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Q58P

Expert-verifiedFound in: Page 384

Book edition
9th Edition

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

Pages
1624 pages

ISBN
9781133947271

**(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 ${\mathbf{3}}{\mathbf{.}}{\mathbf{60}}{\mathbf{\times}}{{\mathbf{10}}}^{{\mathbf{6}}}{\mathbf{}}{\mathit{N}}{\mathbf{/}}{{\mathit{m}}}^{{\mathbf{2}}}$, will the board break? Determine the convergence set of the given power series.**

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

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

(a)

$\begin{array}{l}\Delta t=0.002s\\ m=1m\\ {v}_{1}=10\text{\hspace{0.17em}}\frac{m}{s}\\ {v}_{2}=1\text{\hspace{0.17em}\hspace{0.17em}}\frac{m}{s}\end{array}$

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

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

(b)

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

Board surface area is equal to:

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

Calculating shear stress

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

(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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