(II) 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?

Verified step by step guidance

1. Calculate the cross-sectional area of the tennis racket string using the formula for the area of a circle, \( A = \pi r^2 \), where \( r \) is the radius of the string. Given the diameter is 1.00 mm, first convert this to meters and then find the radius by dividing by 2.
2. Identify the material properties of nylon, specifically the tensile strength, which is the maximum stress the material can withstand without breaking. This value can be found in material property tables or engineering handbooks.
3. Use the formula for tensile stress, \( \sigma = \frac{F}{A} \), where \( F \) is the force applied and \( A \) is the cross-sectional area calculated in step 1. Rearrange this formula to solve for the maximum force (tension) \( F \) as \( F = \sigma \times A \).
4. To answer part (b), understand that using thicker strings increases the cross-sectional area, which allows the string to withstand a greater force before reaching its tensile strength limit. Thus, to prevent breakage and allow for tighter strings, use thicker strings.
5. Discuss the cause of string breakage when hit by a ball: The impact of the ball causes a high force concentration on a small area of the string, which can exceed the string's tensile strength if the force is too great or the string is too thin, leading to breakage.

Key Concepts

Tension in Strings

Tension is the force transmitted through a string or rope when it is pulled tight by forces acting from opposite ends. In the context of a tennis racket string, the maximum tension is determined by the material properties of the string, its diameter, and the forces applied during play. Understanding how tension affects the performance and durability of the string is crucial for optimizing racket design.

Material Properties

The material properties of a string, such as tensile strength and elasticity, dictate how much force it can withstand before breaking. Nylon, commonly used in tennis racket strings, has specific characteristics that allow it to stretch and absorb impact. Knowing these properties helps in selecting the right string for desired performance and durability.

String Thickness and Breakage

The thickness of a string affects its tension capacity and durability. Thicker strings can generally withstand higher tensions without breaking, while thinner strings may provide more spin and feel but are more prone to breakage under high tension. When considering tighter strings, one must balance the benefits of thickness against the risk of breakage due to increased tension and impact forces.