Introduction to tensile stress

Summary

In this educational video, the concept of stress is introduced as force per unit area, using a relatable scenario of two ropes with different diameters to illustrate the idea. The video explains how stress increases with a smaller cross-sectional area and introduces 'ultimate strength' as the maximum stress a material can withstand before breaking. Through a practical example involving ropes and weights, the lesson demonstrates how to calculate the breaking point of objects made of the same material without physical testing, highlighting the importance of understanding material properties in engineering and physics.

Takeaways

• 😀 The video is an educational lesson from dapps Academy on the concept of stress and its relation to material failure.
• 🔍 The example of two strings with different diameters is used to illustrate the concept of stress and how it affects the breaking point of an object.
• 📏 The first string with a 0.1-inch diameter breaks under 100 pounds, which is used to calculate the ultimate strength of the material.
• 📐 Stress is defined as force per unit area, and understanding this helps in predicting when an object will fail under pressure.
• 🌳 The video uses the analogy of choosing between a thick and thin rope to climb down from a tree, emphasizing the intuitive understanding of stress.
• 🔢 The formula for stress is force divided by the cross-sectional area, which is crucial in determining the stress a material experiences.
• 🔍 The video explains that the units for stress can be pounds per square inch (PSI) or Newtons per square meter (Pascals).
• 🏗️ Ultimate strength is the maximum stress a material can withstand before breaking and is a material property.
• 📉 The ultimate strength of the material is calculated using the area of the cross-section of the 0.1-inch diameter string and the force at which it broke.
• 🔄 Since both strings are made of the same material, they share the same ultimate strength, which is used to calculate the breaking force of the 0.2-inch diameter string.
• 📚 The video concludes by solving the initial riddle, showing that the 0.2-inch diameter string can hold four times the weight (400 pounds) before breaking, due to its larger cross-sectional area.

Q & A

What is the main topic of the lesson in the provided transcript?

The main topic of the lesson is understanding stress and determining when an object will break.

What is the first vocabulary word introduced in the script, and what does it describe?

The first vocabulary word introduced is 'stress,' which describes force per unit area.

Why would a person trust a thick rope more than a thin one when climbing down from a tree?

A person would trust a thick rope more because it has a larger cross-sectional area, resulting in less stress compared to a thin rope when the same force is applied.

What is the unit for stress commonly used in the script?

The common units for stress mentioned in the script are PSI (pounds per square inch) and Pascal (Newtons over square meters).

What is 'ultimate strength' in the context of materials?

'Ultimate strength' is the maximum amount of stress a material can take before it breaks.

What is the method to calculate the cross-sectional area of a circular object?

The cross-sectional area of a circular object is calculated using the formula π times the radius squared (A = πr^2).

How did the script determine the ultimate strength of the 0.1 inch diameter string?

The ultimate strength was determined by dividing the maximum force that broke the string (100 pounds) by its cross-sectional area (.0025π square inches).

What is the relationship between the diameters of the two strings and the force required to break them?

The second string with a diameter of 0.2 inches can withstand a force four times greater than the first string (0.1 inch diameter) because its cross-sectional area is four times larger.

How much weight can the 0.2 inch diameter string hold before breaking, according to the script?

The 0.2 inch diameter string can hold 400 pounds before breaking, which is four times the weight that broke the 0.1 inch diameter string.

What is the significance of the ultimate strength being a material property?

The significance is that two objects made of the same material will have the same ultimate strength, regardless of their size or shape.

What is the humorous twist at the end of the script, and how does it relate to the lesson?

The humorous twist is that the video, expected to have a punchline for April Fools' Day, instead provides a lesson on physics, which is an unexpected yet educational outcome.

Outlines

00:00

🔍 Introduction to Stress and Ultimate Strength

This paragraph introduces the concept of stress in a physics context, distinguishing it from the emotional stress. Stress is defined as force per unit area, and the importance of the cross-sectional area in determining the stress on an object is highlighted. The paragraph uses the example of choosing between a thick and thin rope to illustrate the concept of stress intuitively. It also introduces the term 'ultimate strength,' which is the maximum stress a material can withstand before breaking. The video script sets up a problem involving two strings of the same material with different diameters and asks viewers to predict the breaking point of the thicker string based on the thinner one's breaking weight.

05:02

📚 Calculation of Breaking Force for Different Diameters

The second paragraph delves into the calculation of the force required to break a string with a diameter of 0.2 inches, given the breaking force of a 0.1-inch diameter string. It explains the process of finding the ultimate strength of the material by using the area of the cross-section of the 0.1-inch string and the force at which it broke. The ultimate strength is then used to calculate the force needed to break the 0.2-inch string, revealing that it can withstand four times the weight of the thinner string. The paragraph concludes with a light-hearted reference to April Fools' Day, indicating that the video's content was more educational than expected.

