What is the Force Due to Extension for a Particle on an Elastic String?

In summary, the problem involves a particle attached to an elastic string of natural length a and modulus mg, which is fixed at one end and released from rest at a horizontal distance of a+L from the fixed point. The force due to the extension of the string can be calculated using the equation F = kL, where k is the spring constant. The answer given, mgx/a, is not reasonable as it does not include the amount of stretch, L, and contains g which is not relevant in this horizontal problem.
  • #1
osy044
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Homework Statement


A particle of mass m is attached to one end of a light elastic string of natural length a and modulus mg, the other end of the sting is attached to a fixed point O on smooth horizontal surface. The particle is released from rest at horizontal distance a+L from O.

calculate the force due to extension of string.


Homework Equations





The Attempt at a Solution


obviously one of the force will be 'mg' but force due to extension is hard to calculate. the answer for that one is mgx/a.
Also I am not sure if that modulus means young modulus
PLEASE help me
 
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  • #2
The spring is stretched distance L. The force due to the stretch is
F = kL, where k is the spring constant.

The mgx/a answer you quote is unreasonable because it does not contain the amount of stretch, L, and does contain g which is not involved in a purely horizontal problem.
 
  • #3
i thought so too. its seemingly unreasonable.
 

What is Young's modulus?

Young's modulus, also known as the modulus of elasticity, is a measure of a material's stiffness or resistance to deformation when a force is applied. It is defined as the ratio of stress (force per unit area) to strain (change in length per unit length) under elastic deformation.

How is Young's modulus calculated?

Young's modulus is calculated by dividing the stress by the strain. The stress is typically measured in units of pascals (Pa) or newtons per square meter (N/m^2), while the strain is a unitless quantity representing the change in length divided by the original length of the material.

What factors affect Young's modulus?

The Young's modulus of a material is affected by several factors, including the type of material, its microstructure, temperature, and strain rate. Generally, materials with stronger atomic bonds tend to have a higher Young's modulus.

Why is Young's modulus important?

Young's modulus is an important property to consider in engineering and material design. It helps determine the amount of force a material can withstand before it permanently deforms or breaks. It also helps in selecting the right material for a specific application based on its stiffness and strength.

How is Young's modulus used in real-world applications?

Young's modulus is used in various real-world applications, such as designing buildings, bridges, and other structures that can withstand certain loads. It is also used in the production of consumer products, such as cars and airplanes, to ensure their safety and structural integrity. It is also an important factor in the development of new materials for various industries.

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