Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

(a) What is the radius of a bobsled turn banked at $75.0 °$ and taken at $30.0 m / s$ , assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?

(a) The radius is $24.6 m$ .

(b) $36.6 m/s$ is centripetal acceleration.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of Centripetal acceleration

The rate of change of transverse velocity is known as centripetal acceleration.

Step 2: Calculating radius of bobsled turn

(a) The ideal velocity for a banked road is,

$v = \sqrt{R g \tan θ}$

Here, R is the radius of the turn, g is the acceleration due to gravity, and $θ$ is the ideal angle of banking.

Rearranging the above equation in order to get an expression for the radius of the turn,

$R = \frac{v^{2}}{g \tan θ}$

Substitute $30.0 m/s$ for v, ${9.8 m/s}^{2}$ for g, and $75 . 0^{0}$ for $θ$ ,

$R = \frac{{(30.0 m / s)}^{2}}{(9.8 m / s^{2}) \times \tan (75 . 0^{0})} = 24.6 m$

Here, the radius of the bobsled turn is $= 24.6 m$

Step 3: Calculating centripetal acceleration

(a) The centripetal acceleration is,

$a_{c} = \frac{v^{2}}{r}$

Substitute $30.0 m/s$ for v , and $24.6 m$ for r,

$a_{c} = \frac{{(30 m/s)}^{2}}{(24.6 m)} {= 36.6 m/s}^{2}$

Hence, the centripetal acceleration is $36.6 m/s$ .

Step 4: Determining is acceleration seem larger

The proportion of centripetal to gravitational acceleration is,

$\frac{a_{c}}{g} = \frac{{36.6 m/s}^{2}}{{9.8 m/s}^{2}} = 3.7 = 3.7g$

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College Physics (Urone)

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Short Answer

(a) What is the radius of a bobsled turn banked at $75.0 °$ and taken at $30.0 m / s$ , assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?

Step by Step Solution

Step 1: Definition of Centripetal acceleration

Step 2: Calculating radius of bobsled turn

Step 3: Calculating centripetal acceleration

Step 4: Determining is acceleration seem larger

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College Physics (Urone)

Answers without the blur.

Short Answer

(a) What is the radius of a bobsled turn banked at 75.0°and taken at 30.0 m/s, assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?

Step by Step Solution

Step 1: Definition of Centripetal acceleration

Step 2: Calculating radius of bobsled turn

Step 3: Calculating centripetal acceleration

Step 4: Determining is acceleration seem larger

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(a) What is the radius of a bobsled turn banked at $75.0 °$ and taken at $30.0 m / s$ , assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?