Trabajo

Clasificado en Física

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TEMA : TRABAJO - POTENCIA - ENERGIA

1..Concepto de Trabajo

En la vida diaria, el término trabajo se aplica a toda clase de actividad que demande un esfuerzo, sea éste de origen muscular o intelectual.
Así, levantar un cuerpo, barnizar un mueble, construir un puente o un edificio, planificar una reforma de cualquier índole, escribir un libro, etc. son ejemplos de actividades en que el hombre trabaja.
Sin embargo, en Física el concepto de trabajo se usa en un sentido mucho más restringido.
Diremos que se efectúa trabajo mecánico cuando se vence una fuerza a lo largo de su propia línea de acción.
Este concepto de trabajo implica, pues, como necesarias, las dos condiciones siguientes:
a) una fuerza vencida, y
b) un desplazamiento de ésta a lo largo de su línea de acción
Por lo tanto, no habrá trabajo mecánico cuando cualquiera de estos dos factores sea nulo o no exista.
¿Cómo influyen estos factores en el trabajo realizado?
Si queremos levantar un cuerpo a cierta altura tendremos que vencer su peso efectuando un determinado trabajo. Resulta evidente que si la altura es doble o triple, el trabajo efectuado será también doble o triple. O sea: El trabajo realizado para vencer una fuerza dada es directamente proporcional al desplazamiento que experimenta a lo largo de su línea de acción.
Por otra parte, si queremos levantar un cuerpo de doble o triple peso que el anterior, a la misma altura, el trabajo efectuado será también doble o triple. Luego: El trabajo realizado para vencer una fuerza en un determinado camino a lo largo de su línea de acción es directamente proporcional a la intensidad de la fuerza vencida.

trabajo = fuerza vencida × desplazamiento

Si llamamos T al trabajo, F a la fuerza y d al desplazamiento, entonces tendremos la siguiente fórmula para medir el trabajo.
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1.1 Trabajo y fuerza aplicada
Ahora bien, para vencer una fuerza es necesario aplicar otra en sentido contrario, de manera que cada vez que movemos un cuerpo lo hacemos aplicando una fuerza en sentido contrario a aquéllas que se oponen al movimiento.
Esta fuerza aplicada no siempre tiene la dirección del desplazamiento.
Supongamos, entonces, un cuerpo que se desplaza horizontalmente bajo la acción de una fuerza F, que forma un ángulo a con la dirección del desplazamiento.
La fuerza F se descompone en dos: F1, en la dirección del desplazamiento , y F2, perpendicular a ella. F1 tiende a arrastrar el cuerpo horizontalmente y F2 a levantarlo verticalmente. Como F2 es anulada por el peso del cuerpo, sólo F1 efectúa trabajo.

Por lo tanto: 12710434-4 654321 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O sea:
El trabajo mecánico efectuado por una fuerza para mover un cuerpo se obtiene multiplicando el desplazamiento por la componente de la fuerza en la dirección del desplazamiento.

4.3(20%)3.3(25%)5.6(25%)

Pero el módulo de F1 depende del ángulo a que F forma con la dirección del desplazamiento y, como es una componente de F, se tiene que:

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en que cos a es un factor que indica cómo varía F1 en relación con el ángulo a y cuyo valor es menor o igual a 1.
Por consiguiente, el trabajo mecánico está dado por:

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que representa la expresión más general para medir el trabajo mecánico efectuado por una fuerza.

F2


a F1


d
Sólo efectúa trabajo la componente paralela al desplazamiento

De los diferentes valores de cos a interesan los dos siguientes:

1) Cos a = 1
El factor cos a tiene el valor máximo 1 cuando a vale cero, es decir, cuando la fuerza F y el desplazamiento tienen la misma dirección.
En tal caso, la relación precedente se reduce a T= F × d en la que la fuerza aplicada tiene igual módulo que la fuerza vencida, pero en sentido contrario.

2) Cos a = 0
El factor cos a tiene el valor cero cuando a vale 90º, ó sea, cuando la fuerza F y el desplazamiento son perpendiculares. Pero si cos a = 0, entonces el trabajo efectuado también es cero .Esto significa que no se requiere trabajo para desplazar el punto de aplicación de una fuerza en dirección perpendicular a ella.

