Unit Dynamics Module Applications of Newton s Three Laws page 1 of 1 Solving Problems Using Newton s Laws Inclines and the Normal Force The normal force also called the contact force is the force perpendicular to the contact surface between two objects For problems involving inclines it s easiest to choose the x axis parallel to the inclined plane and the y axis perpendicular to it There is no formula for the normal force its magnitude and direction adjusts depending on the physics of the situation so that the object doesn t pass through the surface On an incline with no friction the acceleration is gsin and the normal force is mgcos where is the angle of the incline relative to the horizontal Consider an object resting on a table The objects weight is a force in the downward direction You know that an object at rest is not accelerating so by Newton s second law the net force on the object must be zero There must be a force in the upward direction that balances the force of gravity This force is the normal force also called the contact force and it is the force perpendicular to the contact surface between two objects In this example the magnitude of the contact force is equal to the object s weight Consider a cart on an air track tilted at an angle Use Newton s second law First focus on one object the cart Next draw a force diagram The weight of the object is in the downward direction and the normal force is perpendicular to the air track Finally choose a coordinate system Since the acceleration can only be along the track it is easiest to choose the x axis parallel to the inclined plane and the y axis perpendicular to it First find the normal force Since it is in the ydirection write Newton s second law for the ycomponents The y component of the weight is mgcos There is no acceleration in the y direction so N mg cos Next find the cart s acceleration Solve the xcomponents of Newton s second law for acceleration and substitute mgsin for the xcomponent of the weight Acceleration is gsin in the positive x direction Notice that the acceleration is independent of mass www thinkwell com info thinkwell com Copyright 2001 Thinkwell Corp All Rights Reserved 1844 doc rev 03 29 2001
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