Inclined Plane

              The inclined plane is one of the original six simple machines; as the name suggests, it is a flat surface whose endpoints are at different heights. By moving an object up an inclined plane rather than completely vertical, the amount of force required is reduced, at the expense of increasing the distance the object must travel. The mechanical advantage of an inclined plane is the ratio of the length of the sloped surface to the height it spans; this may also be expressed as the cosecant of the angle between the plane and the horizontal. Note that due to the conservation of energy, the same amount of mechanical energy is required to lift a given object by a given distance, except for losses from friction, but the inclined plane allows the same work to be done with a smaller force exerted over a greater distance.

               The inclined plane is a plane surface set at an angle, other than a right angle, against a horizontal surface. The inclined plane permits one to overcome a large resistance by applying a relatively small force through a longer distance than the load is to be raised.

                The inclined plane is a plane surface set at an angle, other than a right angle, against a horizontal surface. The inclined plane permits one to overcome a large resistance by applying a relatively small force through a longer distance than the load is to be raised.

                The inclined plane and its active twin brother the wedge. In the broadest sense, the wedge includes all devices for cutting and piercing .

•       It is easier to understand how a wedge works by looking at the inclined plane, which is nothing more than a wedge sliced in half. The wedge does its job by moving. The inclined plane is held stationary while the "wedged material" is moved over it.

•       The secret of the plane's mechanical advantage lies in its ability to split the force of gravity into two smaller forces; one perpendicular to and one parallel to the plane. It is only the parallel force which needs to be counteracted by pushing an object laying on the plane.

•       If there is no friction on the plane, the pushing effort required will be 1/10th the weight if the length of the plane is 10 times its height. A similar relationship holds for any plane: the extra distance makes it possible to apply an effort smaller than the weight.

wedge

 

Calculation of forces acting on an object on an inclined plane

            To calculate the forces on an object placed on an inclined plane, consider the three forces acting on it.

•       The normal force (N) exerted on the body by the plane due to the force of gravity i.e. mg cos θ

•       The force due to gravity (mg, acting vertically downwards) and

•       The frictional force (f) acting parallel to the plane.

           We can decompose the gravitational force into two vectors, one perpendicular to the plane and one parallel to the plane. Since there is no movement perpendicular to the plane, the component of the gravitational force in this direction (mg cos θ) must be equal and opposite to normal force exerted by the plane, N. If the remaining component of the gravitational force parallel to the surface (mg sin θ) is greater than the static frictional force f_s – then the body will slide down the inclined plane with acceleration (g sin θ − f_k/m), where f_k is the kinetic friction force – otherwise it will remain stationary.

           When the slope angle (θ) is zero, sin θ is also zero so the body does not move.