1.2 Trabajo en un campo gravitatorio

Si un cuerpo se encuentra libre en un campo gravitacional las fuerzas propias del campo lo aceleran hacia el centro de gravitación correspondiente, de tal modo que ellas realizan el trabajo de trasladar el cuerpo.
Luego, no se requiere trabajo externo para trasladar un cuerpo en el sentido y dirección del campo respectivo. Por el contrario, para trasladarlo en sentido opuesto, es necesario efectuar un trabajo externo contra el peso, o sea contras las fuerzas del campo. Es lo que ocurre cuando levantamos verticalmente un cuerpo; el trabajo efectuado es T = P × h
en que h es la altura correspondiente.
Si el cuerpo lo desplazamos entre dos puntos del campo que tienen igual intensidad, el trabajo es nulo, pues en este caso el cuerpo no ha variado su distancia al centro de gravitación y, por consiguiente, sólo se ha trasladado perpendicularmente a la dirección de las fuerzas del campo.
Es el, caso de un cuerpo que se traslada en un plano horizontal: no se efectúa trabajo para vencer su peso, sino solamente para vencer el roce.

1.3 Unidades de trabajo
En general, de acuerdo con la fórmula, una unidad de trabajo se obtiene multiplicando una unidad de fuerza por una unidad de longitud.
En el sistema SI la unidad se llama joule.

1 joule = 1 newton × 1 m

Un joule es el trabajo efectuado por la fuerza de 1 newton al desplazar su punto de aplicación en 1 m en la misma dirección y sentido de la fuerza.

2 .Concepto de Potencia

En la definición de trabajo, no está incluido el concepto de tiempo. En la práctica, el trabajo se realiza por medio de máquinas o motores que se caracterizan por la mayor o menor cantidad de trabajo que pueden desarrollar en un tiempo determinado, esto es, por su potencia.
Potencia de una máquina o motor es el trabajo que es capaz de realizar por unidad de tiempo.
Esto es:
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Si designamos la potencia por P, tenemos:

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En la práctica, es corriente expresar la potencia como el trabajo ejecutado en un segundo, es decir, se la considera como la rapidez con que se efectúa un determinado trabajo.

2.1 Unidades de potencia
En general, una unidad de potencia se obtiene dividiendo una unidad de trabajo por una unidad de tiempo.
En el sistema SI la unidad se denomina watt.
1 watt = 1 Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000120000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff040000000600000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c000000000000046000000000000000000000000308309c98a05ca0103000000c00500000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000030000008801000000000000feffffff02000000feffffff040000000500000006000000070000000800000009000000feffffff0b000000fefffffffeffffff0e0000000f00000010000000110000001200000013000000fefffffffeffffff16000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020400000000000000000000000000000078011500ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff4c0000000000000000000800450400008c0400006c0200009402000000000000000000000000000000000000e8030000e8030000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff080045048c040e22010009000003b20000000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c022004e0030e00000026060f001200ffffffff000008000000c0ffb9ffa003d9030b00000026060f000c004d617468547970650000e00008000000fa0200001000000000000000040000002d010000050000001402fd014000050000001302fd01960315000000fb0280fe0000000000009001010000000002001054696d6573204e657720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Un watt es la potencia de una máquina que puede realizar el trabajo de 1 joule en cada segundo.
Además se emplea el kilowatt, que es un múltiplo del watt.

1 kw = 1000 w

Por ser esta unidad pequeña, en la práctica se emplea un múltiplo de ella, llamado caballo vapor.
También se utiliza la unidad de potencia inglesa denominada caballo de fuerza o horse power ( hp ).
1 cv = 735 W = 0,735 Kw
1 hp = 746 W = 0,746 Kw

2.2 Otras unidades de trabajo:

Son el watt-hora y el kilowatt-hora.
Un watt-hora es el trabajo realizado en 1 hora por un motor de 1 watt de potencia.
Como 1 watt = 1 joule / seg. y 1 hora = 3600 segundos, se tiene:
1 wh = 1 joule / s × 3600 s
1 wh = 3600 joule
Un kilowatt-hora es el trabajo realizado en 1 hora, por un motor de 1 kw de potencia.
JCVB - FISICA 2004

Puesto que dicho motor efectúa un trabajo de 1000 joule en cada segundo, el trabajo realizado en 1 hora es:
1 kwh = 1000 joule / s × 3600 s
o sea 1 Kwh = 3.600.000 joule

Problema 1: Un motor eléctrico levanta 4410 N a 30 m de altura en 30 segundos.Calcula su potencia en cv.

