Inclined plane
This article deals with the physical structure. For related terms, see canal inclined plane, funicular, or fixed-wing aircraft (airplane).
Definition
A plane is a line that connects two points. An inclined plane is a one end elevated line, a perfect example is a right triangle, where only one side is slanted. Incline planes are used to reduce the force necessary to overcome the force of gravity when elevating or lowering a heavy object. In civil engineering the slope (ratio of rise/run) is often referred to as a grade or gradient. It may also be called 'tilt'.
Examples
Examples of inclined planes are ramps, sloping roads, chisels, hatchets, plows, air hammers, carpenter's planes and wedges. The most canonical example of an inclined plane is a sloped surface; for example a roadway to bridge a height difference.
Ramps
The ramp makes it easier to move a physical body vertically by extending the distance traveled horizontally (run) to achieve the desired elevation change (rise). By changing the angle of the ramp one can usefully vary the force necessary to raise or lower a load.
Ramps are used as alternatives for stairways, for wheelchairs, buggies and shopping carts. Ramps may zigzag. There are also moving ramps such as the mobile staircases by which passengers board and leave an aircraft.
For example: A wagon trail on a steep hill will often traverse back and forth to reduce the gradient experienced by a team pulling a heavily loaded wagon. This same technique is used today in modern freeways which travel through steep mountain passes. Some steep passes have separate truck routes that reduce the grade by winding along a separate path to rejoin the main route after a particularly steep section is past while smaller automobiles take the straighter steeper route with a resulting savings in time.
Blade
Other simple machines based on the inclined plane include the blade, in which two inclined planes placed back to back allow the two parts of the cut object to move apart using less force than would be needed to pull them apart in opposite directions.
History
The ramp or inclined plane was useful in building early stone edifices, roads and aqueducts. It was also used for military assault of fortified positions.
Experiments with inclined planes helped early physicists such as Galileo Galilei quantify the behavior of nature with respect to gravity, mass, acceleration, etc.
Detailed understanding of inclined planes and their use helped lead to the understanding of how vector quantities such as forces can be usefully decomposed and manipulated mathematically. This concept of superposition and decomposition is critical in many modern fields of science, engineering, and technology.
Physics Incline Plane Problem
Incline plane is an interesting subject in Physics, because of its effect on the object that is on the incline plane (see picture below). In Physics, it is important to analyze the forces that is acting on the block (Newton's Laws), and to create an equation out of the analysis.
For example, the picture below has 3 vectors (neglecting air resistance and the mass is sliding down the incline plane, meaning the horizontal force of gravity has overcame static friction).
One vector is the normal force, which is always perpendicular to the ground. It is also the force that is stopping the object from accelerating at gravity's full acceleration (On Earth, gravity acceleration is 9.8 meters/seconds squared).
The second vector is gravity, the planet's attractive force. Within the gravity vector, there are two components, horizontal and vertical force in the incline plane perspective. As you can see the angle is on the lower left corner, what happens if we make that angle zero degrees? The plane will be horizantally straight, and the only force acting on it is gravity (pointing downwards)and normal force (pointing upwards). The only Trig. function that makes zero degree one is Cosine, so cosine must be the vertical force, since gravity is in its entirety. With this fact, we can go back to the incline plane and use the cosine function to find the vertical force, and the sine function to find the horizontal force.
The incline plane is also in contact with the massed block, and the contact causes friction. So the third vector is friction. Since the block is sliding downwards, the friction vector is going the opposite of the horizontal force of gravity.
Taking all these vectors into consideration, we can say the normal force and the vertical component of gravity balences out, because it is not accelerating upwards nor downwards, but side ways. And since, friction is going the opposite direction of the horizontal gravity force, the whole equation is mgSinθ - f= mA. m is the mass, A is acceleration, g is gravity acceleration, and f is friction force. The mA part is derived from Newton's laws of force.
Key:
N = Normal_Force that is perpendicular to the plane
m = Mass of object
g = Gravity of the planet
θ (theta) = Angle of elevation of the plane
f = Frictional_force of the inclined plane
When θ = 0; mgSinθ = 0 and mgCosθ = 1 which is a regular flat surface.
mgSinθ - f = Net Force of the object on the inclined plane.
Sources
- Lesson 3: Forces in Two Dimensions StudyWorks Online