Kinematics
For kinematics, there are three major formulas.
- Xf=Xi+Vit+1/2at^2
- Vf=Vi+at
- Vf= Vi+2a(delta)X
Our cart had a motion that was not constant which first led me to think that we need to keep the acceleration (a), and not change it to zero. If it was constant, then I would change it to zero. Then after that I compared the knowledge that I had towards the carts motion to the variables in the equation. In order to find the final position(Xf) I needed to know the initial position(Xi), the initial velocity(Vi), time(t), and acceleration(a). Once I knew all the variables above I could find the final position and final velocity.
Position Vs. Time Graph Velocity Vs. Time Graph
- Xf=Xi+Vit+1/2at^2
- Vf=Vi+at
- Vf= Vi+2a(delta)X
Our cart had a motion that was not constant which first led me to think that we need to keep the acceleration (a), and not change it to zero. If it was constant, then I would change it to zero. Then after that I compared the knowledge that I had towards the carts motion to the variables in the equation. In order to find the final position(Xf) I needed to know the initial position(Xi), the initial velocity(Vi), time(t), and acceleration(a). Once I knew all the variables above I could find the final position and final velocity.
Position Vs. Time Graph Velocity Vs. Time Graph
Forces
![Picture](/uploads/3/9/0/7/39078025/3793797.png?475)
Newtons second law of motion states that the greater the mass of the object being accelerated, the greater the amount of force needed to accelerate the object. Because the cart is rolling down an incline, and has a weight attached to it, the amount of force needed to make the cart roll down the ramp is less compared to if it was rolling on a level path. The law did not apply very much in this case because the cart was on a incline going down so not much force was needed compared to if the cart was going up the incline or across a flat surface.
Energy
For the different types of energy, Kinetic and Potential, there are different formulas:
-Kinetic Energy: 1/2 mv^2
-Potential Energy: mgh
The variables in the above formulas are Mass(m), Velocity(v), Gravitational acceleration(g), and height(h).
For our cart the variables are:
-Mass=99.6g
-height=85.5 inches
The law of conservation of Energy states that energy cannot be created nor destroyed, but transferred from one object to another.
![Picture](/uploads/3/9/0/7/39078025/7096750.png?1411405758)
Kinetic Energy Graph