3. Potencia y velocidad
Es importante considerar y medir también la potencia desarrollada , en un momento dado, por una máquina en movimiento.
Sea F una fuerza continua y constante que actúa sobre un cuerpo en movimiento. Si consideramos un intervalo de tiempo D t , suficientemente pequeño como para estimar instantánea la velocidad, y el camino recorrido D d , en ese intervalo, entonces el trabajo realizado por la fuerza F es:
T = F ×D d

y la potencia instantánea correspondiente será:

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o sea: P = F
×Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000120000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff040000000600000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c000000000000046000000000000000000000000308309c98a05ca0103000000000600000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000003000000c801000000000000feffffff02000000feffffff0400000005000000060000000700000008000000090000000a000000feffffff0c000000fefffffffeffffff0f000000100000001100000012000000130000001400000015000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020400000000000000000000000000000078011500ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff4c0000000000000000000800c102000045040000900100006c02000000000000000000000000000000000000e8030000e8030000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0800c1024504ce44010009000003d30000000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02e00380020e00000026060f001200ffffffff000008000000c0ffb9ff400299030b00000026060f000c004d617468547970650000c00008000000fa0200001000000000000000040000002d010000050000001402fd014000050000001302fd01380210000000fb0280fe0000000000009001000000020002001053796d626f6c0036040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. Pero el cuociente Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000120000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff040000000600000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c000000000000046000000000000000000000000d0090bc98a05ca0103000000000600000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000003000000c801000000000000feffffff02000000feffffff0400000005000000060000000700000008000000090000000a000000feffffff0c000000fefffffffeffffff0f000000100000001100000012000000130000001400000015000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020400000000000000000000000000000078011500ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff4c0000000000000000000800c102000045040000900100006c02000000000000000000000000000000000000e8030000e8030000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0800c1024504ce44010009000003d30000000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02e00380020e00000026060f001200ffffffff000008000000c0ffb9ff400299030b00000026060f000c004d617468547970650000c00008000000fa0200001000000000000000040000002d010000050000001402fd014000050000001302fd01380210000000fb0280fe0000000000009001000000020002001053796d626f6c00360400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representa la velocidad instantánea del cuerpo en movimiento. Luego, la relación anterior se reduce a:

Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000140000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff04000000060000000800000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c000000000000046000000000000000000000000d0090bc98a05ca0103000000c00600000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000030000002802000000000000feffffff02000000feffffff0400000005000000060000000700000008000000090000000a0000000b000000feffffff0d000000fefffffffeffffff1000000011000000120000001300000014000000150000001600000017000000fefffffffeffffff1a000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0100000204000000000000000000000000000000c062ff04ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff4c00000000000000000008003b090000340200003c0500004001000000000000000000000000000000000000e8030000e8030000000000000000000000000000000000000000000000000000ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff08003b093402ce44010009000003fd0000000200150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02000260080e00000026060f001200ffffffff000008000000c0ffc0ff2008c0010b00000026060f000c004d617468547970650000500015000000fb0280fe0000000000009001010000000002001054696d6573204e657720526f6d616e000000040000002d01000009000000320a60016000010000007000c00009000000320a60014104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4. Concepto de Energía
En todos los casos en que se efectúa un trabajo, el ente que lo realiza requiere de algoque le permita disponer de la fuerza necesaria. Así, por ejemplo, cuando el motor de un automóvil quema combustible para poner en movimiento el vehículo, esealgoque le proporciona la fuerza está en el combustible, pero debe quemarlo para disponer de ella. A ese algo se le da el nombre de energía y, por lo tanto, podemos decir que:
Energía de un cuerpo o de un sistema es su capacidad para efectuar trabajo mecánico.
En la práctica, usamos corrientemente el término energía unido a otro que nos permite caracterizarla por su fuente de origen. De este modo, cuando hablamos de:

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estamos señalando diversas formas de energía, asociadas con su fuente de origen.
Tan importante es la presencia de la energía en la naturaleza, que difícilmente puede encontrarse algún fenómeno en el cual no tenga intervención directa o indirecta. Y su vinculación con la materia es tan estrecha que podemos también agregar: la energía no es más que una forma diferente de materia o de comportamiento de ésta.

