# Coefficient of friction problem

If the coefficient of friction is derived by f=un...
and u can be calculated as u=sinx/cosx or tanx;
Then why is there still friction on a level surface where x=0 and tanx also equals 0?

Im a beginner in physics. i just need help understanding Tide
Homework Helper
I am not exactly clear on what you are asking but it seems that you are talking about two entirely different things. First, the coefficient of friction is not "derived." Rather it measured and it appears you are referring to a particular form of measurement. Namely, you place an object on an inclined plane (the object and plane having the desired composition) and determine the tilt of the plane when the object begins to slop. Obviously, if the object is sitting on a level surface it's not going to slip of its own accord. That all refers to the measurement of the coefficient.

Once you have measured the coefficient then you can use it for doing calculations such as how much work would be done by dragging the object across a level surface!

Co-efficient of friction

CaptainDave,

You are right. You can calculate the co-effiecient of friction as

$$\mu =\frac{sin x}{cosx}$$

But, this is case in the following situation. You have a block on an incline, and you go on increasing the angle of the incline. The block remains at rest initially. But, a stage comes when the angle of incline is sufficient to make the block move off. This is the angle you must use as x in the above equation. You can't use the angle at just any position.

So in case of a horizontal surface, you need to find other methods.

( weight of box is equal to the normal rection )

spacetime
www.geocities.com/physics_all/index.html

To add to what spacetime said...

When you say that

$$\mu =\frac{\sin\alpha}{\cos\alpha}$$

you are giving the value of the coefficient at the instant motion is about to begin. This $$\alpha$$ is called the Angle of Repose. It is the angle at which motion (naturally) begins.

On a horizontal surface, there are two possibilites: no-motion (rest) or motion. If no external force acts on a body and the body is at rest, the friction force is indeed zero. However, as the force on it is increased from zero, the frictional force also increases so as to oppose relative motion of the body with respect to the surface (Friction always opposes relative motion).

The body however remains at rest so long as the applied force is less than the maximum static friction on the horizontal surface ($$f_{s,max} = \mu_{s}N$$) since the static friction force in this case being less than fsmax is self-adjusting and makes itself equal to the applied force. At the instant the applied force equals fsmax, motion "just" starts. This can be better explained by the "kink" in the graph of frictional force vs applied force. For subsequent times, friction equals coefficient of Kinetic Friction times the normal reaction. The usage of the word "just" is not correct mathematically but it is conveniently explained by the notion of left and right handed limits if you're interested.

Hope that helps...
Cheers
vivek