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

• I
• One human
In summary, the equation states that there is a force of air resistance against the moving object. This force is inversely proportional to the velocity of the object and is always opposite.

#### One human

TL;DR 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 ?

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.

• SammyS, Lnewqban, PeroK and 1 other person
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

• sophiecentaur, topsquark and malawi_glenn
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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• malawi_glenn
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 . ## 1. What is the equation for calculating the forces of gravity and friction on a mass?

The equation is F= - mg - kv, where F is the net force, m is the mass of the object, g is the acceleration due to gravity, k is the coefficient of friction, and v is the velocity of the object.

## 2. How is the force of gravity calculated?

The force of gravity is calculated by multiplying the mass of the object by the acceleration due to gravity (9.8 m/s²).

## 3. What is the role of the coefficient of friction in the equation?

The coefficient of friction, represented by k, is a measure of the resistance between two surfaces in contact. It is used to calculate the force of friction, which is the opposing force that acts against the motion of an object.

## 4. How does velocity affect the net force in the equation?

The velocity, represented by v, affects the net force in the equation because it determines the magnitude of the force of friction. As the velocity increases, the force of friction also increases, resulting in a larger net force.

## 5. Can this equation be applied to objects in motion on an inclined plane?

Yes, this equation can be applied to objects in motion on an inclined plane. The only difference is that the acceleration due to gravity, g, will be the component of gravity acting parallel to the inclined plane rather than the full acceleration due to gravity.