Keywords

💡Stress

Stress, in the context of the video, refers to the force applied per unit area. It is a fundamental concept in physics and engineering to understand the strength of materials. The video defines stress as the ratio of force to the cross-sectional area over which that force is distributed. This concept is crucial in determining when an object will break under load. For example, the video uses the scenario of choosing between a thick and a thin rope to climb down from a tree, illustrating that the thick rope, with a larger cross-sectional area, will experience less stress for the same force, making it a safer choice.

💡Ultimate Strength

Ultimate strength is the maximum amount of stress a material can withstand before it fails or breaks. It is a material property and is essential in engineering to ensure that structures are designed to handle the expected loads. In the video, ultimate strength is used to calculate the force at which a string made of a certain material will break. The concept is demonstrated by determining the breaking force of a second string with a different diameter but made of the same material, using the ultimate strength as a constant value.

💡Cross-Sectional Area

The cross-sectional area is the area of a slice of an object taken perpendicular to the direction of a force acting on it. It is critical in calculating stress, as stress is the force divided by this area. The video explains that a larger cross-sectional area results in lower stress for the same force applied, which is why a thicker rope is preferred for safety. The calculation of the area of a circle (pi times the radius squared) is used to find the cross-sectional area of the strings in the example.

💡Diameter

Diameter is a measure of the distance across the widest part of an object, such as a string or rope. In the video, the diameter of the strings is used to calculate their cross-sectional areas and to determine the stress they experience under load. The difference in diameter between the two strings (0.1 inches and 0.2 inches) is a key factor in the problem-solving process to find out how much weight each can support before breaking.

💡Force

Force is a push or pull upon an object that has the potential to cause a change in its motion or shape. In the context of the video, force is what is applied to the strings in the form of weights, and it is the numerator in the stress formula (force per unit area). The video uses the example of hanging weights on a string to demonstrate how increasing force can lead to the string breaking, indicating the limit of stress the material can handle.

💡Pounds per Square Inch (PSI)

Pounds per square inch (PSI) is a unit of pressure or stress used to quantify the force applied over a unit area of one square inch. The video mentions PSI as one of the common units for stress, which helps in comparing the stress experienced by different materials or structures. The ultimate strength of a material can be expressed in PSI, which is useful in engineering to design objects that can withstand certain pressures.

💡Pascal

A Pascal is the SI unit of pressure or stress, defined as one newton per square meter. The video mentions Pascal as an alternative unit for stress, equivalent to one newton per square meter. It is used in scientific contexts where the metric system is preferred, and it provides a standardized way to measure stress across different systems.

💡Material Property

A material property is a characteristic of a substance that defines its behavior under various conditions, such as stress, temperature, or chemical exposure. In the video, ultimate strength is highlighted as a material property because it is an intrinsic quality that determines how a material will respond to stress. The same material property applies to both strings in the example, allowing for the comparison of their breaking points.

💡Area of a Circle

The area of a circle is calculated using the formula pi times the radius squared (A = πr^2). This formula is essential in the video to determine the cross-sectional area of the strings, which is then used to calculate the stress they experience. The area calculation is a fundamental step in solving the problem of how much weight each string can support.

💡Physics Lesson

The term 'physics lesson' refers to the educational content provided in the video, which is centered around the principles of physics, specifically stress and ultimate strength. The video uses a practical example to teach these concepts, making the lesson relatable and understandable. The 'physics lesson' is the main theme of the video, with the problem-solving process serving as the lesson's practical application.

Highlights

Introduction to a basic lesson on stress and determining when an object will break.

Illustrative example of two strings of different diameters made of the same material to demonstrate stress.

Definition of stress as force per unit area, with an intuitive example comparing thick and thin ropes.

Explanation of why the thick rope is preferred despite the same force acting on both ropes due to lower stress.

Introduction of units for stress, including PSI (pounds per square inch) and Pascal (Newtons per square meter).

Definition of ultimate strength as the maximum stress a material can withstand before breaking.

Use of a chart to show ultimate strengths of common materials.

Solving the problem of determining the breaking weight of the 0.2 inch diameter string without physical testing.

Calculation of the cross-sectional area of the 0.1 inch diameter string using the formula for the area of a circle.

Determination of the ultimate strength of the material by dividing the breaking force by the cross-sectional area.

