Constructive and Deconstructive Wave Intereference

Interference is the addition of two or more waves that results in a new wave pattern. Interference usually refers to the interaction of waves that are correlated or coherent with each other either because they come from the same source or because they have the same or nearly the same frequency.

Waves don't usually reflect when they strike other waves. Instead, they combine. If the amplitudes of two waves have the same sign (either both positive or both negative), they will add together to form a wave with a larger amplitude. This is called constructive interference. If the two amplitudes have opposite signs, they will subtract to form a combined wave with a lower amplitude. This is called destructive interference.

Sound waves with higher amplitudes sound louder than sound waves with lower amplitudes. Constructive interference will make a sound louder while destructive interference will make a sound quieter.

Two waves that add together may have different frequencies. That means that the crests and troughs won't add up the same way with each new wave because one is moving faster than the other. Part of the waves will interfere constructively and part will interfere destructively.

Energy!!

Energy is the capacity of a system to do work. there are many different forms fo energy. Energy cannot be either created or destroyed. It instead transforms from one form to another. There are many different kinds of energy but however most of them fall under two categories. These two categories are Potential Energy and Kinetic Energy. Now lets look at different kinds of energies.

-Potential Energy is the energy stored in a body or in a system. The SI unit for measurement of energy and work is Joule (J).

-Chemical Energy is the potential of a chemical substance to undergo a transformation through a chemical reaction or to transform other chemical substances.

-Gravitational Energy is energy an object possesses because of its position in a gravitational field.

-Elastic Energy is  stored in objects that are stretched, compressed, bent, or twisted. It is the energy that represents the elastic distortion of a solid or a fluid.

-Kinetic Energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its velocity. it is the energy described in motions of waves, molecules, objects, substances etc. 

-Mechanical Energy is the energy stored in the movement of the objects. Mechanical energy is created by the physical movement or rotation, revolution etc of anything.

-Thermal Energy is the vibration and the movement of atoms and molecules in a substance. It is the total mechanical energy of the particles in a substance.

-Sound Energy is  a wave of vibrations in a material. It is the movement of energy in materials through different kinds of waves.

Best Canon :D

In order to make a perfect canon which has the greatest horizontal range covered, one needs to keep in mind the angle of the barrel which must be 45 degrees above the horizontal. This angle would be perfect in order to make the canon go as further as it could. We can use the following formula in order to determine the angle at which the canon covers the maximum range:

R = V²sin(2θ)/g

Using this formula, we can determine the value of θ that will maximize the value of sin(2θ), which will maximize the range of the projectile since v and g do not change. The maximum value of sin(2θ) is 1, which occurs at sin(90). Therefore the value of θ must be 45 degrees above the horizontal. 

Newton's Problems

1: Equilibriums
Assumption:
-Positive axes
-∑F = 0 ( ∑Fx = 0 , ∑Fy = 0), a = 0
- no friction
- no air resistance
- rope is weightless

When calculating, divide all the force to x-axis and y-axis,
Fx = max        Fy = may
Fx = 0              Fy = 0

2: Inclines
a) object is at rest
Assumptions:
- postive is along the incline direction
- ∑F = 0, a = 0
- no air resistance
- FN is perpendicular to incline
                     ∑F = ma 
∑Fx = max                ∑F = may
∑Fx = 0                       ∑F = 0
Fgx - f = 0                 FN - Fgy = 0

b) object is moving
Assupmtions:
- positive is along the incline direction
- ∑Fy = 0 , ∑F is not equal to 0
- no air resistance
- FN is perpendicular to incline
use the same method of calculation as when object is at rest

3: Pulley
Assumptions:
- polley is frictionless
- rope is frictionless and weightless
- no air resistance
- 2 systems (2 FBDs)
- T1 = T2
- a of the system is the same (ay1 = ay2)

Note that ∑Fx = 0 for both objects
Do the calculation by dividing the foerces into x and y.
4: Trains
Assumptions:
- Use 3FBDs  to find T
- no air resistance
- ay = 0
- cables are weightless
- positive is in the direction of a
- a is consistant

Assume the whole system as an object to calculate the acceleration
Then use 3 FBDs to find tension amoung the masses

Projectile Motion

Projectile motion is a special case of two dimensional motion with constant acceleration. Here, force due to gravity moderates linear motion of an object thrown at certain angle to the vertical direction. The resulting acceleration is a constant, which is always directed in vertically downward direction.

There is a very useful aspect of two dimensional motion that can be used with great effect. Two dimensional motion can be resolved in to two linear motions in two mutually perpendicular directions : (i) one along horizontal direction and (ii) the other along vertical direction. The linear motion in each direction can, then, be analyzed with the help of equivalent scalar system, in which signs of the attributes of the motion represent direction. The x-axis in the projectile motion represents the horizontal direction of the motion and the y-axis represents the vertical axis.

Flight of base ball, golf ball etc. are examples of projectile motion. In these cases, the projectile is projected with certain force at certain angle to vertical direction. The force that initiates motion is a contact force.

Adding vectors!

To add vectors one must follow some simple rules in order to get the answer:

1. We should always set our positive directions before starting to work on the question ( N and E)
2. To make your solution more organized, create a table for x and y components of the vectors
3. Do not forget to add the positive and negative signs. This helps in calculating the total result.
4. After putting all the values for x and y, calculate the total resultant for both the components (x and y)
5. Now you can use the resultants (x and y) to find the hypotenus of the vector and its angle by using Pythagora Theorem
6. Do not forget to write the correct units and to round off the number to the correct number of significant figures
7. Do not forget to write the directions with your final answer (North or South and East or West)

Pythagoran Theorem:

For calculating the angle: