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As an experienced tutor registered on UrbanPro, I'd approach this problem systematically. UrbanPro is an excellent platform for online coaching and tuition, offering personalized assistance to students.
Firstly, let's understand the concept at play here. The elongation of a wire under a load can be calculated using Hooke's Law, which states that the elongation (change in length) of an elastic object is directly proportional to the force applied to it, given the formula:
Elongation=Force×LengthYoung’s modulus×AreaElongation=Young’s modulus×AreaForce×Length
Given that the wires are under tension and assuming they remain within their elastic limits, we can use this formula to find their elongations. The area of the wire can be calculated using the formula for the area of a circle (πr2πr2).
Let's start with the steel wire:
Given:
We need to find the force applied to the steel wire. Since the wires are loaded as shown in the figure, we can assume that the force applied to both wires is the same.
Next, let's find the area of the steel wire (AsteelAsteel):
Asteel=π×(0.00252)2Asteel=π×(20.0025)2
Now, let's find the force applied to the steel wire. Since the force is the same for both wires, we can calculate it using the elongation formula for the brass wire:
Force=Young’s modulus×Area×ElongationLengthForce=LengthYoung’s modulus×Area×Elongation
Given:
Let's find the area of the brass wire (AbrassAbrass) using the same formula as for the steel wire:
Abrass=π×(0.00252)2Abrass=π×(20.0025)2
Now, we can find the force applied to both wires using the elongation formula for the brass wire:
Force=Young’s modulus×Area×ElongationLengthForce=LengthYoung’s modulus×Area×Elongation
Elongationbrass=Force×LengthYoung’s modulusbrass×AreabrassElongationbrass=Young’s modulusbrass×AreabrassForce×Length
Now, we have all the necessary information to calculate the elongations of both the steel and brass wires. Let's plug in the values and solve for the elongations.
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