Overview:
For this project, we would have to roll a metal ball bearing down an incline plane and recording the time it takes to travel down a horizontal track. The challenge of this project is to figure out at which angle of inclination of the incline plane will the ball bearing roll down the fastest. Concepts such as conservation of energy, kinetic and potential energy will be used during this project.
What is a vector?
It is geometry with both length and direction. They are used to represent physical quantities which have magnitude and direction. An example of that physical quantity is force. The vector quantity is presented by the magnitude which has a direction. If the magnitude is A, the convention for vectors is 'A' with an arrow on top.
Vector addition is when 2 vectors(eg, A and B) are added together to form a resultant R = A + B.
Taken from Project 3A Manual
The subtraction of vectors are alike to adding of vectors. A - B = A + (-B) which forms a resultant C = A + (-B). A negative vector is the same as a positive vector, only pointing in the opposite direction.
What is Conservation of Energy?
Energy is the ability a physical system can do work on other systems. Work is the amount of energy transferred to another system by a force acting through a distance. The law of conservation of energy is that energy cannot be created nor destroyed. Energy is only transformed from one state to another.
By identifying the initial and final energy of the isolated system(ball and track), we are able to apply it in the experiment.
1st Equation: E(initial) = Gravitational Potential Energy
= mgh
m = mass of the steel ball
g = acceleration due to gravity (assuming g = 9.81 m.s ⁻²)
h = vertical displacement
2nd Equation: E(final) = Kinetic Energy
= 1/2 mv²
v = speed of the ball
3rd Equation: E(initial) = E(final)
mgh = 1/2mv²
v = √2gh
However, an isolated system of just a ball and a track is impossible to find. Therefore, some of the GPE would be converted into other forms of energy. An example would be sound energy.
http://en.wikipedia.org/wiki/Vector_%28mathematics_and_physics%29
