)
To find C, we subtract one equation from the other:
W = 325 + C - 300 - C
The constant C cancels out, leaving us with:
W = 25N
Therefore, the work done to stretch the string from 12cm to 13cm is 25N.
To find the work done in stretching the string from 13cm to 14cm, we use a similar process. The difference in displacement is:
Δx = (14cm) - (13cm) = 1cm
Integrating the force function over this displacement range yields:
W = ∫ (25N) dx
= ∫ 25 dx
= 25x + C
Since we're evaluating the limits from 13cm to 14cm, we have:
W = (25(14) + C) - (25(13) + C)
W = 350 + C - 325 - C
The constant C cancels out again, leaving us with:
W = 25N
Therefore, the work done to stretch the string from 13cm to 14cm is also 25N.