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

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SUMMARY

The equation F = -mg - kv describes the forces acting on an object under the influence of gravity and friction, where mg represents the gravitational force and kv represents the frictional force proportional to velocity. The negative sign in front of kv indicates that the frictional force opposes the direction of motion, which is intuitive when considering the positive direction as upward. This equation can be expressed in vector notation as F = m*g - k*v, clarifying the relationship between the forces and their directions. Understanding this concept is crucial for students studying mechanics, particularly in the context of Symon's mechanics.

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  • Understanding of Newton's laws of motion
  • Familiarity with basic mechanics concepts from Symon's mechanics
  • Knowledge of vector notation and its application in physics
  • Basic understanding of forces, including gravity and friction
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This discussion is beneficial for students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the dynamics of forces acting on objects in motion.

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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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