# Dynamic Friction between surfaces

• Laiva-59
In summary, the question asks for the dynamic friction force between two bodies, V1 and V2, in contact over a flat surface S. The normal force F exists between the bodies at point P and acts along the unit normal vector N. The body V1 is moving with a velocity V, and the friction force is given by the formula Ffriction = mu*F, where mu is the coefficient of friction. The direction of the friction force is opposite to the direction of motion, and its components can be calculated using the formula Ffriction,x = mu*|F|*U_x, Ffriction,y = mu*|F|*U_y, and Ffriction,z = mu*|F|*U
Laiva-59

## Homework Statement

We have a body V1, which is in contact over body V2 over a flat (i.e. planar) surface S. (The planar approximation can be considered a good one). Body V1 is moving, V2 is stationary.

A normal force F exists between the bodies at surface S, acting in point P. This force acts along the unit normal vector N.

The body V1 is moving with a body velocity V.

Q: What is the dynamic friction force between V1 and V2?

I think I found the solution, but I'd like a double check. Or a rebuttal with correct answer...

## Homework Equations

Ffriction = mu*F, acting opposed to the relative motion of the surfaces in contact.

## The Attempt at a Solution

1. We find the relative speed in the plane S.

As follows:
N = unit normal surface vector in P.
V = body velocity in point P.

U = orthonormal projection of V on plane S. I think this is the speed the surfaces slide over each other. Is this correct?

U = V - (V dot N)N

2. The components of U have dimension [m/s], but as the friction force is independent of speed, we need to normalise vector U. I.e. we only need to know which direction U has.

U_ = U/norm(U) = [U_x,U_y,U_z]

3. The components of the friction force now become

Ffriction,x = mu*|F|*U_x
Ffriction,y = mu*|F|*U_y
Ffriction,z = mu*|F|*U_z

I think your solution is correct. The formula you have used for the friction force is the correct one, where mu is the coefficient of friction (which can vary depending on the materials in contact). The direction of the friction force will always be opposite to the direction of motion, so your calculations for the components of the force are also correct. However, I would recommend double checking your calculations to ensure that your final answer is correct. Also, keep in mind that the coefficient of friction can sometimes be a range of values, so you may need to use the average or maximum value depending on the situation. Overall, it seems like you have a good understanding of the problem and have used the correct approach to find the solution. Good job!

## What is dynamic friction?

Dynamic friction is the force that resists the motion between two surfaces that are in contact and sliding against each other.

## How is dynamic friction different from static friction?

Static friction is the force that resists the initial movement of two surfaces in contact, while dynamic friction is the force that resists the continuous movement of two surfaces in contact.

## What factors affect the magnitude of dynamic friction?

The magnitude of dynamic friction is affected by the nature of the two surfaces in contact, the normal force between the surfaces, and the roughness of the surfaces.

## How is dynamic friction measured?

Dynamic friction can be measured using a device called a friction force sensor, which measures the force required to keep two surfaces in motion against each other.

## What is the significance of dynamic friction in everyday life?

Dynamic friction plays a crucial role in many everyday activities, such as walking, driving, and using machinery. It helps to prevent slipping and sliding and allows us to have control over our movements.

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