(II) (a) What is the maximum tension possible in a...

Name: Problem 51, Chapter 9: Physics: Principles with Applications
Uploaded: 2020-12-10T16:17:24-08:00
Duration: 5 min 2 s
Channel: Sarah Mccrumb
Description: (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?

(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?

Key Concepts

Tensile Strength and Maximum Tension

This concept relates to the maximum force that a material, like nylon, can withstand before failure. In the context of a tennis racket string, the maximum tension represents the product of the material’s tensile strength and its cross-sectional area. If the force applied to the string exceeds this limit, the string breaks. This is fundamental in understanding the limits of material performance under tension.

Cross-Sectional Area and Diameter

The cross-sectional area of a string, determined by its diameter, is critical in distributing the applied load. A thicker string (larger diameter) has a greater cross-sectional area, which means that for the same applied tension, the stress (force per unit area) is lower. This makes thicker strings less likely to reach the material's failure point compared to thinner strings, which is essential when aiming for tighter yet durable string setups.

Dynamic Impact Loading and Fatigue

During play, tennis strings are repeatedly impacted by balls, causing rapid load changes and transient high stresses. Such dynamic loading can lead to fatigue, where microscopic defects gradually accumulate and propagate over time. This fatigue process ultimately results in the breaking of the strings. Understanding how dynamic impacts affect materials highlights why material properties and string design are crucial for durability.

Transcript

0:00 Hi, everybody.

00:01 So this question is asking, what is the maximum tension possible in a one -middle -meter diameter nylon tennis racket string? so let's do like a little string here.

00:15 And then we have a diameter of d as 1 millimeters.

00:22 And b, if you want to tighter strings, what do you do to prevent breakage? okay.

00:27 So here, let's just find, we have diameter, and you know the drill is when we find the diameter, we always have to find the radius, okay? it's just one of those things that it's just good.

00:39 Even if you don't need it, it's sometimes one of those things.

00:42 It's just good to find it.

00:43 And it's still going to be one.

00:46 And we're going to convert this really quick to meters because we like meters in this household.

00:55 And so we have 1083 m squared, divide by one millimeter.

01:02 Okay.

01:03 And we're just going to, hoop, hoop.

01:07 Okay.

01:08 And zero point, zero.

01:10 0 .05 meters.

01:13 Okay.

01:14 And so we've got to find the tensile strength of the nylon, okay, which is with f before we begin.

01:20 Then when we do this, we have to find the maximum tension of the nylon tennis racket.

01:26 And we do this again with f over a force.

01:32 So before we do this, we are actually going to be using this equation here.

01:38 F equals a area.

01:40 A is for area.

01:41 Area, and this is going to equal to 500 times 106 in m squared.

01:52 And that's what we're going to use just to solve for a, okay? and that's what we'll be doing.

01:57 We're trying to find f for this equation.

02:00 Okay, so let's start solving...

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