Vector Dynamics Reflection

For the second unit of the year, we reviewed and further studied Vector Dynamics. To begin with, we reviewed Newton's Three Laws of Motion:

1. Every object in a state of uniform motion remain in that state unless an external force is applied to it. This is also called the Law of Inertia because inertia is the resistance of an object to change its motion. This means that if an object is moving at a constant speed, it will keep going unless another force act on it. Similarly for object at rest, they will remain at rest until a force acts on it.

http://www.physicsclassroom.com/class/newtlaws/u2l1a.cfm

2. The relationship between an object's mass, its acceleration, and the applied force is F=ma. This allows us to quantitatively calculate dynamics.

3. For every action there is an equal and opposite reaction. This is exemplified when we look at a pulley system. The acceleration of one mass going down is the same as the acceleration of the other mass in the opposite direction.

http://session.masteringphysics.com/problemAsset/1131786/3/Figure_8.47.jpg

Using these principles, we looked at problems applying our knowledge from grade 11 to solve problems. To solve any dynamics problem, we start by drawing a free body diagram, and identifying all the forces acting on the object. From here, we write our force equation, and then can solve for missing values depending on the information given. 

The grade 12 portion of this was looking at forces in 2 dimensions. An example of a type of question would be an object on a ramp. The difference between objects on an inclined plane, and an object on a flat surface would be that the force of gravity (Fg) can be split into a parallel and perpendicular force of gravity, relative to the inclined plane. The components from Fg create a right triangle, where θ of the ramp is equal to the angle of the right triangle.

http://simple.wikipedia.org/wiki/Inclined_plane

If we know the angle of the ramp, Fg parallel can be found using the equation, Fg parallel=mg sin θ, and Fg perpendicular=mg cos θ. Therefore, the normal force (Fn) and Fg perpendicular balance, and Fg parallel is parallel to the ramp. Now that we can find these components, we can solve for various values, for example, the force of friction, or the acceleration of the object, amongst other values. With this concept in mind, we can also solve more complicated problems, incorporating pulleys on inclined planes.

http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section3.rhtml

The biggest difficulty I had with this unit was learning to think of Fg as 2 components, and then using these components to find which forces balance and which attribute to the net force. To overcome this, it was really important for me to draw a proper free body diagram, to correctly label all the forces acting on an object, and have all my arrows going in the appropriate direction. Once I had all my forces identified and laid out properly, it became much easier to see which forces balance, and which ones don't and then I could solve for the missing value. An example of this would be dealing with the force of friction on an inclined plane. Depending on the direction the object is moving, the force of friction could be going either way on the ramp, therefore it was extremely important for me to draw the correct free body diagram, and have the force of friction going the correct direction, which is opposite to the way the object is moving.