# 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.

Last edited:
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 formula for calculating the forces of gravity and friction on a mass?

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

## 2. How does the force of gravity affect an object?

The force of gravity is a downward force that pulls objects towards the center of the Earth. It is directly proportional to the mass of the object, meaning that the more massive an object is, the greater the force of gravity acting on it.

## 3. What is the role of friction in the F = - mg - kv formula?

Friction is a force that opposes the motion of an object. In the F = - mg - kv formula, k represents the coefficient of friction, which takes into account the type of surface the object is moving on and the force needed to overcome friction.

## 4. How does the velocity of an object affect the net force?

The velocity of an object is represented by v in the F = - mg - kv formula. As the velocity increases, the force of friction also increases, resulting in a higher net force acting on the object. This can cause the object to slow down or come to a stop.

## 5. Can the F = - mg - kv formula be used for objects in free fall?

Yes, the F = - mg - kv formula can be used for objects in free fall. In this case, the force of gravity is the only force acting on the object, as there is no contact with a surface to create friction. Therefore, the formula becomes F = -mg.

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