UNIVERSIDAD PRIVADA DE TACNA FACULTAD DE INGENIERÍA ESCUELA PROFESIONAL DE INGENIERÍA CIVIL
TALLER HIDROSTÁTICA CURSO: FÍSICA II ALUMNO: Gutiérrez Manrique, Juan Jesús DOCENTE: ING JENNY HUAYTA CICLO: III SECCIÓN: “D”
TACNA – PERÚ
2018
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TALLER DE HIDROSTÁTICA UTIERREZ MANRIQUE, JU AN JESUS APELLIDOS Y NOMBRES: G NOMBRES: GUTIERREZ 1. Una esfera uniforme de plomo y una de aluminio tienen la misma masa ¿Qué relación hay entre el radio de la esfera de aluminio y el radio de la esfera de plomo? SOLUCIÓN:
= 43 = 43 4 = 4 3 3 = = 11.3 10 2.7 10 =1.61
2. La ventana de una oficina tiene 3.43 m por 2.08 m. Como resultado del paso de una una tormenta, la presión del aire exterior decae a 0.962 atm, pero en el interior la presión se mantiene en 1.00 atm. ¿Qué fuerza neta empujará a la ventana hacia afuera? SOLUCIÓN
= = 10.962 10.962 7.1344 = 3849. 3849.4 7.1344 344 = 2.7575 10 3. Se está diseñando una campana de de buceo que resista resista la presión del mar a 250m 250m de profundidad. a) Cuánto vale la presión manométrica a esta profundidad. b) Que fuerza neta ejerce el agua de mar sobre la ventanilla circular de 30 cm de diámetro, si l a presión dentro de la campana de buceo es de 1 atm. SOLUCIÓN
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= 2.52 1010
b)
= = =0.15 2.52 10 101300 = 1.7171 10 4. Una caja herméticamente herméticamente cerrada con una tapa de 7,74x10-3 m2 se le aplica un vacío vacío parcial. Se requiere una fuerza de 480,4 N para retirar la tapa de la caja siendo la presión del exterior igual a la presión atmosférica ¿Cuál es la presión dentro de la caja? SOLUCIÓN
= = = = =101300 7.74480. 104 − = 3.9292 10 5. Una presión de 4 N/mm2 sobre la piel es dolorosa. Un clavo clavo puede tener una superficie de 1 mm2. Si un faquir tiene un peso de 700 N, ¿cuál es el menor número de clavos que debe utilizar para no experimentar dolor? ¿Por qué debe ser muy cuidadoso cuando se acueste o levante de una de tales camas? SOLUCIÓN
-
= = 10700 − = 7 1010
Vemos cuántas cuántas veces veces es mayor la presión sobre sobre un solo clavo clavo que la presión máxima sin dolor sobre todos los clavos.
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6. Se puede usar un barómetro básico para para medir la altura de un edificio. Si las lecturas lecturas barométricas en las partes superior e inferior del edificio son de 730 y 755 mm Hg, respectivamente, determine la altura del edificio. Suponga una densidad promedio del aire de 1.18 kg/m3. SOLUCIÓN
11325 = 730 730 760 = 9732 97325.5.32 11325 = 750 750 760 = 99991 99991..78 → = ℎ 97325.32 ℎ = 99991.1.7188 9.8 ℎ=230.35 7. A menudo los globos globos se llenan con con gas helio porque porque pesa sólo alrededor de un séptimo de lo que pesa el aire en condiciones idénticas. La fuerza de flotación, la cual se puede expresar como E= fluido.Vfluido.g, impulsará al globo hacia arriba. Si éste mide 10 m de diámetro y transporta dos personas, de 70 kg cada una, determine la aceleración del globo cuando se acaba de liberar. Suponga que la densidad del aire es de aire =1.16kg/m3, y desprecie el peso de las cuerdas y la canastilla. SOLUCIÓN
= ℎ = = = = 43 5 140 [ 1. 1 6 14 0 ] ] 9. 8 = 140 =32072 8. Una espuma espuma de plástico (= 0.58 g/cm3) se usa como salvavidas. ¿Qué cantidad de
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SOLUCIÓN
80 = 1040 = 0.077 077 = 0.077 077 80% 80% = 0.0616 0616 = = 0.0616 1000 10 = 616 = 80 10 = 800 800 = =800616 = 184 184 = 1000 10 = 1000 184 10 = 0.0184 0184 9. Se usa una grúa grúa para bajar objetos pesados en el mar (densidad= 1 025 kg/m3) para un un proyecto de construcción submarina. Determine la tensión en el cable de la grúa debida a un bloque rectangular de concreto de 0,4x0,4x3 m (densidad =2 300 kg/m3) cuando está a) suspendido en el aire y b) sumergido totalmente en el agua.