De cualquier modo, el concepto de energía va siempre tan unido al de trabajo que su medida está dada precisamente por el trabajo que puede realizar el cuerpo que la posee.

Para efectuar la medición es necesario considerar las condiciones bajo las cuales se encuentra el cuerpo, ya que éstas determinan los factores que permiten practicarla.
De los diversos casos que pueden presentarse consideremos los siguientes, que son los más característicos:
a))Cuerpos en movimiento: un proyectil, un vehículo, una corriente de agua, masas de aire en movimiento, etc.En este caso la posibilidad de realizar trabajo depende fundamentalmente de la velocidad con que se desplaza el cuerpo.Así, un proyectil penetra tanto más profundamente cuanto mayor sea su velocidad; una corriente de aire hace girar las aspas de un molino tanto más rápidamente cuanto mayor es su propia rapidez. etc.
b)Cuerpos a cierta altura: una lámpara, un depósito de agua, un avión en vuelo, etc. La posibilidad de efectuar trabajo, ésta vez depende de la altura a que se encuentra el cuerpo. Esta posibilidad se concreta cuando el cuerpo cae, debido al aumento de velocidad que va experimentando. De este modo, el agua de un depósito es capaz de hacer funcionaran turbina si se la deja caer desde una altura que le permita adquirir la velocidad necesaria para ponerla en movimiento.
c)Cuerpos elásticos deformados: un resorte comprimido o estirado, una cuerda de reloj enrollada, un gas comprimido, un arco tenso, etc. En este caso la posibilidad de realizar trabajo depende de las fuerzas de la elasticidad, que impelen al cuerpo a recobrar su forma normal o primitiva. Así, un arco tenso puede lanzar una flecha, el aire comprimido al expandirse acciona las balatas deteniendo al vehículo que pose este tipo de frenos, una cuerda de reloj pone en marcha su mecanismo al desenrollarse lentamente, etc.
d)Cuerpos combustibles y explosivos : el petróleo y sus derivados , las maderas, el carbón, la pólvora, la dinamita, etc. En el caso de los combustibles, la posibilidad de efectuar trabajo depende del calor que producen, y en el de los explosivos, depende de la fuerza expansiva originada por la combustión del material respectivo.

5. Formas de Energía Mecánica
La energía se presenta de diversas formar en la Naturaleza: energía mecánica, calórica, eléctrica, luminosa, etc.
La energía mecánica se manifiesta a su vez en dos formas diferentes: energía potencial o latente y energía cinética o activa.
Un cuerpo posee energía potencial o latente, si debido a su posición, forma, composición química, etc., es capaz de efectuar un trabajo.
En los ejemplos citados, un cuerpo situado a cierta altura posee energía potencial debido exclusivamente a la posición que ocupa. En este caso hablaremos de energía potencial de posición o energía potencial gravitatoria.
Los cuerpos elásticos deformados los distinguiremos como ejemplos de energía potencial elástica y los casos de energía almacenada por un combustible, como ejemplos de energía potencial debido a su composición química.

En cambio, un cuerpo en movimiento puede realizar trabajo debido a su velocidad. Para detenerlo será necesario aplicarle una fuerza que se desplazará a lo largo de un trayecto, realizando un trabajo. En este caso, se habla de energía cinética o activa.
Un cuerpo posee energía cinética si, debido a su velocidad es capaz de efectuar un trabajo.

Tienen energía potencial:
1los cuerpos que se encuentran a cierta altura del suelo o de cualquier nivel de referencia en un campo gravitacional.
2los cuerpos elásticos deformados(resortes comprimidos o estirados, gases comprimidos, etc.)
3los explosivos
4los combustibles ( madera, carbón, petróleo, etc.)
5los alimentos ( combustible de los seres vivos)
6etc.


Tienen energía cinética:
7los cuerpos que caen, en un campo gravitatorio
8los resortes comprimidos o estirados, al ser liberados
9los gases comprimidos, al expandirse
10los explosivos, al ser detonados
11los combustibles, al quemarse
12los alimentos, al ser digeridos
13las corrientes eléctricas
14las corrientes de agua
15los vientos
16etc.

