Relationship of Young's modulus and impulse force

• Howard_SSS
In summary, the conversation discusses the possibility of obtaining a relationship between Young's modulus of a spring and impulse force with given information. The suggested equation is J/t = (EA/L)*(x), but it is noted that the cross-sectional area A is an essential value and cannot be omitted. It is mentioned that for a regular coiled spring, Young's modulus is more suitable and already incorporates the details of the spring structure, and can be expressed as Y=kL0.
Howard_SSS

Homework Statement

Is that possible to obtain the a relationship between Young's modulus of a spring and impulse force with below information ? I personally think that we cannot if without the given cross-sectional area A and the given spring constant k.

The particle is connect to a elastic spring, then an external impulse force horizontally was added to it.
(Smooth plate)

The given values are :

Particle mass ''m'', spring of modulus of elasticity ''E'', spring's natural length ''L'', received impulse ''J'', impulse reaction time ''t'', displacement ''x''

2. Homework Equations

The Attempt at a Solution

[/B]
F = kx => J/t = (EA/L) * (x)

Looks like the area is an essential value or we cannot express the equation for them.

Howard_SSS said:
E there is not Young's modulus of a spring. Young's modulus, often written as Y, is related to the spring constant k by Y=kL0.
Howard_SSS said:
F = kx => J/t
Not in this case. J=∫F.dt. You can only simplify that to J=Ft if F is constant.

haruspex said:
E there is not Young's modulus of a spring. Young's modulus, often written as Y, is related to the spring constant k by Y=kL0.

Not in this case. J=∫F.dt. You can only simplify that to J=Ft if F is constant.
Thanks for this reminding.

For Y=k*L0, may I know why you can remove the A (cross sectional area) ?

Howard_SSS said:
Thanks for this reminding.

For Y=k*L0, may I know why you can remove the A (cross sectional area) ?
EA, where E is the elastic modulus (not Young's modulus) is for a stretched wire. A regular coiled spring works by torsion, not by stretching of the material. Young's modulus is more suitable, and already incorporates the details of the spring structure. It is defined as the force per fractional change in spring length, so Y=kL0.

Howard_SSS

1. What is Young's modulus and how is it related to impulse force?

Young's modulus, also known as the modulus of elasticity, is a measure of a material's stiffness. It represents the amount of stress a material can withstand before it starts to deform. The relationship between Young's modulus and impulse force is that the modulus of elasticity determines how much a material will compress or elongate when a force is applied to it, which is directly related to the impulse force acting on the material.

2. How does the value of Young's modulus affect the impact of an impulse force?

A higher Young's modulus means that a material is stiffer and less likely to deform when an impulse force is applied. This means that the impact of the impulse force will be smaller and the material will experience less compression or elongation. On the other hand, a lower Young's modulus indicates a less stiff material that will undergo more deformation when an impulse force is applied.

3. Can Young's modulus be used to predict the effects of an impulse force on different materials?

Yes, Young's modulus is a useful tool for predicting how different materials will respond to an impulse force. By knowing the modulus of elasticity of a material, we can determine its stiffness and how much it will deform when a force is applied. This information can be used to select the appropriate material for a specific application and to estimate the impact of an impulse force on that material.

4. How is Young's modulus measured and what units is it expressed in?

Young's modulus is typically measured through tensile testing, where a material is subjected to a force and its deformation is recorded. The modulus of elasticity is calculated as the ratio of stress to strain. It is expressed in units of pressure, such as pascals (Pa) or megapascals (MPa), which represent force per unit area.

5. Are there any limitations to the relationship between Young's modulus and impulse force?

While Young's modulus is an important factor in understanding the response of materials to impulse forces, it is not the only factor that affects the magnitude of the impact. Other factors such as the shape, size, and composition of the material can also play a role. Additionally, the relationship between Young's modulus and impulse force may not hold true for materials that exhibit non-linear behavior under stress.

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