Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

(a) Estimate the force with which a karate master strikes a board, assuming the hand's speed at the moment of impact is 10.0 m / s} and decreases to 1.00 m /s during a 0.00200-s time interval of contact between the hand and the board. The mass of his hand and arm is 1.00Kg.
(b) Estimate the shear stress, assuming this force is exerted on a 1.00cm -thick pine board that is 10.0 cm wide.
(c) If the maximum shear stress a pine board can support before breaking is $3.60 \times 10^{6} N / m^{2}$ , will the board break? Determine the convergence set of the given power series.

$\begin{array}{l} a) F = 4500 N \\ b) S = 4.5 \times 10^{6} \frac{N}{m^{2}} \end{array}$

c) We can see that karate master applies greater shear stress than board can handle, so it will break.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: We are given following data for a karate master striking a board:

(a)

$\begin{array}{l} Δ t = 0.002 s \\ m = 1 m \\ v_{1} = 10 \frac{m}{s} \\ v_{2} = 1 \frac{m}{s} \end{array}$

Calculating the force that karate master use to strike a board:

$\begin{array}{l} F & = m \times a = m \times \frac{Δ v}{Δ t} = m \times \frac{v_{1} - v_{2}}{Δ t} = 1 \times \frac{10 - 1}{0.002} \\ = 4500 N \end{array}$

Step 2: Board dimensions are given by

(b)

$\begin{array}{l} t = 0.01 m \\ 2 = 0.1 m \end{array}$

Board surface area is equal to:

$A = t \times w = 0.01 \times 0.1 = 0.001 m^{2}$

Calculating shear stress

$\begin{matrix} S = \frac{F}{A} \\ = \frac{4500}{0.001} \\ = 4.5 \times 10^{6} \frac{N}{m^{2}} \end{matrix}$

Step 3: Maximum shear stress a pine board can support is equal to

(c)

$S = 3.6 \times 10^{6} \frac{N}{m^{2}}$

We can see that karate master applies greater shear stress than board can handle, so it will break.

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Short Answer

Step by Step Solution

Step 1: We are given following data for a karate master striking a board:

Step 2: Board dimensions are given by

Step 3: Maximum shear stress a pine board can support is equal to

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: We are given following data for a karate master striking a board:

Step 2: Board dimensions are given by

Step 3: Maximum shear stress a pine board can support is equal to

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