6. Medida de la Energía Potencial Gravitatoria

Supongamos que un cuerpo de peso P cae verticalmente desde una altura h sobre el suelo o respecto de cualquier nivel de referencia.


A

P


h


B


Para llevarlo hasta esa altura fue necesario realizar un trabajo T = P× h equivalente al que el cuerpo es capaz de efectuar al caer nuevamente al suelo.
Este trabajo mide la energía potencial gravitatoria del cuerpo cuando se encuentra a la altura h.
Luego: Ep = P × h


7. Medida de la Energía Cinética
La energía cinética se mide por el trabajo necesario para comunicar a un cuerpo de masa m la velocidad v .
Sobre el cuerpo, inicialmente en reposo, aplicamos la fuerza F, con lo cuál este adquiere la aceleración a , tal que F = m × a


Supongamos que la fuerza actúa sobre el cuerpo durante un tiempo t a lo largo de un camino d, que será recorrido con movimiento uniformemente acelerado, por lo cual:

Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000140000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff04000000060000000800000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c000000000000046000000000000000000000000d0090bc98a05ca0103000000c00700000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000030000008802000000000000feffffff02000000feffffff0400000005000000060000000700000008000000090000000a0000000b0000000c0000000d000000feffffff0f000000fefffffffeffffff12000000130000001400000015000000160000001700000018000000190000001a0000001b000000fefffffffeffffff1e000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020400000000000000000000000000000078011500a013f105080000006d757363756c61721401c0009500a800c0006b00c000950013000000320aa0134c0000000000000000000800b707000045040000600400006c02000000000000000000000000000000000000e8030000e80300000000000000000000000000000000000000000000000000000000320aa013aa19050000007669766f7300a8006b00a800c000950010000000320ae015f10506000000656f6c696361a800c0000800b70745049e30010009000003310100000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02e00300070e00000026060f001200ffffffff000008000000c0ffb9ffc00699030b00000026060f000c004d617468547970650000c00008000000fa0200001000000000000000040000002d010000050000001402fd01da02050000001302fd01ca0315000000fb0280fe0000000000009001010000000002001054696d6573204e657720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Entonces, el trabajo efectuado es T = F × d
o sea: T = m×a×Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000120000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff040000000600000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c00000000000004600000000000000000000000070900cc98a05ca0103000000400500000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000030000008801000000000000feffffff02000000feffffff040000000500000006000000070000000800000009000000feffffff0b000000fefffffffeffffff0e0000000f000000100000001100000012000000fefffffffefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020400000000000000000000000000000078011500a013f105080000006d757363756c61721401c0009500a800c0006b00c000950013000000320aa0134c0000000000000000000800a701000045040000f00000006c02000000000000000000000000000000000000e8030000e80300000000000000000000000000000000000000000000000000000000320aa013aa19050000007669766f7300a8006b00a800c000950010000000320ae015f10506000000656f6c696361a800c0000800a70145048e30010009000003a90000000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02e00380010e00000026060f001200ffffffff000008000000c0ffb9ff400199030b00000026060f000c004d617468547970650000c00008000000fa0200001000000000000000040000002d010000050000001402fd014000050000001302fd01300115000000fb0280fe0000000000009001000000000002001054696d6573204e65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de donde: T =
Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000140000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff04000000060000000800000007000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c00000000000004600000000000000000000000070900cc98a05ca0103000000c00700000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000030000008802000000000000feffffff02000000feffffff0400000005000000060000000700000008000000090000000a0000000b0000000c0000000d000000feffffff0f000000fefffffffeffffff12000000130000001400000015000000160000001700000018000000190000001a0000001b000000fefffffffeffffff1e000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff010000020000000000000000000000000000000078011500a013f105080000006d757363756c61721401c0009500a800c0006b00c000950013000000320aa0134c00000000000000000008009d0600008c040000c00300009402000000000000000000000000000000000000e8030000e80300000000000000000000000000000000000000000000000000000000320aa013aa19050000007669766f7300a8006b00a800c000950010000000320ae015f10506000000656f6c696361a800c00008009d068c043e31010009000003280100000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02200400060e00000026060f001200ffffffff000008000000c0ffadffc005cd030b00000026060f000c004d617468547970650000c00008000000fa0200001000000000000000040000002d0100000500000014023d0240000500000013023d02a60515000000fb0280fe0000000000009001010000000002001054696d6573204e657720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pero el producto a × t = v ( velocidad adquirida por el cuerpo),


luego: T = 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y como la energía se mide por el trabajo realizado, se tiene que:

