Forces in Two Dimensions - Mission F2D5 Detailed Help


An object of mass 'm' is resting upon an inclined plane with an incline angle of 'theta.' The coefficient of friction between the object and the plane is 'mu.' The object is at rest upon the incline. The free-body diagram is shown with the weight vector resolved into parallel and perpendicular components. Which of the following mathematical statements are correct?


 
Newton's Laws of Motion:
If an object is at rest and staying at rest, 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 Once done, the gravity force can be ignored because it has been replaced by its two components.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. The two forces perpendicular to the inclined surface (Fnorm and Fperpendicular) will balance each other. If there is no acceleration, then the net force will be 0 N and the two forces parallel to the inclined surface (Fparallel and Ffriction) will also balance each other.


 
The force of friction (Ffrict) experienced by an object is often calculated using the equation: 
 
Ffrict= mu • Fnorm

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.