I F= - mg - kv ? (forces of gravity and friction on a mass)

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The equation F = -mg - kv represents the forces acting on an object, where -mg indicates the force of gravity acting downward and -kv represents air resistance opposing the object's motion. The negative sign in -kv indicates that the force of friction acts in the opposite direction to the velocity of the object, which can be either positive or negative depending on the object's movement. When considering upward motion, the velocity is positive, making -kv negative, thus aligning with the downward direction of friction. Using vector notation clarifies this relationship, showing that the forces can be expressed in terms of their respective directions. Understanding these signs is crucial for correctly interpreting the dynamics of the system.
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A simple question.
Hi I'm just a student so this:
F = - mg - kv
(Being kv friction) doesn't sound intuitive. Looks like both are going in the same direction... I just don't get it. But that's what my book says (Symon mechanics) and my classmates are also using "-"kv .

Can someone explain me please? Shouldn't "kv" be positive ?
 
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The -mg part suggests that this is an object moving straight up/down close to the surface of the Earth (or another planet with atmosphere). It also suggests that positive direction is up. Then if the object is moving up, the air resistance force should be down, i.e. negative. Moving up means v is positive, hence -kv is negative, directed down. You can work out the case where the object is moving down.

It should be very intuitive, -kv means that the force is proportional to v, but has oppsitive direction as v.
 
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One needs to let v be any negative or positive value. Then the minus sign in F= -kv implies that the laminar wind force is always opposite the velocity.
Usually up is chosen as the the positive direction and the gravity force is then written as
F=-mg where g is taken to be a positive constant (but gravity is down). Notice this means that up velocities are positive and that down velocities negative.
A more definitive way to deal with all of this is to just use vector notation. The equation in question is then written as $$\vec F =m\vec g-k \vec v$$ where k and m are positive numbers. The initial equation is just the z component of this vector equation
 
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For example, a car rolling with velocity v over a horizontal road experiences a force of air resistance F = -kv, where k is a positive constant.
 
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One human said:
Summary: A simple question.

Hi I'm just a student so this:
F = - mg - kv
(Being kv friction) doesn't sound intuitive. Looks like both are going in the same direction... I just don't get it. But that's what my book says (Symon mechanics) and my classmates are also using "-"kv .

Can someone explain me please? Shouldn't "kv" be positive ?
Hello @One human .

:welcome:
 
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