Mission F2D5 Inclined Plane Concepts
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An object of mass 'm' is upon an inclined plane with an incline angle of 'theta.' The object is moving downwards along the incline and speeding up as it moves. The free-body diagram is shown with the weight vector resolved into parallel and perpendicular components. Which of the following mathematical statements are correct?
If an object moves with a constant speed in the same direction, then the individual forces that act upon it must be balanced.
When analyzing an inclined plane situation, the gravity force is resolved into two components. One component is directed parallel to the plane and the other component is directed perpendicular to the plane. This has been done for you on the diagram. Once done, the gravity force can be ignored because it has been replaced by its two components. The remaining four forces can be compared. There is no acceleration perpendicular to the inclined plane; thus, the two forces perpendicular to the inclined surface (Fnorm and Fperpendicular) will balance each other. There is an acceleration down the inclined plane. Thus there is more force down and along the inclined plane than upward and along the inclined plane. That is, the parallel component of the gravity force (Fparallel) must be greater than the friction force (Ffriction). The net force would be the difference between these two forces: Fparallel - Ffriction.
where mu is the coefficient of friction (dependent predominantly upon the nature of the two surfaces that are in contact) and Fnorm is the normal force.
