different types of energy

Thermal energy
-  A specialized term that refers to the part of the internal energy of a system which is the total present kinetic energy resulting from the random movements of atoms and molecules.


sound energy
-  sound energy is the energy produced by sound vibrations as they travel through a specific medium. Sound vibrations cause waves of pressure which lead to some level of compression and rarefaction in the mediums through which the sound waves travel.


Mechanical potential energy
-  mechanical energy is the sum of energy in a mechanical system. This energy includes both kinetic energy, the energy of motion, and potential energy, the stored energy of position. A mechanical system is any group of objects that interact based on basic mechanical principles.


Chemical potential energy
-   Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction.


Gravitational potential energy
-   Gravitational potential energy is energy an object possesses because of its position in a gravitational field. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/s².


Elastic potential energy
-  Elastic potential energy is Potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched.

cannon!

yeah!! we'll be building our cannons on Thusday!! the cannon is made of 5 pop cans. according to last unit(projectile motion), we know that the best angle to set our cannons is 45°、because it would reach the farthest distance.
But of course, the real cannon is not made of pop cans..
A cannon is any piece of artillery that uses gunpowder or other usually explosive-based propellants to launch a projectile.

Newton!!!

For equilibrium:
assumptions:

-          no air resistance

-          no friction

-          a=0 ( ax=0 and ay=0 )

-          break down in to x and y components

-          T1x=T2x

-          set positive axis⊕

for inclined problems：

assumptions：

-          no air resistance

-          FN  perpendicular to the surface

-         ＋axis is the direction of the motion

-          break down in to x and y components

-          acceleration does not equal to zero

-          FN-Fgy=0

-          Fgx-f=ma

 

for pulley problems:

assumptions:

-          pulley is frictionless

-          rope is frictionless

-          no air resistance

-          + axis is the position of the

-          2 Free Body Diagrams

-          T1=T2

-          ay1 = ay2

-          break down in to x and y components acceleration

 

for train prblems,

we consider the trains as a whole, to solve for ax.

Assumptions:

- 3 FBD to find T

- no air resistance

- ay = 0

- cables weightless

- positive along acceleration

- acceleration is consistent

projectile motion

when we do projectile motion problems, we always break the motion into to components. x component and y component. for x component, the acceleration is always zero, in other words, no acceleration for x. for y component, the acceleration is the same as gravity which is 9.8m/s
 

there are 4 types of projectile motion:
-the first one is when someone throw something from the higher level to the horizon.



-the second one is someone throw something from the horizon to the horizon.


-the third one is someone throw something from the horizon to the higher level.

-the last one is someone throw something from the horizon to the lower level.

physics behind roller coaster

Gravity is an important component of a roller coaster, the gravity pulls the roller coaster down to the ground, so that so roller coaster won't move vertically forward.
For a non-idealized roller coaster system, not all of the energy is conserved.  Friction is the main cause of energy leaks in the system and the reason why mechanical energy is not fully conserved for a real roller coaster.  This is because friction is a nonconservative force.  Nonconservative forces are forces that cause a change in total mechanical energy.  Friction opposes motion by working in the opposite direction.  The friction between the train and its tracks as well as between the train and the air take energy out of the system, slowing the train and creating both heat and sound.  This effect is most noticeable at the end of the ride as all remaining kinetic energy is taken out of the system though brakes.  Because of the energy leaks due to friction, each successive hill or loop on a roller coaster must be shorter than all the hills or loops previous to it, otherwise the train will not have enough energy to make it all the way over.

vector addition

     When we are doing vector additon question, we basically just add the X and Y. For each vector, we calculate the X and Y by doing the math, we use sine or cosine to calculate the value for "x" and the value for "y". And we add all the X together, also, add all the Y together, to obtain the final result Dx and Dy. Once we get that value, we can simply get the final result by using the pythagorean theory, and then use tangent law to calculate the angle.
And That is the Final Answer /!!!

equation 4