Understanding that ultimate strength is a material property, so objects of the same material have the same ultimate strength.

Calculation of the cross-sectional area for the 0.2 inch diameter string and comparison with the smaller string.

Equation setup to find the force required to break the 0.2 inch diameter string based on the ultimate strength.

Conclusion that the 0.2 inch diameter string can hold four times the weight before breaking compared to the 0.1 inch string.

Acknowledgment that the lesson covers only the basics of stress and provides a simplified approach.

A humorous ending to the lesson, revealing it as an April Fools' Day video with an unexpected physics lesson instead of a punchline.

Transcripts

welcome to dapps Academy and in this

lesson we are going to be taking a basic

look at stress and how to determine when

an object will break

imagine you have two strings made of the

same material hanging from the ceiling

one string has a diameter of 0.1 inches

and the other one has a diameter of 0.2

inches you start to tie increasingly

heavy weights on the 0.1 inch string and

you find that the string finally breaks

once you place a hundred pounds on it

the without physically testing the other

string how much weight can you put on it

until it breaks now at first this may

seem like a riddle with a trick answer

or something but I'm going to show you

how to solve this problem

so firstly before we solve this we need

to learn two vocab words the first one

is stress stress no it's not the feeling

you get before a big test or when you

realize your dad is never going home by

the way I have a video for that stress

is a term used to describe force per

unit area now I know that might sound

confusing at first but believe it or not

you should already have an intuitive

sense of what stress is let me show you

in another example

imagine you were stuck in a very high

tree and you want to get down to your

right there is a branch with a thick

media rope securely tied to it and to

your left a branch with a very thin rope

which rope would you trust more to climb

down

the majority of those Among Us would

choose the thick rope but why is that

I mean your weight doesn't change

depending on your choice if you weigh

150 pounds and go down the thick Row the

thick rope would have 150 pounds of

force acting upon it if you also went

down the thin rope the thin rope would

have 150 pounds of force acting upon it

also

150 pounds is 150 pounds right so

wouldn't it not matter which rope you

choose

well let's go back to our definition of

stress force divided by unit area the

unit area is the important part if we

took each of our ropes and cut out a

tiny slice from it called a cross

section you can see that the area of the

cross section of the thick rope is a lot

larger than the area of the cross

section of the thin rope if stress is

the value of this fraction Force divided

by area the force is your body weight

which goes in the numerator and the

cross-sectional area goes in the

denominator when the cross-sectional

area is smaller like with the thin Row

the value of this stress fraction

increases basically the thin rope would

have more stress than the thick rope if

you chose to trust the thick root more

your brain likely recognized it would

have less stress even if you weren't

aware of what stress was exactly

anyways there are a lot of units for

stress most common ones you might see is

PSI pounds per square inch or Newtons

over squared meters also known as a

pascal you might notice that pounds and

Newtons are unit of force and square

inches or square meters are units of

area Force divided by unit area stress

now the second term we need to learn is

called ultimate strength yes I know this

sounds like something that an anime

character would say in a fight but in

this case ultimate strength describes

the maximum amount of stress a material

can take before it breaks

here is a chart of some common materials

along with their ultimate strengths

so now that we have learned the

vocabulary we can go and solve the

original question I asked in the

beginning of the video

I encourage you to pause the video to

try to solve it yourself okay so let's

start solving we know that the 0.1 inch

diameter string broke when a maximum

force of a hundred pounds was applied to

it if you recall from before the maximum

amount of stress a material can take

before it breaks is called the ultimate

strength

so using these two values we will have

to find the ultimate strength

if the string is 0.1 inch diameter the

radius of the string is 0.05 inches

using the area of the circle formula pi

times radius squared we get a

cross-sectional area of

.0025 Pi square inches

I kept the pi as Pi because it would

make it easier to solve this problem and

I also don't have a calculator with me

so solving for the ultimate strength we

get a value of 40 000 divided by pi

pounds per square inch

the problem says that the strings are

both made of the same material and

ultimate strength is a material property

so two objects of the same material will

have the same ultimate strength

we know the second string has a diameter

of 0.2 inches

which solving for the cross section we

get 0.01 Pi inches squared

so what we need to do is to equate these

two equations and then we're going to

find the force that it takes to break

the 0.2 inch diameter string

we find the answer to be 400 pounds four

times more than the force required to

break the 0.1 inch string since the

cross-sectional area is four times

greater

now this video is a pretty simplified

look into stress that only covers the

very Basics but if you got this far I

hope you enjoyed waiting six minutes for

a punchline to come and instead getting

a physics lesson happy April Fools