Question

(II) (a) What is the maximum tension possible in a 1.00 mm diameter nylon tennis racket string? (b) If you want tighter strings, what do you do to prevent breakage: use thinner or thicker strings? Why? What causes strings to break when they are hit by the ball?

Short answer

(a) The maximum possible tension of the racket is 393 N.

(b) If you want a tighter string, you need a thicker string because the tensile strength is constant. If you increase the force, you should increase the area to maintain the constant value of the tensile strength.

During some hard-hit of a ball, the racket breaks if the tensile force exceeds the maximum possible tolerable tensile.

Step-by-step solution

Concepts

For this problem, you should use the relation between the tensile strength, force, and area, which is$\mathbf{t}\mathbf{e}\mathbf{n}\mathbf{s}\mathbf{i}\mathbf{l}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{r}\mathbf{e}\mathbf{n}\mathbf{g}\mathbf{t}\mathbf{h}=\frac{F}{A}$.

Explanation

The diameter of the nylon tennis racket is $d=1.00\mathrm{m}\mathrm{m}=1\times {10}^{-3}\mathrm{m}$.

The cross-sectional area of the racket is $A=3.0\times {10}^{-4}{\mathrm{m}}^2$.

You know that the tensile strength of the nylon is $500\times {10}^6\mathrm{N}/{\mathrm{m}}^2$.

Let F be the maximum possible tensile.

Calculation for part (a)

The area of the racket is $A=\pi {\left(\frac{d}{2}\right)}^2$.

You know that

$\begin{array}{c}\frac{F}{A}=\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\\ \frac{F}{\pi {\left(\frac{d}{2}\right)}^2}=\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{g}\mathrm{t}\mathrm{h}\\ \frac{F}{\pi {\left(\frac{1.00\times {10}^{-3}m}{2}\right)}^2}=500\times {10}^6\mathrm{N}/{\mathrm{m}}^2\\ F=393\mathrm{N}\end{array}$.

Hence, the maximum possible tension of the racket is 393 N.

Calculation for part (b)

If you want a tighter string, you need a thicker string because the tensile strength is constant. If you increase the force, you should increase the area to maintain the constant value of the tensile strength.

During some hard-hit of a ball, the racket breaks if the tensile force exceeds the maximum possible tolerable tensile.