En la tienda de mascotas "Animalo-T", se desea elevar un elefante de 2,900 kg utilizando una elevadora hidráulica de plato grande circular de 75 cm de radio y plato pequeño circular de 13 cm de radio. ¿Calcula cuánta fuerza hay que hacer en el émbolo pequeño para elevar al paquidermo?

Answers

Answer 1

Answer:

Se requiere una fuerza de 854.473 newtons sobre el émbolo pequeño.

Step-by-step explanation:

Por el Principio de Pascal se conoce que el esfuerzo experimentado por el elefante es igual a la presión ejercida por el plato pequeño. Es decir:

[tex]\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}[/tex] (1)

Donde:

[tex]F_{1}[/tex] - Fuerza experimentada por el elefante, medida en newtons.

[tex]F_{2}[/tex] - Fuerza aplicada sobre el plato pequeño, medida en newtons.

[tex]A_{1}[/tex] - Área del plato grande, medida en metros cuadrados.

[tex]A_{2}[/tex] - Área del plato pequeño, medida en metros cuadrados.

La fuerza aplicada sobre el plato pequeño es:

[tex]F_{2} = \left(\frac{A_{2}}{A_{1}} \right)\cdot F_{1}[/tex]

La fuerza experimentada por el elefante es su propio peso. Por otra parte, el área del plato es directamente proporcional al cuadrado de su diámetro. Es decir:

[tex]F_{2} = \left(\frac{D_{2}}{D_{1}} \right)^{2}\cdot m\cdot g[/tex] (2)

Donde:

[tex]D_{1}[/tex] - Diámetro del plato grande, medido en centímetros.

[tex]D_{2}[/tex] - Diámetro del plato pequeño, medido en centímetros.

[tex]m[/tex] - Masa del elefante, medida en kilogramos.

[tex]g[/tex] - Aceleración gravitacional, medida en metros por segundo cuadrado.

Si sabemos que [tex]D_{1} = 0.75\,m[/tex], [tex]D_{2} = 0.13\,m[/tex], [tex]m = 2900\,kg[/tex] y [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], entonces la fuerza a aplicar al émbolo pequeño es:

[tex]F_{2} = \left(\frac{0.13\,m}{0.75\,m} \right)^{2}\cdot (2900\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)[/tex]

[tex]F_{2} = 854.473\,N[/tex]

Se requiere una fuerza de 854.473 newtons sobre el émbolo pequeño.


Related Questions


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Answers

Answer: No solution

Step-by-step explanation:

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Answer : 36
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Answer:

n = 36

Step-by-step explanation:

4 : 5 = n : 45

It can be also written as :-

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[tex]=> \frac{4}{5} \times 45 = \frac{n}{45} \times 45[/tex]

[tex]=> n = 4 \times 9 = 36[/tex]

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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56.3

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Step-by-step explanation:

Answer:

A boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?: √3170≈56.3 km.

A 25-foot ladder rest against a house at a point 24.1 feet above the ground. How far away from the house is the base of the ladder?: √44.19≈6.65 ft.

Step-by-step explanation:

For these questions, we will need to use the pythagorean theorem: a²+b²=c², where a and b are the legs of the right triangle and c is the hypotenuse.

A boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?

In this question, we are looking for the hypotenuse.

19 and 53 are the legs of the triangle, so we can plug it into the equation:

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361+2809=c²

3170=c²

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56.30275304103699, or approximately 56.3 km.

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25 is the hypotenuse since it is leaning sideways and is the longest side. 24.1 is one of the legs.

In this question, we are looking for one of the legs.

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Check:

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Step-by-step explanation:

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Now we have to,

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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