Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Show that the acceleration of any object down a frictionless incline that makes an angle $θ$ with the horizontal is $a = gsin (θ)$ . (Note that this acceleration is independent of mass.)

Acceleration of an object is $a = gsin (θ)$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of acceleration

The rate at which velocity changes is referred to as acceleration.

Step 2: Determining acceleration of any object down a frictionless incline

Due to the component of gravitational force along the inclined object will move downward with certain acceleration as there is a constant external force on the object along the incline.

If friction is absent then the object will move only due to the component of gravitational force.

As block is at rest perpendicular to the inclined surface, therefore net force perpendicular to the inclined is zero so

$N - mg \sin (90 - θ) = 0$

or $N = mg \cos (θ)$

Along the inclined there is an external force on the system so applying Newton’s second law along the inclined surface

$Net force = mass \times acceleration$

$mg \cos (90 - θ) = ma$

Therefore, $a = g \sin (θ)$

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College Physics (Urone)

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Short Answer

Show that the acceleration of any object down a frictionless incline that makes an angle $θ$ with the horizontal is $a = gsin (θ)$ . (Note that this acceleration is independent of mass.)

Step by Step Solution

Step 1: Definition of acceleration

Step 2: Determining acceleration of any object down a frictionless incline

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College Physics (Urone)

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Short Answer

Show that the acceleration of any object down a frictionless incline that makes an angle θ with the horizontal is a=gsin(θ) . (Note that this acceleration is independent of mass.)

Step by Step Solution

Step 1: Definition of acceleration

Step 2: Determining acceleration of any object down a frictionless incline

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