Vector Dynamics Application

Vector dynamics can be applied everywhere we look. Although we learned more about vector dynamics, a large part of this unit was focussing on inclined planes, therefore, a practical application of vector dynamics is skiing. Skiing has always been a sport that I have wanted to do more often. I have had the opportunity to ski on local mountains and have loved the few time I have been able to go! There are many different types of skiing, and all would show good examples of how forces act on an object, whether the person is skiing down a hill, or on a flat surface like cross country skiing.

https://www.inkling.com/read/college-physics-openstax-college-1st/chapter-5/example-5-1

In this diagram, we can see that the skier is on a incline of 25 degrees, and the free-body diagram shows that there is a normal force, (Fn) the force of friction (Ff), and the force of gravity (Fg) acting on the skier. The force of friction would come from the snow under skis. As we have learned in this unit, the force of gravity can be split into 2 components, a parallel component, and a perpendicular component. We separate gravity into components so that the perpendicular component balance Fn, and the parallel component is parallel to the direction the object is moving in, and the force of friction. 

We have already learned that we can find Fg perpendicular by using the formula, mg cos θ. In this situation, θ is 25 degrees because the incline of the surface is 25 degrees. Additionally, Fg parallel= mg sin θ. With these components, we could now find values such as the force of friction, and the acceleration of the skier, depending on the other information given. This type of information can be especially useful if you practice ski jumping, which can be based on how fast you accelerate down the hill, and how far you can jump. 

http://www.saugeentimes.com/Pictures/Misc%20Clip%20Art/Cross%20Country%20Skier.jpg

For a cross country skier, who must move on a relatively flat terrain, the forces acting on them are the normal force (Fn) the force of gravity (Fg), and the force of friction, however friction plays a more prominent role in cross country skiing. If you have looked at cross country skis, you will notice that the skis will not lie completely flat against the snow. This is because a cross country skier, needs both high and low friction forces while skiing. Friction needs to be low when the skier is gliding forward, however it needs to be high when you kick back and grip the snow to move. This arch in the ski allows you to adjust your weight depending on the situation. When you guide the ski forward or are going downhill, your weight on the skis decreases, and the arch ensures that the middle portion of your skis do not make contact with snow, therefore, there is less friction. However when you kick back, your body weight pushes on the ski, and the middle section touches the snow, therefore more friction!

http://sciencenordic.com/physics-cross-country-skiing

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.

Vector Kinematics Application

Projectile motion is something we see everyday day in our lives, and a good example of this, is golfing. Many sports display projectile motion, such as football or basketball, but golf has always been a sport that I have enjoyed since I was a little kid, going to the driving range with my dad. Hitting a golf ball with a club creates a parabolic trajectory that is caused by the effect of gravity on the golf ball. We can calculate how far and how high a golf ball will travel, using the principles of projectile motion.

The initial velocity of the golf ball has a vertical and horizontal component. The initial vertical and horizontal components can be found if we know the angle the golf ball was hit, using the equations: Vo horizontal=Vo cos θ and Vo vertical=Vo sin θ, Vo being the speed with which the club hit the ball. The launch angle affects the vertical and horizontal components as seen in the equations above, therefore the launch angle can affect how high the ball will travel, and how far it will travel.

http://sportsnscience.utah.edu/the-in-depth-science-of-golf/

Due to gravity, there is a downward (vertical) acceleration, however, there is no horizontal acceleration, therefore, Ax=0, and Ay=-9.8m/s^2. This means that the horizontal component is moving at a constant velocity. With the horizontal acceleration being 0, the range, or the horizontal distance the ball travels, can be calculated using the equation, Dx=V horizontal × t (time of flight). However, the vertical motion is different as we have to deal with an acceleration due t =o gravity. The vertical component of the initial velocity is upwards, however we have to account for gravity, which is pulling the ball towards the ground, therefore we use the formula, Dy=Vo(y) × t + 1/2 at^2 to find the vertical distance the golf ball travels.

Air resistance, and wind can play a significant role on the trajectory of a golf ball, however this explains why golf balls have dimples to reduce these affects. Although we usually do not account for air resistance in problem solving, this diagram shows an interesting fact that I have learned through this journal entry.

http://io9.com/5606110/why-golf-balls-have-dimples

Projectile motion can be seen almost anywhere, but golf is a sport that solely relies on the trajectory of the ball and where is lands, which really shows the importance and application of projectile motion.