Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 15th Edition

Ch 03: Motion in Two or Three Dimensions

Problema 28b

Capitolo 3, Problema 28b

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?

Guida verificata passo dopo passo

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

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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.

Video consigliato:

Percorso guidato

06:48

Intro to Centripetal Forces

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.

Video consigliato:

Percorso guidato

06:18

Intro to Angular Momentum

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.

Video consigliato:

Percorso guidato

07:32

Weight Force & Gravitational Acceleration

Pratica correlata

Domanda del libro di testo

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

views

Domanda del libro di testo

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

Domanda del libro di testo

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

Domanda del libro di testo

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?

Domanda del libro di testo

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

Domanda del libro di testo

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