Inclined Plane With Friction
Where there is friction between the plane and the load, as for example with a heavy box being slid up a ramp, some of the work applied by the input force is dissipated as heat by friction, Wfric, so less work is done on the load.
Therefore more input force is required, and the mechanical advantage is lower, than if friction were not present. With friction, the load will only move if the net force parallel to the surface is greater than the frictional force Ff opposing it. The maximum friction force is given by
where Fn is the normal force between the load and the plane, directed normal to the surface, and μ is the coefficient of static friction between the two surfaces, which varies with the material. When no input force is applied, if the inclination angle θ of the plane is less than some maximum value φ the component of gravitational force parallel to the plane will be too small to overcome friction, and the load will remain motionless. This angle is called the angle of repose and depends on the composition of the surfaces, but is independent of the load weight. It is shown below that the tangent of the angle of repose φ is equal to μ
With friction, there is always some range of input force Fi for which the load is stationary, neither sliding up or down the plane, whereas with a frictionless inclined plane there is only one particular value of input force for which the load is stationary.
Read more about this topic: Inclined Plane
Famous quotes containing the words inclined, plane and/or friction:
“Genius goes around the world in its youth incessantly apologizing for having large feet. What wonder that later in life it should be inclined to raise those feet too swiftly to fools and bores.”
—F. Scott Fitzgerald (1896–1940)
“At the moment when a man openly makes known his difference of opinion from a well-known party leader, the whole world thinks that he must be angry with the latter. Sometimes, however, he is just on the point of ceasing to be angry with him. He ventures to put himself on the same plane as his opponent, and is free from the tortures of suppressed envy.”
—Friedrich Nietzsche (1844–1900)
“We have got onto slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk so we need friction. Back to the rough ground!”
—Ludwig Wittgenstein (1889–1951)