Introduction to tensile stress
Summary
TLDRIn 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
🔍 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.
📚 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.
Mindmap
Keywords
💡Stress
💡Ultimate Strength
💡Cross-Sectional Area
💡Diameter
💡Force
💡Pounds per Square Inch (PSI)
💡Pascal
💡Material Property
💡Area of a Circle
💡Physics Lesson
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
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