Particle equilibrium with springs Proposed Experiment

Summary

In this lecture, the instructor introduces a common physics problem involving springs and their constants. While explaining Hooke’s Law and how to calculate spring constants, the instructor emphasizes the value of building models to visualize the problem. Using rubber bands as a substitute for springs, the lesson demonstrates step-by-step how to measure elongation and calculate stiffness using known weights. The instructor encourages hands-on learning to deepen understanding, acknowledging the errors that arise in experimentation and highlighting their importance in the learning process.

Takeaways

• 😀 The speaker introduces a common problem involving springs and how students often struggle with it.
• 💡 The focus is on understanding spring constants and solving problems related to spring elongation.
• 📚 The speaker explains that solving the problem involves using geometry, summation of forces, and Free Body Diagrams.
• 🔄 Instead of solving the problem directly, the speaker suggests modeling the problem using physical springs or rubber bands.
• 🛠 Rubber bands can be used as a substitute for springs, with multiple bands increasing the spring constant.
• 🔍 The process for determining spring constants involves using Hooke's Law and measuring elongation under different forces.
• 📏 The speaker emphasizes the importance of accurately measuring the elongation and selecting rubber bands with similar properties.
• ⚖ Weights, such as a bottle of water, can be used to measure forces when performing the experiment.
• 📊 A trendline on a force vs. elongation graph can help calculate the spring constant, with errors expected due to material imperfections.
• 📝 The speaker encourages hands-on experimentation and problem-solving to better understand the concepts of springs and forces.

Q & A

What is the main problem discussed in the video?

The main problem discussed in the video involves solving a common physics problem related to springs and calculating their stretch and constants.

Why do students often struggle with problems related to springs?

Students often struggle with problems related to springs because they don't fully understand how constants work, which leads to difficulties in applying the correct formulas and methods for solving the problems.

What are the two common types of problems involving springs mentioned in the video?

The two common types of problems involve calculating the stretch of a spring when given the constants and equilibrium conditions, and calculating the mass of a block held in equilibrium using the spring's stretch.

What is the method suggested for calculating the stretch of a spring?

The suggested method involves solving for the geometry, summing forces around a point, creating a Freebody diagram, calculating angles for equilibrium, and using the force and constant to find the spring's stretch.

Why does the speaker recommend using rubber bands instead of springs for modeling?

The speaker recommends using rubber bands because they are more accessible and affordable, and their elasticity can still be used to model springs by modifying the constants (e.g., doubling them by using two rubber bands).

How do you calculate the spring constant using rubber bands?

To calculate the spring constant using rubber bands, you apply Hooke's Law (F = kx), measure the elongation of the rubber band when a known force is applied, and divide the force by the elongation to find the constant (k).

What error might occur when using rubber bands instead of actual springs?

Errors might occur because rubber bands have different thicknesses and properties, leading to variations in elongation. Also, over-stretching a rubber band may cause it to enter the plastic range, leading to residual deformation.

What tools does the speaker recommend for building a physical model of the spring problem?

The speaker suggests using simple items like rubber bands, keychain rings, paper clips, and weights (e.g., water bottles or known weights) to build a model of the spring problem.

How does the speaker suggest dealing with inconsistencies in rubber band elasticity?

The speaker advises selecting rubber bands with similar elongations before starting the experiment to reduce errors caused by variations in their elastic properties.

What does the slope in a force vs. elongation graph represent in relation to springs?

The slope in a force vs. elongation graph represents the spring constant (stiffness), which is the ratio of force to elongation, indicating how much the spring stretches per unit of force.

Outlines

00:00

🤔 Introduction to a Common Problem with Springs

The speaker begins by addressing the audience and introducing the problem, a common issue involving springs, frequently encountered in textbooks. Students often struggle with such problems due to difficulties in understanding constants. Despite the common fear of spring-related problems, the speaker reassures viewers by making light of it and clarifying that solving these issues is straightforward once the geometry, force summation, and free-body diagrams are understood. The key to solving this particular problem lies in calculating the forces and the stretch in the springs based on the constants given.

