How much does a string stretch when under load?

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In summary, the question asks for the length of a 12 inch string made of a 10GPa modulus material when a 100 g mass is attached to one end. The initial length of the string is 12 inches and its diameter is 0.5 mm. Using the equations F=kx and k=(EA)/L, the final length can be calculated by solving for Lfinal in the equation F=(EA/Linitial)(Lfinal-LInitial). This method is recommended over using the final length in the equation.
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hm8
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Homework Statement


A 12 inch long string with a 0.5 mm diameter and is composed of a 10GPa modulus
material is fixed at one end and loaded by a 100 g mass at its other end. What is the length
of the string when it is under load? (Note that the length is necessarily greater than 12
inches.)

LInitial = 12 in = .305 m
A = ∏r2 = ∏(.00025)2 = 1.96 * 10-7 m^2
E = 10 N/m2
F= .1 * 9.8 = .98 N


Homework Equations



F=kx

k=(EA)/L


The Attempt at a Solution



Basically I'm just not sure which length to use for finding the spring constant k, the final or initial length?

So should be solving something like this for final length?

F=(EA/Lfinal)(Lfinal-LInitial)

or this:

F=(EA/Linitial)(Lfinal-LInitial)
 
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  • #2
hm8 said:

F=(EA/Linitial)(Lfinal-LInitial)
Use this one. But first correct your value for E you are way off in the number of zeroes after the '10'.
 

FAQ: How much does a string stretch when under load?

How does the material of the string affect its stretching?

The material of the string plays a significant role in its stretching behavior. Materials with higher elasticity, such as rubber, will stretch more than materials with lower elasticity, such as steel. The type and quality of the material will also impact how much the string can stretch before breaking.

What factors determine how much a string can stretch?

The amount a string can stretch is determined by several factors including the material, diameter, and length of the string. Other factors like temperature, tension, and surface conditions can also affect the stretching behavior of a string.

How does temperature affect the stretching of a string?

Temperature can impact the stretching behavior of a string in two main ways. Firstly, as temperature increases, the molecules in the string have more energy and vibrate more, causing the string to stretch more easily. Secondly, extreme temperatures can also affect the material properties of the string, making it more or less elastic.

Can a string stretch indefinitely?

No, a string cannot stretch indefinitely. All materials have a limit to how much they can stretch before they reach their breaking point. This point is determined by the properties of the material and the amount of force being applied to the string.

How can the stretching behavior of a string be measured and calculated?

The stretching behavior of a string can be measured and calculated using various methods such as strain gauges, extensometers, or tensile testing machines. These tools can measure the amount of strain (change in length) in a string when a known amount of force is applied, allowing for the calculation of the elastic modulus or Young's modulus of the string.

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