Chapter 9, Problem 50P

To determine

Maximum tensile force that nylon string can withstand.

The string which has to be used to prevent breakage.

Cause for breaking of string when they are hit by the ball.

Answer to Problem 50P

Solution:Maximum tensile force that nylon string can withstand is $392.5N$ .

To avoid breakage, strings should be thicker. Breakage happens when the strings are hit by a force which is greater than $392.5N$ .

Explanation of Solution

Given:

The diameter of nylon string, $d=1.00\text{ mm}$

Formula Used:

Tensile force that nylon string can withstand before breaking is given by stress formula

  $\begin{array}{l}\sigma =\frac{F}{A}\\ F=\sigma A\end{array}$

Where, A is the area of cross section, F is the required tensile strength, stress is the ultimate tensile strength of nylon here.

Calculation:

Cross-sectionalarea:

  $\begin{array}{l}A=\frac{\pi d^2}{4}\\ A=\frac{\pi {(1\times 10^{-3})}^2}{4}\\ A=7.85\times 10^{-7}{\text{ m}}^2\end{array}$

The ultimate tensile strength for nylon is $\sigma =5.00\times {10}^8{\text{N/m}}^2.$

Tensile force is given by

  $\begin{array}{l}F=\sigma A\\ F=5\times 10^8\times 7.85\times 10^{-7}\\ F=392.5N\end{array}$

Maximum tensile force that nylon string can withstand is $392.5N$ .

To prevent breakage, more thick strings must be used, which would increase the cross-sectional area of the strings, and thereby increment the maximum force. Area is directly related to the force. So, a thicker string will cause more force.

Breakage happens because the strings are hitwith a force which is greater than $392.5N$ .

Conclusion: Maximum tensile force that nylon string can withstand is $392.5N$ . To prevent breakage, thicker strings should be used, breakage occurs because when the strings are hit force which is greater than 392 N.