The inclined plane It is a simple machine that consists of a flat surface that forms an angle with respect to the horizontal. Its purpose is to reduce the effort required to lift an object to a certain height.
A common use is to lift a heavy load onto a construction platform or vehicle. From experience we know that in this way the effort is reduced, in exchange for increasing the distance to be covered a little..
So instead of lifting the object vertically a height h, it is made to travel a distance d over the surface of the inclined plane. Then the surface contributes to balance a part of the weight of the object, specifically the vertical component of the same.
Applied force F It is responsible for moving the horizontal component of the weight, whose magnitude is less than that of the weight itself. Therefore, the magnitude of F is less than the magnitude of the force required to directly raise the body.
The reduction in effort required is called mechanical advantage, a principle discovered by the great ancient physicist Archimedes of Syracuse (287-212 BC). The greater the mechanical advantage, the less effort must be made to carry out the task.
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Simple machines like the inclined plane have been known since prehistoric times. Early humans used cutting instruments made of stone to make arrowheads to hunt and cut wood to make utensils..
The mechanical advantage M of a simple machine is defined as the quotient between the magnitude of the output force and that of the input force. It is therefore a dimensionless quantity.
Usually the magnitude of the output force is greater than the input force and M> 1. But there are very delicate tasks that merit a reduction in the output force, as is the case of the clamps, for which M < 1.
As examples of the application of the inclined plane we have:
Ramps are useful for lifting heavy objects to a certain height, requiring the application of a force of less magnitude than the weight of the object..
The mechanical advantage M of a smooth ramp, without friction, is calculated by making the quotient between its length, called “d” and its height, denoted as “h”:
M = d / h
However, in practice there is friction between the surfaces, therefore the real mechanical advantage is a little less than M (see solved exercise 2).
They consist of a double inclined plane made of resistant material with two contact surfaces, which provide high friction forces due to the cutting edge that forms on the edge..
The cutting edge is able to overcome the resistance of the material and separate it into pieces with the help of a hammer to apply force. The use of the wedge is extended by attaching a handle to it, like an ax.
Knives, axes, and chisels are good examples of the use of wedges as cutting instruments. People's incisor teeth are shaped this way too, to cut food into smaller, chewy pieces.
The longer the wedge and the smaller the angle on the cutting edge, the greater the mechanical advantage of the tool, which is given by:
M = 1 / tg α
Where α is the angle at the cutting edge. Pointy shapes like wedges don't just work to overcome the resistance of wood. Vehicles such as airplanes and boats also feature wedge shapes to overcome air resistance and gain speed..
There is an inclined plane in another everyday device that is used to fix parts: the screw. The screw thread is an inclined plane wound around the cylindrical axis of the screw.
An input force is applied Fi to the screw and when turning one turn of size 2πR, where R is the radius, the screw advances a distance p, called He passed. This distance is the one that separates two consecutive threads of the screw.
The figure shows a free-body diagram of an object on a plane inclined at angle α. Assuming no friction, the forces acting on the object are: the normal N, exerted perpendicularly and W the weight, which is vertical.
The component of the weight in the direction of the normal is WY, that compensates this normal, since the object does not move above the plane, but parallel to it. A force F applied to the object must at least compensate the W componentx so that the object goes up the inclined plane.
If friction is considered, it must be taken into account that it is always opposed to movement or possible movement. When the object moves on the surface of the inclined plane, the kinetic friction acts, if the object is going upwards, the kinetic friction Fk it is directed in the opposite direction and force F has to also be in charge of defeating it.
Find the angle that the tip of a wedge must have for its mechanical advantage to be 10.
In previous sections it was established that the mechanical advantage M of the wedge was given by:
M = 1 / tg α
If M must be worth 10:
1 / tg α = 10
tg α = 1/10 → α = 5.71º
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