One of the core ideas from your mechanics course is that objects accelerate in response to forces. This page collects the key ideas about forces in one place. If your recollection of any of these concepts isn't clear, you may want to go back and review the details in the readings from Physics 183.
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One of the core ideas from your mechanics course is that objects accelerate in response to forces. We will apply the same ideas in this course to understand electricity and magnetism, so it's important that you remember how forces work. This page is a brief review of the key ideas about forces from mechanics. If your recollection of any of these concepts isn't clear, you may want to go back and review the details in the readings from Physics 183.
==== What is a Force? ====
==== What is a Force? ====
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The SI unit of force is the newton (N), which is defined as the force needed to accelerate a mass of 1 kg at a rate of 1 m/s². In other words, 1 N = 1 kg m / s².
The SI unit of force is the newton (N), which is defined as the force needed to accelerate a mass of 1 kg at a rate of 1 m/s². In other words, 1 N = 1 kg m / s².
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==== Net Force and Acceleration ====
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The effect of a force is to cause an object to accelerate, that is, to __change__ its velocity. An object can have a velocity even when no forces are acting on it, and conversely an object may remain at rest with zero velocity even when forces are acting on it (this is Newton's First Law).
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In general, an object may be acted on by several forces at the same time, but it can only accelerate at one rate in one direction. The acceleration of an object depends on the (vector) sum of the forces acting on it, which we call the net force: →Fnet=m→a. This equation is called Newton's Second Law.
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To add multiple forces together to calculate the net force, you need to first break each force into its separate x, y, and z components. (This usually requires a bit of trigonometry.) Then you add the components together separately.
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For example, if you have two forces →F1 and →F2, then the net force is →Fnet=→F1+→F2. This vector equation is really three separate equations: Fnet,x=F1,x+F2,xFnet,y=F1,y+F2,yFnet,z=F1,z+F2,z. You __cannot__ just add the total magnitudes of F1 and F2 together to get the magnitude of Fnet.
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Acceleration is a vector with three components ax, ay, and az, just like force. So Newton's Second Law is also really a set of three equations: Fnet,x=maxFnet,y=mayFnet,z=maz.
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You can calculate the magnitude of the net force or acceleration vector from the individual components using the Pythagorean Theorem: a=√a2x+a2y+a2z, and similarly for Fnet.
==== Interactions, External Forces, and Systems ====
==== Interactions, External Forces, and Systems ====
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**Kinetic friction**, sometimes called dynamic friction or sliding friction, takes over once the surfaces start to slide past each other. Unlike static friction, the magnitude of the kinetic frictional force can always be calculated with a formula: Fk=μkN, where μk is the coefficient of kinetic friction (a pure number without units), and N is the normal force between the two surfaces. The kinetic frictional force always acts in the direction opposite the current motion of the objects.
**Kinetic friction**, sometimes called dynamic friction or sliding friction, takes over once the surfaces start to slide past each other. Unlike static friction, the magnitude of the kinetic frictional force can always be calculated with a formula: Fk=μkN, where μk is the coefficient of kinetic friction (a pure number without units), and N is the normal force between the two surfaces. The kinetic frictional force always acts in the direction opposite the current motion of the objects.
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==== Common Mistakes ====
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* **Not bothering draw a free-body diagram** to keep track of the different forces, which object they act on, and which direction they push. This is a great way to get confused, and often leads to the next error:
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* **Adding the magnitudes of forces together**, as if they were plain numbers instead of vectors. This gives you the correct result __only__ if the forces point in the same direction. Usually, you need to add forces together component by component.
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* **Assuming the force on an object has a constant magnitude**. Sometimes forces __are__ constant, like gravity near the Earth's surface, and in those situations you can use tools like the kinematic equations (xf=12a(Δt)2+v0(Δt)+x0 and so on). But more often the magnitude or direction of a force changes during a problem, like with springs, and then you //can't// use these equations. You also can't solve an equation for a force at one point in time and assume it will have the same magnitude at a later time.
/*Last week, you have read about the [[184_notes:pc_efield|electric field]] and [[184_notes:pc_potential|electric potential]] that is created by a single point charge. Here you will read about what happens when you have two point charges that are near each other. [[184_notes:charge|You have already read about the kind of interaction]] you expect when you place two charges next to each other: either they are attracted to each other (charges have different signs) or repelled from each other (charges have the same sign). As you learned in your mechanics course, we can think about these kinds of pulls or pushes as a force acting on the charge(s). This force results from the interaction of a charge with the electric field produced by the other charge(s). We will call this new force the **electric force**. */
/*Last week, you have read about the [[184_notes:pc_efield|electric field]] and [[184_notes:pc_potential|electric potential]] that is created by a single point charge. Here you will read about what happens when you have two point charges that are near each other. [[184_notes:charge|You have already read about the kind of interaction]] you expect when you place two charges next to each other: either they are attracted to each other (charges have different signs) or repelled from each other (charges have the same sign). As you learned in your mechanics course, we can think about these kinds of pulls or pushes as a force acting on the charge(s). This force results from the interaction of a charge with the electric field produced by the other charge(s). We will call this new force the **electric force**. */