- #1

Laiva-59

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## 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

**F**

_{friction}= 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

**F**

_{friction,x}= mu*

**|F|***U_x

**F**

_{friction,y}= mu*

**|F|***U_y

**F**

_{friction,z}= mu*

**|F|***U_z