05:01

🛠️ Building a Physical Model with Rubber Bands

In this section, the speaker shifts focus from solving the spring problem on paper to creating a physical model using rubber bands. They encourage students to construct the model themselves, as hands-on experimentation can deepen understanding. The speaker provides practical advice on where to find rubber bands and how to use them as simplified spring substitutes. They explain how adding multiple rubber bands alters the spring constant, theoretically doubling it. Students are advised to select rubber bands with similar elongation properties for consistency.

10:03

📏 Measuring and Experimenting with Spring Constants

The speaker demonstrates how to measure the spring constant using rubber bands. By suspending weights from rubber bands, students can measure the elongation and apply Hooke's law to determine the spring constant. A step-by-step method is outlined, including marking points for the initial length, adding weights, and measuring the elongation. The speaker highlights the importance of selecting rubber bands with consistent elongation and explains how to correct for measurement errors. The focus is on experimentation to obtain accurate values for spring constants and improving understanding through practical application.

15:05

📊 Analyzing Results and Understanding Errors in Experimentation

This section provides an in-depth explanation of how to analyze the results of the rubber band experiment. The speaker uses tools like Excel to plot the data and find the spring constant by calculating the slope of a force-elongation graph. They also discuss expected errors and discrepancies between theory and practice, such as variations in rubber band properties and how overstretching can lead to plastic deformation. The focus is on learning from experimental errors and understanding how real-world factors affect the outcomes, which is crucial for students to grasp.

Keywords

💡Springs

Springs are mechanical devices that store energy when compressed or stretched and then release it. In the video, they are used as an example to explain how constants work in physics problems, specifically Hooke's Law. The instructor highlights that many students struggle with understanding spring constants.

💡Hooke's Law

Hooke's Law is a principle in physics stating that the force needed to extend or compress a spring by some distance is proportional to that distance. The formula is F = kx, where F is force, k is the spring constant, and x is the displacement. This concept is central to the video, as the instructor discusses how to apply this law to solve problems related to spring elongation and force.

💡Spring Constant

The spring constant (k) measures the stiffness of a spring and determines how much force is needed to stretch or compress it by a unit length. In the video, the instructor uses rubber bands to illustrate how to calculate spring constants experimentally, by measuring force and displacement.

💡Equilibrium Position

The equilibrium position refers to the state where all forces acting on an object are balanced, resulting in no net movement. In the video, the instructor explains that springs are in equilibrium when they are neither stretched nor compressed. Understanding this concept is important for calculating forces and displacements in spring problems.

💡Freebody Diagram

A freebody diagram is a graphical representation of the forces acting on an object, used to simplify complex physical problems. The instructor mentions using this technique to solve the spring problem by analyzing the forces acting at specific points and calculating angles.

💡Rubber Bands

Rubber bands are used as an inexpensive alternative to springs in the video to demonstrate how to model and calculate spring constants. The instructor emphasizes that while rubber bands are not perfect, they can still be used to teach the basics of elasticity and Hooke's Law.

💡Stretch Length

Stretch length refers to the amount a spring or elastic material extends when a force is applied. The instructor discusses how to measure the stretch length of rubber bands experimentally to determine the spring constant.

💡Force

Force is a vector quantity that represents the push or pull on an object. In the video, force is discussed in relation to how it stretches or compresses springs, following Hooke's Law. The instructor uses different weights to demonstrate how force affects the elongation of rubber bands.

💡Elongation

Elongation is the extension of a material (like a spring or rubber band) when a force is applied. In the video, elongation is used to calculate the spring constant by measuring how much a rubber band stretches under known weights.

💡Experimentation

Experimentation involves conducting practical tests to observe physical phenomena. The instructor encourages students to build models and conduct their own experiments with rubber bands to better understand the principles of springs and forces. This hands-on approach is shown to deepen understanding beyond solving problems on paper.

Highlights

The lecturer emphasizes that this problem is common in every book but often misunderstood by students.

The lecturer jokingly mentions students' 'nightmares with springs' and encourages them not to be afraid.

Students are instructed to build a model of the problem instead of just solving it.

Rubber bands are suggested as a simplified alternative to springs for the model.

The lecturer explains how to modify spring constants by adding more rubber bands, introducing a practical hands-on tip.

Hooke’s law is explained in a relatable way, using force and elongation to demonstrate how to calculate the spring constant.

A humorous note is made about using household objects like water bottles to approximate weights for the experiment.

