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 29b

3장, 문제 29b

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?

검증된 단계별 안내

First, understand that the acceleration experienced by the astronaut in the centrifuge is due to centripetal acceleration, which is given by the formula: \( a = \frac{v^2}{r} \), where \( v \) is the tangential velocity and \( r \) is the radius of the circular path.

The maximum acceleration experienced by the astronaut's head is given as 12.5g, where \( g \) is the acceleration due to gravity (approximately \( 9.81 \text{ m/s}^2 \)). Therefore, the maximum acceleration \( a_{head} = 12.5 \times 9.81 \text{ m/s}^2 \).

The radius for the head is the full length of the arm, \( r_{head} = 8.84 \text{ m} \). For the feet, the radius is reduced by the height of the astronaut, so \( r_{feet} = 8.84 \text{ m} - 2.00 \text{ m} = 6.84 \text{ m} \).

Using the centripetal acceleration formula, the acceleration at the feet \( a_{feet} \) can be calculated by substituting \( r_{feet} \) into the formula: \( a_{feet} = \frac{v^2}{r_{feet}} \).

Finally, the difference in acceleration between the head and the feet is \( a_{head} - a_{feet} \). Substitute the values of \( a_{head} \) and \( a_{feet} \) to find this difference.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

10m

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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 = v^2/r, where v is the tangential velocity and r is the radius of the circle. In the context of the centrifuge, this concept helps determine the acceleration experienced by different parts of the astronaut's body.

Gravitational Acceleration (g)

Gravitational acceleration, denoted as g, is the acceleration due to Earth's gravity, approximately 9.81 m/s². In hypergravity conditions, accelerations are expressed as multiples of g, such as 12.5g, indicating the force experienced is 12.5 times that of normal gravity. Understanding this helps quantify the extreme conditions astronauts face in the centrifuge.

Relative Motion in Rotating Systems

Relative motion in rotating systems involves understanding how different points on a rotating body experience different accelerations due to their varying distances from the axis of rotation. In the centrifuge, the astronaut's head and feet are at different radii, causing a difference in centripetal acceleration. This concept is crucial for calculating the acceleration difference between the head and feet.

관련 실천

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

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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 in rpm (rev/min) is the arm turning to produce the maximum sustained acceleration?

2272

views

교과서 질문

A railroad flatcar is traveling to the right at a speed of 13.0 m/s relative to an observer standing on the ground. Someone is riding a motor scooter on the flatcar (Fig. E3.30). What is the velocity (magnitude and direction) of the scooter relative to the flatcar if the scooter's velocity relative to the observer on the ground is 18.0 m/s to the right?

3001

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교과서 질문

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?

2074

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교과서 질문

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

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교과서 질문

A 'moving sidewalk' in an airport terminal moves at 1.0 m/s and is 35.0 m long. If a woman steps on at one end and walks at 1.5 m/s relative to the moving sidewalk, how much time does it take her to reach the opposite end if she walks in the same direction the sidewalk is moving?

2204

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