(I) A nylon string on a tennis racket is under a tension of 275 N. If its diameter is 1.00 mm, b

step 1 So once again welcome to a new problem. This time we have a tennis racket. We have a tennis rock

(I) A nylon string on a tennis racket is under a tension of...

Key Concepts

Young's Modulus

Young's Modulus is a measure of the stiffness of a material. It is defined as the ratio of stress to strain within the elastic limit of a material and is used to predict how much a material will deform under a given load.

Strain

Strain is the measure of deformation of a material defined as the ratio of change in length to the original length. This dimensionless quantity indicates how much a material has been stretched or compressed relative to its initial size.

Elasticity

Elasticity refers to a material's ability to return to its original shape after an applied force is removed. It is a fundamental property that governs how materials deform under stress and is central to the analysis of deformations under tension.

Tension

Tension is the pulling force transmitted along a string, rope, cable, or similar object. It is the external force applied to a material which causes it to stretch, and calculating its effects requires understanding how force distributes through the material.

Stress

Stress is defined as the force per unit area within a material and is a key concept in understanding how forces act inside substances. It helps in quantifying the internal forces that arise from an externally applied tension or compression.

Transcript

00:01 So once again welcome to a new problem.

00:05 This time we have a tennis racket.

00:09 We have a tennis rocket and then there's a nylon string that just runs across the rocket like that.

00:21 And there's a force of 275 newtons being applied on the rocket.

00:34 And also the string itself has a span or length.

00:42 This is a nylon string has a length of 30 centimeters.

00:48 We can change that to meters right away by dividing by doing a conversion, unit conversion, one meter per 100 centimeters.

01:01 And that gives us 0 .3 meters.

01:04 Also the will given that the nylon itself from a cross -section so if you look at the nylon from this side for example you see a cross -section with the diameter of one millimeter and that's pretty small but we can change that to meters by multiplying one centimeter is in ten millimeters and then shifting that to one meter in a hundred centimeters and that's going to give us 0 .001 meters so that's the cross -section of the nylon and this problem we want to find we want to find the the the change in length when the force is applied.

02:20 So what we're saying is that the initial length is 0 .3 meters.

02:29 And then, you know, when the force is applied, it stretches.

02:34 So there's a force being applied right there.

02:36 And then, you know, the whole string stretches.

02:39 And we want to find out, you know, if this was, if this happened to the, be the initial length.

02:46 And this is the final length.

02:51 Then we're interested in finding the change in length, which is the difference between the final length and the initial length.

02:59 So it's being stretched.

03:07 The concept, the main concept that we're going to use is young modulus, young modulus of elasticity.

03:18 Okay, young modulus of elasticity.

03:22 I was going to say elasticity, but it's elasticity.

03:27 So this is young modulus of elasticity, and it so happens that e is the same as stress over strain.

03:39 And the reason why we're going this route is because we do have information or we can get information about the elasticity of the nylon e...

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