Newton’s Second Law of Motion: Difference between revisions
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===A Mathematical Model=== | ===A Mathematical Model=== | ||
At the most basic level, Newton's Second Law of Motion states that force is equal to mass multiplied by acceleration, or '''F=ma'''. At face value, this means the force applied on an object is dependent on only two factors, the mass of the object and the acceleration, or change of momentum of the object. However, Newton's Second Law of Motion provides us with more information than simply that. First, it shows that the force applied on an object must be in the same direction as the acceleration, as mass is simply a positive constant. Additionally, this law can be re-written to show that '''<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math>''' where dp/dt represents change of momentum. | At the most basic level, Newton's Second Law of Motion states that force is equal to mass multiplied by acceleration, or '''F=ma'''. At face value, this means the force applied on an object is dependent on only two factors, the mass of the object and the acceleration, or change of momentum of the object. However, Newton's Second Law of Motion provides us with more information than simply that. First, it shows that the force applied on an object must be in the same direction as the acceleration, as mass is simply a positive constant. This can be further investigated to show that the force increases as the magnitude of acceleration increases, meaning acceleration, momentum, and force all have a positive relationship. | ||
Additionally, this law can be re-written to show that '''<math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math>''' where dp/dt represents change of momentum. Therefore, the greater the change in momentum, the greater the force being applied on the object. | |||
===A Computational Model=== | ===A Computational Model=== | ||
Revision as of 14:46, 27 November 2016
Claimed by Rahul Singi Fall 2016
History
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Main Idea
A Mathematical Model
At the most basic level, Newton's Second Law of Motion states that force is equal to mass multiplied by acceleration, or F=ma. At face value, this means the force applied on an object is dependent on only two factors, the mass of the object and the acceleration, or change of momentum of the object. However, Newton's Second Law of Motion provides us with more information than simply that. First, it shows that the force applied on an object must be in the same direction as the acceleration, as mass is simply a positive constant. This can be further investigated to show that the force increases as the magnitude of acceleration increases, meaning acceleration, momentum, and force all have a positive relationship.
Additionally, this law can be re-written to show that [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where dp/dt represents change of momentum. Therefore, the greater the change in momentum, the greater the force being applied on the object.
A Computational Model
How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript
Manipulate the code to see the different motions of the cart. See what changing the direction of the force, the net force, or the mass of the ball does to the momentum and final position of the cart.
Example Problems
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Connection to Newton's Other Laws
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External Links
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References
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