Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 03: Motion in Two or Three Dimensions

문제 26b

3장, 문제 26b

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the radial acceleration of the blade tip expressed as a multiple of g?

검증된 단계별 안내

First, understand that radial acceleration, also known as centripetal acceleration, is given by the formula:

a = ω^{2} r

, where

ω

is the angular velocity in radians per second and

r

is the radius.

Convert the angular velocity from revolutions per minute to radians per second. Use the conversion factor:

1 rev = 2 π rad

and

1 \min = 60 s

Calculate the angular velocity

ω

using the formula:

ω = 550 \times 2 π / 60

Substitute the values of

ω

and

r

(which is 3.40 m) into the radial acceleration formula:

a = ω^{2} \times 3.40

Finally, express the radial acceleration as a multiple of

g

(where

g = 9.81 m/s ²

) by dividing the calculated radial acceleration by

g

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Centripetal Acceleration

Centripetal acceleration is the acceleration experienced by an object moving in a circular path, directed towards the center of the circle. It is calculated using the formula a_c = ω²r, where ω is the angular velocity and r is the radius of the circle. This concept is crucial for determining the radial acceleration of the helicopter blade tip.

Angular Velocity

Angular velocity is a measure of how quickly an object rotates around a central point, expressed in radians per second. It is calculated by converting revolutions per minute (rev/min) into radians per second using the formula ω = 2π × (rev/min) / 60. Understanding angular velocity is essential for calculating centripetal acceleration.

Gravitational Acceleration

Gravitational acceleration, denoted as g, is the acceleration due to Earth's gravity, approximately 9.81 m/s². When expressing radial acceleration as a multiple of g, it involves dividing the calculated centripetal acceleration by g to find how many times greater the radial acceleration is compared to gravitational acceleration.

관련 실천

교과서 질문

The earth has a radius of 6380 km and turns around once on its axis in 24 h. If a_rad at the equator is greater than g, objects will fly off the earth's surface and into space. (We will see the reason for this in Chapter 5.) What would the period of the earth's rotation have to be for this to occur?

4555

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교과서 질문

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. How fast must the astronaut's head be moving to experience this maximum acceleration?

2337

views

교과서 질문

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. How fast in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

2272

views

교과서 질문

At its Ames Research Center, NASA uses its large '20-G' centrifuge to test the effects of very large accelerations ('hypergravity') on test pilots and astronauts. In this device, an arm 8.84 m long rotates about one end in a horizontal plane, and an astronaut is strapped in at the other end. Suppose that he is aligned along the centrifuge's arm with his head at the outermost end. The maximum sustained acceleration to which humans are subjected in this device is typically 12.5g. What is the difference between the acceleration of his head and feet if the astronaut is 2.00 m tall?

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the linear speed of the blade tip, in m/s?

4040

views

교과서 질문

The earth has a radius of 6380 km and turns around once on its axis in 24 h. What is the radial acceleration of an object at the earth's equator? Give your answer in m/s² and as a fraction of g.

3288

views