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10. De un globo de helio de volumen 20 litros cuelga cuelga una cuerda de densidad lineal lineal 10 gr/m, tal y como muestra la figura (el globo está en reposo). Si la masa del globo deshinchado es 20 gr, la densidad del helio 0.2 kg/m3 y la del aire 1.3kg/m3, calcular la l ongitud h(en m) de la parte de la cuerda que queda vertical. (g=10m/s2) SOLUCIÓN
= 0 = = ℎ = 0 ℎ = 102 ℎ = 0.2 11. Un bloque de volumen 0.002 m3 y densidad 300Kg/m3 . Determinar la deformación del resorte de coeficiente de elasticidad K=100N/m. SOLUCIÓN
= = 100 = = 300 9.8 0.002 = 0.059 12. ¿Qué tiempo empleará un cuerpo de masa 8 kg y densidad 800 kg/m3 en llegar a la superficie libre del agua, si se deja en libertad en el punto A mostrado en la figura? (g =9.8 m/s2). SOLUCIÓN
= ( ) = = 1000800 800 =2.45
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2. 4 5 20= 2 = 4.04 13. Una esfera hueca de aluminio flota a la mitad sumergida en agua. El radio exterior de la esfera es de 50 cm. Hallar el radio interior de la esfera. ( ) SOLUCIÓN
= 2700 2700 /3 /3
=50 = 2700 ∑=0 = ∗ ∗ = ∗ ∗ ∗ 12 ∗ 43 =∗ = 43 43 ∗ 12 43 = ∗ 43 ∗ ∗ = ∗ ∗ 12 = 1 =1 1000 =501 2 ∗ 2700 2700
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15. Una mujer de 50.0 kg se equilibra sobre un par de zapatillas con tacón de aguja. Si el tacón es circular y tiene un radio de 0.500 cm, ¿Qué presión ejerce sobre el piso? SOLUCIÓN
16. Determine la masa de la atmósfera de la Tierra, si su radio es de 6.37 x 106 m y la la presión atmosférica en la superficie es . SOLUCIÓN
1.013 10 / = 4 = 4 ∗ 3.1416 416 ∗ 6.37∗10 = 509.904∗ 04 ∗ 10 =∗ =1.013∗10 ∗509.904∗10 =516.5327∗10 516. 5 327∗10 = = 9.8/ =52.7∗10
17. Un medidor de presión tiene un resorte de constante de fuerza igual a 1000 N/m y su pistón tiene un diámetro de 2.00 cm. A medida que el manómetro se baja dentro del agua, ¿Qué cambio en profundidad hace que el pistón se mueva 0.500 cm? SOLUCIÓN
=1000 =2 =0.01 = ==3.3.114.416∗ 41616∗6 ∗∗ 100.−01 =0. 0 05 ℎ = ∗
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SOLUCIÓN
= = +∗∗ℎ = ∗∗ℎ∗ 600 − 780∗8∗ 9.8 ∗ 25∗10− = 800∗10 = 30.87 19. Dos manómetros, uno de carátula y otro de tubo en U, están sujetos a un tanque de gas para medir supresión. Si la lectura l ectura en el manómetro de carátula es de 125 kPa, determine la distancia entre los dos niveles del fluido en el de tubo en U, si el fluido es e s a) mercurio ( = 13 600 kg/m3), b) agua ( = 1 000 kg/m3).
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muestra en la figura. La presión atmosférica local es de 0.97 bar y la aceleración gravitacional es de 9.8 m/s2. a) Determine la presión en el interior del cilindro. b) Si se transfiere algún calor al gas y su volumen se duplica, ¿esperaría que cambiara la presión en el interior del cilindro?
SOLUCIÓN
=60 =0.04 =97000∗ = +
=97000+ 60∗9.8 0.04
=97000+14715 =11175 21. La presión sanguínea máxima en el antebrazo de una persona sana es de alrededor de 120 mm Hg. Se conecta a la vena un tubo vertical abierto a la atmósfera, en el brazo de una persona. Determine la altura hasta la que ascenderá la sangre en el tubo. Tome la densidad de la sangre como 1 050 kg/m3.
