SCIENCE: Energy conversion from hydroelectric power plant to the house

simple energy conversion from hydroelectric power plant to the house

Water-->Turbine-->Generator-->Transformer-->House Circuit Breaker--->House Power line-->Motor-->Electric Fan


Water

Hydropower, hydraulic power or water power is power that is derived from the force or energy of moving water


Turbine

A turbine is a kind of engine that extracts energy from a fluid and used to turn generators

From Latin turbo + binis (whirling object)


Generator

A generator converts mechanical energy into electrical energy


Transformer

An electrical device for changing the voltage of an alternating current


Circuit breaker

A circuit breaker is an automatically-operated electrical switch designed to protect an electrical circuit from damage caused by overload or short circuit


Power line

Power is transmitted through power lines then to wall sockets


Motor

A motor is a device for converting electrical energy into mechanical energy

From Latin motor = mover, "movere" = move


Electric Fan

A fan run by an electric motor used for cooling

SCIENCE: Physics - Charles' law, Gay-Lussac's law, gas law

Charles' law

Also known as the law of volumes, Gay-Lussac's law

V T curve is a straight line

At constant pressure, the volume of a fixed mass of gas varies directly with the absolute temperature

At constant volume, the gas pressure varies directly with the absolute temperature



V1/T1 = V2/T2  ---> if p = constant


p1/T1 = p2/T2  ---> if v = constant


where:

p1 = absolute pressure at point1

p2 = absolute pressure at point2

V1 = gas volume at point1

V2 = gas volume at point2

T1 = absolute temperature at point1

T2 = absolute temperature at point2



1. Problem:

Air occupies a volume of 70 L at 300 K. If the pressure remains constant, find the temperature of the air when the volume increased to 140 L.


find:

T2 = temperature of the air at V2 = 140 L


given:

p = c

V1 = 70 L

T1 = 300 K

V2 = 140 L


solution:

V1/T1 = V2/T2

70/300 = 140/T2

T2 = 300 * 140/70

T2 = 600 K

thus, direct proportion between volume and absolute temperature. The initial volume of 70 L was doubled to 140 L and therefore 300 K is also doubled giving 600 K.




2. Problem:

In a constant volume process, oxygen has a temperature of 80 C under a pressure of 4 atm. If the pressure is halved, calculate the final temperature.


find:

T2 = final temperature


given:

v = c

T1 = 80 + 273

T1 = 353 K

p1 = 4 atm

p2 = 2 atm


solution:

p1/T1 = p2/T2

4/353 = 2/T2

T2 = 353 * 2/4

T2 = 176.5 K ---> T2 also halved when p2 is halved

SCIENCE: Physics - Mechanical work (variable force)

Work

- amount of energy transferred by a force acting through a distance

- Work can be zero even when there is a force


W = S(a b) F * dx


where:

W = mechanical work done

F = variable force applied

dx = differential distance (delta x, change in x)

S(a b) = integral from a to b

a = lower limit, initial point

b = upper limit, final point



1. Springs - as springs get stretched, the harder it is to pull

The car suspension system steel spring has a spring constant of 12 lb/in. Find the work needed to stretch from an initial amount of 2 in to a final amount of stretch of 4 in.


find:

W = work done by stretching the spring 2 in to 4 in amount of stretch


given:

k = 12 lb/in

a = 2 in

b = 4 in


solution:

The force needed to stretch the spring increases as the spring gets extended

F = kx ---> equation1


W = S(a b) F * dx


substituting,

W = S(a b) kx * dx

W = k * S(a b) x * dx

W = 12 * S(a b) x dx

W = 12/2 [x^2, (2 4)]

W = 6 * (4^2 - 2^2)

W = 6 * (16 - 4)

W = 6 * 12

W = 72 in.lb


thus,

W = 1/2 k (b^2 - a^2)  ---> for springs

SCIENCE: Physics - Mechanical work (constant force)

Work

- amount of energy transferred by a force acting through a distance

- Work can be zero even when there is a force


W = (F cos A) * d


where:

W = mechanical work done

F = constant force applied

A = angle between F and d

d = distance travelled as a result of the application of force



1. Force and distance on the same line

A toy cart is placed in a rail that is flat on a table. A pulling force of 10 N is applied resulting in a distance of 2 m travelled by the toy cart. Calculate the work done.


find:

W = work done


given:

F = 10 N

A = 0 degrees

d = 2 m


solution:

W = (F cos A) * d

W = (10 * cos 0) * 2

W = (10 * 1) * 2

W = 20 N m



2. Force is at an angle with the direction of motion

If the force is applied with an angle of 30 degrees, calculate the work done.


find:

W = work done


given:

F = 10 N

A = 30 degrees

d = 2 m


solution:

W = (F cos A) * d

W = (10 * cos 30) * 2

W = 17.3 N m



3. The rail is at an angle of 15 degreees with the table


If (in problem #2) the toy cart is moved down, calculate the work done.


find:

Wd = work done if the toy cart is moved down


given:

F = 10 N

a1 = 30 degrees, angle of the force

a2 = 15 degrees, angle of the rail

d = 2 m


solution:

reference is the rail --> direction of the displacement


A = a1 + a2

A = 30 + 15

A = 45 degrees


Wd = (F cos A) * d

Wd = (10 * cos 45) * 2

Wd = 14.1 N m



If (in problem #2) the toy cart is moved up, calculate the work done.


find:

Wu = work done if the toy cart is moved up


given:

F = 10 N

a1 = 30 degrees, angle of the force

a2 = 15 degrees, angle of the rail

d = 2 m


solution:

reference is the rail --> direction of the displacement


A = a1 - a2

A = 30 - 15

A = 15 degrees


Wu = (F cos A) * d

Wu = (10 * cos 15) * 2

Wu = 19.3 N m

C++ TUTORIAL FOR BEGINNERS: Program to calculate Circumference, Area of a Circle, and the Volume of a Sphere

The Basketball ball of the NBA has a standard dimension of 4.7 inch in radius, 9.4 inch in diameter, 29.5 inches in circumference,  22 ounces (size 7) in weight, and 7.5 - 8.5 pounds per square inch of air pressure.

Objective: Calculation of the Circumference, Area of a Circle and the Volume of a Sphere
Directive: #include <iostream>, #include <cmath>
Namespace: std
Function: main
Variables:
CircleRadius
double CircleCircumference
double CircleArea
double SphereVolume
Data types of variables: double
Statements: cout, cin, return
Input: Radius of the circle
Output:
Circumference of the Circle
Area of the Circle
Volume of the Sphere

C++ source code:

/*
PROGRAM : Circumference, Area of a Circle; Volume of a Sphere
AUTHOR: eternaltreasures
DATE: 2010 September 1
*/

#include <iostream>
#include <cmath>
using namespace std;

#define PI 3.14159
#define NEWLINE '\n'     

int main ()
{

double CircleRadius;
double CircleCircumference;
double CircleArea;
double SphereVolume;


cout << "Enter the Radius of the Circle = ";
cin >> CircleRadius;

// Circumference of a Circle
CircleCircumference = 2 * PI * CircleRadius;
cout << "Circumference of the Circle = " << CircleCircumference;
cout << NEWLINE;

// Area of a Circle
CircleArea = PI * pow(CircleRadius, 2);
cout << "Area of the Circle = " << CircleArea;
cout << NEWLINE;

// Volume of a Sphere
SphereVolume = 4 * PI/3 * pow(CircleRadius, 3);
cout << "Volume of the Sphere = " << SphereVolume;
cout << NEWLINE;

return 0;
}