Equation.301050000020000000b0000004571756174696f6e2e3300000000000000000000160000d0cf11e0a1b11ae1000000000000000000000000000000003e000300feff0900060000000000000000000000010000000100000000000000001000000200000001000000feffffff0000000000000000fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffdffffff05000000feffffff0400000006000000080000000700000009000000fefffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff52006f006f007400200045006e00740072007900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000016000500ffffffffffffffff0400000002ce020000000000c00000000000004600000000000000000000000070900cc98a05ca0103000000400800000000000001004f006c00650000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a000201ffffffffffffffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000001400000000000000030050004900430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000a0002000100000003000000ffffffff000000000000000000000000000000000000000000000000000000000000000000000000010000004c0000000000000003004d004500540041000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000c000201ffffffffffffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000003000000c802000000000000feffffff02000000feffffff0400000005000000060000000700000008000000090000000a0000000b0000000c0000000d0000000e000000feffffff10000000fefffffffeffffff130000001400000015000000160000001700000018000000190000001a0000001b0000001c0000001d000000fefffffffeffffff20000000feffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff0100000204000000000000000000000000000000780115000100000000000000fdffffff000000000000000000000000000000000000000000000000000000004c0000000000000000000800da0700008c040000740400009402000000000000000000000000000000000000e8030000e8030000000000000000000000000000000000000000000000000000fe030000000000000000000000000000feffffffff010000fe030000982ff204fbffffff0000000000000000d068ff04000000000800da078c04a6380100090000034e0100000300150000000000050000000902000000000400000002010100050000000102ffffff00040000002e01180005000000310201000000050000000b0200000000050000000c02200420070e00000026060f001200ffffffff000008000000c0ffadffe006cd030b00000026060f000c004d617468547970650000c00008000000fa0200001000000000000000040000002d0100000500000014023d026c030500000013023d02c80615000000fb0280fe0000000000009001010000000002001054696d6573204e657720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De esta fórmula se desprende que:
1A igualdad de velocidad, las energías cinéticas de dos o más cuerpos son directamente proporcionales a los cuadrados de su velocidades respectivas.
2A igualdad de masa, las energías cinéticas de dos o más cuerpos son directamente proporcionales a los cuadrados de sus velocidades respectivas.
Esto significa que si un cuerpo duplica su velocidad, su energía cinética se cuadruplica; si triplica su velocidad, su Ec aumenta nueve veces, etc..
Digamos, finalmente, que las unidades en que se expresa la medida de la energía mecánica son las mismas en que se mide el trabajo.

8. Principio de Conservación de la Energía Mecánica
Cuando un cuerpo asciende verticalmente, su velocidad va disminuyendo, en forma gradual, hasta hacerse cero, cuando alcanza su altura máxima.
Esto implica, evidentemente, una variación de la energía cinética del cuerpo, que es máxima en el punto de partida y nula en el punto de mayor altura.
Pero a medida que el cuerpo asciende, su energía potencial va aumentando paulatinamente hasta hacerse máxima cuando alcanza su mayor altura.
Esto significa que la energía cinética va transformándose gradualmente en energía potencial, cuando el cuerpo sube, y de igual modo, la energía potencial se transforma en energía cinética, al descender el cuerpo.
Esta transformación es tal que, en cualquier punto de la trayectoria del cuerpo la disminución de Ec equivale al aumento de Ep y viceversa.
En otras palabras, en cualquier punto de la trayectoria se tendrá:
Ec + Ep = constante
Este sencillo ejemplo nos proporciona una clara idea de lo que es el principio de conservación de la energía, que puede enunciarse en los términos siguientes:

En un sistema aislado, la energía mecánica total permanece constante.

Un sistema aislado es aquel en el cuál no se efectúa intercambio de energía con cuerpos ajenos al sistema. A un sistema con esta característica se le llama sistema conservativo.

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