Spring Force: Difference between revisions
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==The Main Idea== | ==The Main Idea== | ||
The spring force is represented by the equation <math>\vert \vec{F} \vert = k_s \vert s \vert </math>, where <math> \vert s \vert </math> is the absolute value of the stretch of the spring <math>s = L - L_0</math>. | The spring force models the force in a system due to the presence of a stretched or compressed spring. This force is based upon two factors of the spring: the spring's stiffness and the distance the spring has been stretched. The spring's stiffness is a constant that represents how much force is required to stretch or compress a spring over a certain distance. | ||
===A Mathematical Model=== | |||
The magnitude of the spring force is represented by the equation <math>\vert \vec{F} \vert = k_s \vert s \vert </math>, where <math> \vert s \vert </math> is the absolute value of the stretch of the spring <math>s = L - L_0</math>. | |||
<math>L_0</math> is the relaxed length of the spring, when the spring is neither stretched nor compressed.<br /> | <math>L_0</math> is the relaxed length of the spring, when the spring is neither stretched nor compressed.<br /> | ||
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<math>k_s</math> is the spring stiffness, which is a constant inherent to the property of the spring. | <math>k_s</math> is the spring stiffness, which is a constant inherent to the property of the spring. | ||
This equation can also be represented in vector | |||
What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. | ||
Revision as of 20:22, 5 December 2015
Claimed by Arjun Chib
Spring Force is the non-constant, elastic force exerted by a spring upon a system.
The Main Idea
The spring force models the force in a system due to the presence of a stretched or compressed spring. This force is based upon two factors of the spring: the spring's stiffness and the distance the spring has been stretched. The spring's stiffness is a constant that represents how much force is required to stretch or compress a spring over a certain distance.
A Mathematical Model
The magnitude of the spring force is represented by the equation [math]\displaystyle{ \vert \vec{F} \vert = k_s \vert s \vert }[/math], where [math]\displaystyle{ \vert s \vert }[/math] is the absolute value of the stretch of the spring [math]\displaystyle{ s = L - L_0 }[/math].
[math]\displaystyle{ L_0 }[/math] is the relaxed length of the spring, when the spring is neither stretched nor compressed.
[math]\displaystyle{ L }[/math] is the length that the spring has been stretched or compressed.
[math]\displaystyle{ k_s }[/math] is the spring stiffness, which is a constant inherent to the property of the spring.
This equation can also be represented in vector
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
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