**TI83F*
AppVariable file 10/26/06, 23:57#
VECTORTE€óG¿¯VECTORTESliding Plane problemsÖÖThere are 4 forces at workÖFk: the action force down the planeÖFf: friction force opposing motion (up the plane)ÖFN: normal force ^ to the planeÖW: weight points straight downÖÖSliding Plane problemsÖÖThe formulasÖFk: mgsin?ÖFf: Ãmgcos?ÖFN: mgcos?ÖW: mgÖÖWhere m = mass of the object, and g is 9.8m/s2ÖÖDisplacement ProblemsÖÖFirst sum the values in the X direction, creating one composite X vectorÖNext, sum the values in the Y direction, creating one composite Y vectorÖCreate a right triangle with the composite X and Y as the legs of the triangleÖFind the hypotenuse of the triangle length and angle measure and that is the resultant vector of the problemÖÖTravel ProblemsÖÖBoat & Plane problems that occur in a medium that is moving (has its own vector component)ÖDraw a picture of the scenario, showing both direction & magnitude of the vehicle and the medium it is traveling inÖKeep X and Y values separate when solving parts of the problemÖÖHanging Sign ProblemsÖÖThe sum of the Y components of the involved vectors must equal the weight of the object being heldÖThe hypotenuse of the triangle formed by the X and Y components is the tension in the rope or wire, it is equal to ÖHypotenuse = Y/Sin ?ÖÖ-------ÖÖInclined Plane:ÖYou must first solve for X and for YÖCOSq=y/mg --> Y = mg COSq \ÖFN = mg COSq ÖSINq=X/mg --> X = mg SINq \ÖFk = mg SINq ÖFf = mkFNÖFf = mk mg COSqÖFnet = Fk - mkFN= ma ÖFnet = mg SINq - mk mg COSq = ma Öma = mg SINq - mk mg COSq Öma = mg (SINq - mk COSq)ÖÖa = g (SINq - mk COSq)ÖÖRolling FrictionÖFf = kgvÖWhere Ö k = coefficient of rolling frictionÖ g = gravityÖ v = average velocityÖÖSo our new equation is...Öa=g(sinq- kvAB)ÖÖRolling friction is related to velocity, so it must be accounted for within our equation.ÖÖÖ™–