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= 1050 = 9.8 ℎ =? = 15997 ℎ = ∗ 15997 ℎ = 1050 9. 8 ∗ ℎ=1.55 22. Un submarino navega a una profundidad oceánica de 1000 m. Suponga que la densidad del agua de mar es 1024 kg/m3 y el aire arriba ejerce una presión de 101,3 KPa. Calcule: a) La presión absoluta a dicha profundidad y b) A esta profundidad, ¿Qué fuerza debe ejercer el marco alrededor de una ventanilla submarina circular que tiene 30cm de diámetro para contrarrestar la fuerza que ejerce el agua? SOLUCIÓN a)
b)
= +∗∗ℎ =101300+1024∗9.8+1000 =101.362∗10 =1.01∗10 óó é é = 101. 101.362 362 ∗ 10 1.01∗10 =0.30 =0.15 = 3.1=416∗ 4160.0∗70.15 =100.352∗10 = óó é é ∗ ∗0.07 =7.09∗10
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1500∗3 = 200 =225 24. Para el sótano de una nueva casa, se cava un hoyo en el suelo con lados verticales que bajan 2.40 m. Una pared de cimiento de concreto se construye horizontal a los 9.60 m de ancho de la excavación. Esta pared de cimiento mide 0.183 m desde el frente del hoyo del sótano. Durante una tormenta, el drenaje de la calle llena el espacio enfrente de la pared de concreto, pero no el sótano detrás de la pared. El agua no se filtra en el suelo de arcilla. Encuentre la fuerza que ejerce el agua sobre la pared de cimiento. En comparación, la fuerza gravitacional que se ejerce sobre el agua es (2.40 m) (9.60 m) (0.183 m) (1000 kg/m3 ) (9.80 m/s2 ) = 41.3 KN.
SOLUCIÓN Para hallar la fuerza del lado A de la piscina, es necesario conocer la presión media en el costado y el área del costado A de la piscina. Presión media =
..ℎ . Presión media = ∗ 1 ∗ ∗ ∗2.4 Presión media = 11760 N/ Área costado A = ancho * alto
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SOLUCIÓN
a) P =
= = = ∫ = =1000 ∗9.8 ∗2∗ 32 b)= 294=∗ 1010 = = ∫ 1 ῒ = 1 ῒ
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27. En un tubo de U se vierte mercurio, como se muestra en la parte a de la Figura 3. El brazo izquierdo del tubo tiene área de sección transversal A1 de 10.0 cm2 y el brazo derecho tiene un área de sección transversal A2 de 5.00 cm2 . A continuación se vierten 100 g de agua en el brazo derecho como se muestra en la parte b de la Figura 3. Determine: a) La longitud de la columna de agua en el brazo derecho del tubo en U y b) Dado que la densidad del mercurio es 13.6 g/cm3 , ¿Qué distancia h se eleva el mercurio en el brazo izquierdo?
SOLUCIÓN
ℎ=20∗10 = ∗− ∗ ℎ = + ∗∗ℎ = + ℎ ∗ ℎ ℎ = ℎ =1.47∗10− c) ∗ ℎ = ∗ ℎ ℎ = ℎ = ℎ a)
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ℎ=0.76060.002 ℎ=0.7586 29. Un globo ligero se llena l lena con 400 m3 de helio. A 0° C el globo puede levantar una carga. Determine: a) La masa que puede levantar y b) La carga que puede levantar el globo si se llena con hidrógeno. Datos: He = 1.79 x 10-1 kg/m3 y Hi = 8.99 x 10-2 kg/m3 Datos:
SOLUCIÓN
=1.79∗10− =8.99∗10− ℎ ℎ== 1.79∗ 79 ∗ 10− ∗ 400 ℎ ℎ = 71. 71.6 ℎ=8.99∗10 − ∗ 400 ℎ ℎ = 35. 35.96
30. Una plancha de hielo flota en un lago de agua dulce ¿Qué volumen mínimo debe tener para que una mujer de 45 Kg pueda pararse en ella sin mojarse m ojarse los pies? SOLUCIÓN
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9.8 = 1000 10002.29×10 2.29×10−9. = 2.2525 = =2.250.189 = 2.061 32. En la Figura 4, la fuerza gravitacional que se ejerce sobre un objeto sólido es 5.00 N. Cuando el objeto se suspende de una balanza de resorte y se sumerge en agua, la lectura en la balanza es 3.50 N. Encuentre la densidad del objeto.
SOLUCIÓN
==× 5 = 9.8 = 0.51 += 3.50+××=× 3.5+1000××9.8=0.51×9.8
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SOLUCIÓN
0.1 =1.2×10− = 0.12 20.0.10. 0.055 = 101.3×10− + 1000 10009.9.80. =1.0179×10
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SOLUCIÓN
==× ××=× 1000 1000 × ℎ =× 1000 10000.2×0.2 0.2×0.20.20 0.20 = 650 6508×10 8×10− = 0.07 + = = × × = 1000650 10006500.0.2 = 2.8080 35. ¿Cuántos metros cúbicos de helio se requieren para levantar un globo con una carga de 400 kg