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| 183_notes:momentum_principle [2021/02/04 23:13] – [The Momentum Principle] stumptyl | 183_notes:momentum_principle [2021/09/06 13:34] (current) – dmcpadden |
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| In these notes, you will be introduced to the idea of a system, net force, and how a system's momentum and the net force it experiences are related (i.e., through [[https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_second_law|"Newton's Second Law of Motion"]]). In another set of notes, you find a few useful formula for when the net force acting on a system is a constant vector (fixed magnitude and direction). | In these notes, you will be introduced to the idea of a system, net force, and how a system's momentum and the net force it experiences are related (i.e., through [[https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Newton.27s_second_law|"Newton's Second Law of Motion"]]). In another set of notes, you find a few useful formula for when the net force acting on a system is a constant vector (fixed magnitude and direction). |
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| ==== Lecture Video ===== | ==== Lecture Video ===== |
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| {{youtube>Q-950pb-aXQ?large}} | {{ youtube>Q-950pb-aXQ?large }} |
| ==== System and Surroundings ==== | ==== System and Surroundings ==== |
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| {{ :183_notes:system_and_surroundings.001.png?250}} | {{ 183_notes:week2_sys_sur.png?500}} |
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| ==== Net Force ==== | ==== Net Force ==== |
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| //A force is a vector that quantifies the interactions between two objects.// | **A force** is a vector that quantifies the interactions between two objects. The units of force in SI are **Newtons (N)**. 1 Newton is equal to 1 kilogram-meter-per-second squared (1 N = 1 $\dfrac{kg\:m}{s^2}$). |
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| There are two types of forces that you will work with in mechanics: [[183_notes:gravitation|gravitational forces]] and electrostatic forces. As you will learn, all interactions that you will consider in mechanics are a result of objects either having mass and, thus, attracting gravitationally, or being charged, and thus, interacting through electrical repulsion or attraction. | There are two types of forces that you will work with in mechanics: [[183_notes:gravitation|gravitational forces]] and electrostatic forces. As you will learn, all interactions that you will consider in mechanics are a result of objects either having mass and, thus, attracting gravitationally, or being charged, and thus, interacting through electrical repulsion or attraction. |
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| The units of force in SI are Newtons (N). 1 Newton is equal to 1 kilogram-meter-per-second squared (1 N = 1 $\dfrac{kg\:m}{s^2}$). | |
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| Systems might interact with several objects in their surroundings, and thus, experience a variety of forces. Fortunately to make predictions of the motion, the Momentum Principle only requires that you know the net force. | Systems might interact with several objects in their surroundings, and thus, experience a variety of forces. Fortunately to make predictions of the motion, the Momentum Principle only requires that you know the net force. |
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| //The Net Force is the vector sum of all forces acting (at an instant) on a system as due to the systems' surroundings.// | The **Net Force** is the vector sum of //all forces// acting (at an instant) on a system as due to the systems' surroundings. |
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| Mathematically, we can represent this sum using vector notation: | Mathematically, we can represent this sum using vector notation: |
| where each interaction/force (at an instant) is counted as a specific $\vec{F}_{i}$. These interactions may be "field interactions" (e.g., [[183_notes:gravitation|the gravitational field]]) or "contact interactions" (e.g., the [[183_notes:friction#the_normal_force|normal force]] or the [[183_notes:friction#friction|frictional force]]). [[183_notes:friction|Contact interactions]] are the result of the electromagnetic field and are, thus, truly field interactions (as all interactions are). | where each interaction/force (at an instant) is counted as a specific $\vec{F}_{i}$. These interactions may be "field interactions" (e.g., [[183_notes:gravitation|the gravitational field]]) or "contact interactions" (e.g., the [[183_notes:friction#the_normal_force|normal force]] or the [[183_notes:friction#friction|frictional force]]). [[183_notes:friction|Contact interactions]] are the result of the electromagnetic field and are, thus, truly field interactions (as all interactions are). |
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| == Impulse == | \\ |
| //Impulse is the product of a force and a time interval over which that force acts, which is mathematically equivalent to the change in momentum (Impulse = $\vec{J} \equiv \vec{F} \Delta t$).// | === Impulse === |
| | **Impulse** is the product of a force and a time interval over which that force acts, which is mathematically equivalent to the change in momentum (Impulse = $\vec{J} \equiv \vec{F} \Delta t$). |
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| Sometimes, you might find it useful to think about the impulse applied to a system as being responsible for the change in momentum of the system. An impulse may be calculated for each force (e.g., //impulse delivered by the gravitational force//) or the total force (i.e., //the "net" impulse applied to the system//). | Sometimes, you might find it useful to think about //the impulse applied to a system as being responsible for the change in momentum of the system.// An impulse may be calculated for each force (e.g., //impulse delivered by the gravitational force//) or the total force (i.e., //the "net" impulse applied to the system//). |
| ===== Examples ===== | ===== Examples ===== |
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| * [[:183_notes:examples:netForce|Calculating the net force]] | * [[:183_notes:examples:netForce|Calculating the net force]] |
| * [[:183_notes:examples:impulse|Calculating the change in momentum]] | * [[:183_notes:examples:impulse|Calculating the change in momentum]] |