# Friction force decelleration

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Hello, this is probably a really simple question for those who understand.

Lets say I have a box that I'm pushing on a flat surface. I let go of the box and it carries on moving, decellerating until it stops. I know the friction coefficient and momentum, etc.

How do I calculate the friction force on the box?

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The force friction exerts on a moving object is equal to the coefficient of dynamic friction times the normal force. This is oriented in the direction opposing the velocity vector.

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So, I normalise the velocity and reverse it. Then multiply that by the magnitude of the normal force. Then multiply by the coefficient of friction... is that right?

I.e.

F = -v/|v| * |mass*gravity| * mu

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Yes that's right. But... you also calculate the force that when applied in this direction would stop all motion in that direction over the following timestep. Then you apply the minimum of the two forces.

The reason for doing this is so that your object doesn't start oscillating when it nearly comes to rest.

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Quote:
 I have a box that I'm pushing on a flat surface.

The above equations are good if the flat surface is also horizontal - i.e., perpendicular to the direction of gravity. Otherwise you need to apply the surface normal to mass*gravity, as gravity is a vector.

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Also, if the force pushing on the box isn't exactly parallel to the surface then that will also change the normal force.

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Thanks for all the help guys. As always, gamedev, best site on the net.

Quote:
 Original post by MrRowlYes that's right. But... you also calculate the force that when applied in this direction would stop all motion in that direction over the following timestep. Then you apply the minimum of the two forces.The reason for doing this is so that your object doesn't start oscillating when it nearly comes to rest.

I have noticed this oscillating effect. However, I'm having trouble calculating this max friction force. I.e.:

$\mathbf{v}_{\perp} = \mathbf{v} - \mathbf{n}\,(\mathbf{n}\bullet\mathbf{v})$

$\mathbf{f}_{max} = -m\,\mathbf{v}_{\perp}\,dt$

Where v is velocity, n is surface normal, m is mass, dt is the timestep.

But this gives a force orders of magnitude smaller than the friction as calculated in my post above, so f_max is always chosen, but isn't strong enough to prevent acceleration.

Anyone see what I'm doing wrong?

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OK, turns out I wasn't taking into account the force accumulated over the current timestep along with the velocity from the previous timestep. Seems to work fine now - for linear friction force.

I'm now completely at a loss how to do angular friction. So, to revise my original example: say I've got a box on a flat surface and I apply some torque to get in spinning on the spot (i.e. torque is in the surface normal direction). How do I then calculate the opposing torque due to friction?

EDIT: just had a thought. If friction is a constant force, then applying another constant force that overcomes it will mean constant acceleration... how is it, for example, that cars have a maximum speed? Doesn't friction increase with velocity?

[Edited by - dangerdaveCS on September 30, 2010 9:20:09 AM]

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Quote:
 Original post by dangerdaveCSEDIT: just had a thought. If friction is a constant force, then applying another constant force that overcomes it will mean constant acceleration... how is it, for example, that cars have a maximum speed? Doesn't friction increase with velocity?

The friction you've been considering is Coulomb friction, but the major drag force on a fast-moving car is wind resistance. One very simple approximation to this second force is that it increases with the square of the velocity. A good example of this -- better than a car, honestly -- is the terminal velocity of a falling object. This is the velocity at which the drag force exactly balances the force of gravity so the object stops accelerating.

For a car, there are of course many other factors at work, including that the engine actually starts to produce less torque as it begins to spin too fast.

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OK. So isn't wind resistance a kind of friction? Isn't there some analogue to that for pushing a box along a surface? Maybe assuming the surface is a bit rough? What is the equation governing this kind of friction (or just a relevant link to online material would be good)?

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