October 7, 2012
My Inclined Plane In this model of an inclined plane I will demonstrate the forces that act upon two objects. One object “m” will remain flat on the inclined surface theta while the other object “M” will be connected by yarn and then suspended over the pulley and act as another force on “m”. In building a three dimensional model of this problem we will see firsthand the concepts that are in practice here. It is one thing to talk about physics and another thing to interact with it. First we want to construct the model in use. To do this we will need one sheet of four ply museum board, tacky glue, #11 blade Exacto knife, yarn, one permanent Sharpie marker and last but not least, a set of kids Kinects building toys. First, we cut the two outer triangles with theta being 45 degrees. These will create our two sides. Next, we will cut the flat rectangular pieces to glue to the outer edges of the triangles to give us a three dimensional model. Now that the three dimensional triangle is complete we can begin to build our pulley system, force vector indicators and blocks that will be the moving parts of our project. After these are made and put into place we can begin to label the inclined plane with the appropriate nomenclature to express what is actually happening to the objects as well as giving us a means to derive equations to solve for a variety of different situations.
By labeling all the respective parts we can now derive our most basic equations. For example we can see that F=ma. This is the equation that describes the relationship of the blocks to the inclined plane and the motion that takes place. An object placed on a tilted surface will often slide down the surface. The rate at which the object slides down the surface is dependent upon how tilted the surface is; the greater the tilt of the surface, the faster the rate at which the object will slide down it. In physics, a tilted surface is called an inclined plane. Objects are known to accelerate down inclined planes because of an unbalanced force. To understand this type of motion, it is important to analyze the forces acting upon an object on an inclined plane. There are always at least two forces acting upon any object that is positioned on an inclined plane - the force of gravity and the normal force. The force of gravity (also known as weight) acts in a downward direction; yet the normal force acts in a direction perpendicular to the surface (in fact, normal means "perpendicular").
The first peculiarity of inclined plane problems is that the normal force is not directed in the direction that we are accustomed to. Up to this point in the course, we have always seen normal forces acting in an upward direction, opposite the direction of the force of gravity. But this is only because the objects were always on horizontal surfaces and never upon inclined planes. The truth about normal forces is not that they are always upwards, but rather that they are always directed perpendicular to the surface that the object is on. The task of determining the net force acting upon an object on an inclined plane is a difficult manner since the two (or more) forces are not directed in opposite directions. Thus, one (or more) of the forces will have to be resolved into perpendicular components so that they can be easily added to the other forces acting upon the object. Usually, any force directed at an angle to the horizontal is resolved into horizontal and vertical…