a hydraulic lever uses 2 tubes with a different diameter and a constant pressure to lift weight. the input tube has a radius of 2 . what should the radius of the output tube be in order for the output force to be 16 times the input force

Answers

Answer 1

The radius of the output tube should be one-fourth the radius of the input tube to achieve an output force that is 16 times the input force.

How to determine what should the radius of the output tube be in order for the output force to be 16 times the input force

In a hydraulic lever, the principle of Pascal's law applies, which states that the pressure in an enclosed fluid is transmitted equally in all directions. Based on this principle, we can calculate the required radius of the output tube to achieve the desired output force.

Let's denote the radius of the input tube as r₁ and the radius of the output tube as r₂. According to the principle of Pascal's law, the pressure in the fluid is the same in both tubes.

We can use the formula for pressure in a fluid:

Pressure = Force / Area

The force exerted on the fluid in the input tube is the input force (F₁), and the force exerted on the fluid in the output tube is the output force (F₂). Since the pressure is the same, we can equate the pressure in the input tube to the pressure in the output tube:

F₁ / (π * r₁²) = F₂ / (π * r₂²)

Simplifying the equation:

F₂ = 16 * F₁

Now we can substitute this relationship into the equation:

F₁ / (π * r₁²) = (16 * F₁) / (π * r₂²)

Simplifying further:

r₂² = r₁² / 16

Taking the square root of both sides:

r₂ = r₁ / 4

Therefore, the radius of the output tube should be one-fourth the radius of the input tube to achieve an output force that is 16 times the input force.

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Related Questions

Answer these 2 Circuit Analysis multiple-choice questions: (please explain your reasoning for each answer)

1. It is any source whose value or magnitude is controlled from a functional relationship with another element:

a) Real
b) Ideal
c) Dependent
d)Independent

2.An element can be part of a circuit as long as the relationship between voltage and current between its terminals is known:

a) True
b) False

Answers

1)It is any source whose value or magnitude is controlled from a functional relationship with another element c) dependent. 2) TRUE. An element can be part of a circuit as long as the relationship between voltage and current between its terminals is known.

1) The correct answer is (c) Dependent.

In the given question, the term that best fits the description is "dependent."

A dependent source is a type of electrical or electronic component whose value or magnitude is controlled by a functional relationship with another element in the circuit.

It means that the output of the dependent source depends on the behavior or characteristics of another element within the circuit.

The relationship between the dependent source and the controlling element can be linear or nonlinear, and it affects the overall behavior of the circuit.

On the other hand, a real source (option a) refers to a physical source of energy or signal, such as a battery or a power supply, which provides a fixed value of voltage or current.

An ideal source (option b) is a theoretical concept used in circuit analysis, assuming a source that provides a fixed value of voltage or current without any internal resistance or limitations.

An independent source (option d) is a type of source whose value is not dependent on any other element in the circuit but remains constant.

2) The answer is (a) True.

An element can be part of a circuit as long as the relationship between voltage and current between its terminals is known.

In electrical circuits, the behavior of an element can be described by its voltage-current characteristic, often referred to as the "I-V curve" or "characteristic curve."

The I-V curve represents the relationship between the voltage across the element's terminals and the current flowing through it.

Knowing the voltage-current relationship of an element is crucial for analyzing and understanding its behavior within a circuit.

It allows engineers and designers to determine how the element will respond to different voltage or current inputs and how it will affect the overall circuit operation.

By measuring or calculating the voltage and current values at the terminals of an element, its characteristics can be determined, enabling proper circuit analysis and design.

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