Why is friction proportional to velocity?

In summary, the effective force term -\gamma v is often added to Newton's equation in phenomenological equations to account for frictional effects. This shape is not fundamental, but it is a good approximation in many cases. It is directly proportional to velocity because as a particle moves, it experiences more collisions head-front, resulting in a backwards force. This shape also makes the differential equation more tractable. Friction is not always proportional to velocity, as it depends on the type of flow (laminar or turbulent) and the speed of the object. In general, for solid objects moving at high speeds through a fluid, friction is proportional to the square of velocity, while for low speeds, it is proportional to velocity. This is due
  • #1
nonequilibrium
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We all know in phenomenological equations we like to add a [itex]-\gamma v[/itex] effective force term to Newton's equation to include frictional effects with the environment. Why this specific shape? I understand it's not fundamental, and that it is not always appropriate, but still it seems to be a good approximation in many cases. Why is this? I understand the intuitive idea that a particle moving gets more collisions head-front and as such will experience a backwards force, but why directly proportional to velocity (and not, say, a square root or a quadratic or... etc)?
 
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  • #2
I think it fits as a good first order approximation and makes the DE more tractable.

Similar to the idea with a pendulum system where we assume the angle of oscillation is fairly small so that sin(theta) = theta and the DE become easier to solve.
 
  • #3
My guess would be that if velocity doubles the amount of surface encountered by an object doubles and therefore friction doubles.
 
  • #4
Why is friction proportional to velocity?

In general, it's not. Friction of one dry object against another is fairly constant over a fairly large velocity range. For a solid object moving at a high speed through some fluid, friction is roughly proportional to the square of velocity.

However, friction is roughly proportional to velocity for a solid object moving at a low speed through a fluid. Why proportional to velocity at low speeds, but the square of velocity at high speeds? One key difference is laminar versus turbulent flow.
 
  • #5


Friction is a force that arises when two surfaces are in contact and one is moving relative to the other. It is caused by the interactions between the atoms and molecules on the surfaces, and these interactions are affected by the relative velocity between the surfaces.

The reason why friction is proportional to velocity can be explained by the kinetic theory of gases. According to this theory, gases are made up of particles (atoms or molecules) that are constantly moving and colliding with each other and with the walls of their container. The average speed of these particles is directly proportional to the temperature of the gas.

When a surface is moving, the particles on the surface are also moving with a certain velocity. When these particles collide with the particles on the other surface, they transfer some of their kinetic energy to the other particles, causing them to move as well. This transfer of energy results in a force that resists the motion of the surface, which we perceive as friction.

The force of friction is proportional to the relative velocity between the surfaces because the faster the particles are moving, the more energy they transfer to the other surface, resulting in a larger resistance force. This is why the -\gamma v term is added to Newton's equation, to account for this frictional force.

The specific shape of the -\gamma v term is not fundamental and may vary depending on the specific system and conditions. However, in many cases, a linear relationship between friction and velocity is a good approximation. This is because, in most systems, the average velocity of the particles is proportional to the relative velocity between the surfaces, and therefore the force of friction is also directly proportional to velocity.

In conclusion, friction is proportional to velocity because of the transfer of kinetic energy between the particles on the surfaces, and this relationship is a good approximation in many cases due to the kinetic theory of gases.
 

1. Why is friction proportional to velocity?

Friction is proportional to velocity because as an object moves faster, there is an increased amount of contact between the object and the surface it is moving on. This increased contact results in a greater force of friction, which is directly proportional to the velocity of the object.

2. How does friction affect an object's velocity?

Friction acts in the opposite direction of an object's motion and opposes its velocity. This means that as an object moves, friction acts to slow it down, causing its velocity to decrease.

3. What factors affect the amount of friction proportional to velocity?

The amount of friction proportional to velocity is affected by the nature of the surfaces in contact, the force pressing the surfaces together, and the roughness of the surfaces. The greater the force and roughness, the greater the friction will be.

4. Why is friction important in everyday life?

Friction plays a crucial role in everyday life as it allows us to walk, grip objects, and drive vehicles without slipping or sliding. It also helps to slow down or stop moving objects, making it essential for safety and control.

5. How is friction used in technology and engineering?

Friction is often intentionally used in technology and engineering to prevent slipping, create traction, and control motion. It is also used in brakes, gears, and bearings to slow down or stop the movement of machinery and vehicles.

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