The importance of selecting rubber bands with similar elongation properties is highlighted to avoid experimental errors.

The lecturer shows how to calculate and visualize spring constants using Excel, emphasizing the significance of accuracy in plotting data.

Students are advised to reproduce the experiment physically using common objects like paper clips and rubber bands.

The experimental process includes applying known weights to rubber bands and measuring their elongation.

Students are shown how to identify and mark elongation points on rubber bands for accurate measurements.

The lecturer demonstrates how to create scatter plots in Excel, including adding trend lines to calculate spring constants.

The lecturer humorously acknowledges errors and discrepancies between theory and practice in experiments.

Students are encouraged to embrace errors in experiments as part of the learning process, highlighting the value of hands-on experience.

Transcripts

hello guys how are you doing I'm gonna

start the class again or the lecture by

hello guys today I want to do something

different that I have done in the past

what I want to do is a problem that is a

fairly common problem in every book let

me switch this here talking perfect this

is a problem you see this problem is a

really common problem and I have found

that a lot of a students a problem again

have problems with the problem has

issues with this problem when they try

to solve it because they don't

understand how these constants work and

as I say in a previous video they say a

springs and a star like Springs oh my

god I'm so scared i have nightmares with

the spring and you don't have to have

nightmares with the springs you can have

another type of dimers if you want to

but don't Freddy Krueger for example but

don't have nightmares with the springs

so usually when you have this situation

there are two possibilities that you can

be asked for and I copy both here

either you had a setup like that and you

have questions like the term in the

stretchiness Springs AC this spring here

AC and a B which you already have the

constants and you already have also this

constant is constant in this particular

problem was 40 I guess I think I don't

remember and I don't care because I'm

not gonna solve that problem so you

thought I was gonna solve this problem

you can stop it and then gonna solve the

problem but I'm going to explain you

something more important than solving

the problem so you are here and it says

that the springs are shown in the

equilibrium position meaning that you

have all the distances and everything

else and what you have to find is what

is the stretching in this experience how

do you do that well you saw for the

geometry you for you so for summation of

forces here around this point you do the

Freebody diagram you can calculate the

angles remember this is the angle for

equilibrium and then you

calculate the force because you had the

force and you have the constant you can

calculate how much the screen was a

straight period that's the way you do

that now these are the one he says the

only stretch length of the spring a be

you only have these these on a stretch

length is 3 meters and if the block is

held in equilibrium position this one

calculate the mass is kind of the same

problem you just work back once you've

done problem but you need the original a

stretch length here so you can calculate

the other position later also that's my

cell phone by the way

that's that's really good but I want

what I want you to do right now is not

to solve that problem what I want you to

do right now is make a model of that

problem because the model is I don't

know about you but I learned a lot by

seeing things by doing things so what I

want you to do is try and come out with

that model let me show you the model

again here

and the first thing that you're gonna

say where do I get Springs where do I

get pins how do I do that well I'm gonna

give you use a little tip you can use a

Springs and you can buy Springs and

there are really there are my my office

I'm gonna show you my office because my

office is a really nice place that is my

mace you can find these little devices

they are like a box something a doll or

something and I said those are spring

scales and your problem is soul but then

you have to buy this and you have to get

these if you want used to build a model

for your own use you can be something

more simplified quickly friend type of

Springs rubber bands rubber bands are in

the elastic range but then you're gonna

ask oh how do we modify the constant

well you put two rubber bands then you

have double of the constant Oh

theoretically

and I say theoretically because that's

probably not gonna happen and I

shouldn't be telling you what the errors

are gonna be I should just let you

figure the errors by yourself but I'm

gonna I'm gonna tell you what happened

here so how do you calculate the spring

constant I explain these to my aesthetic

students so if you just apply the Hookes

law which you know because you learned

that from high school and you learn in

physics and probably in calc also if

equal K X F force K the spring constant

which is also called stiffness and it's

not a thing that the slope in that a

force elongation line or equation and

you just have to hold these in a

position hanging away from there and

measure the location theoretically

that's sufficient and I say

theoretically let me turn to this board

that I prepare or we prepare because

there is that person here helping me

with these but let's turn to that board

because that board is going to help me

to do the explanation okay as you can

see here I have I'm the protagonist so

you have to see me kind of I put here

one two three rubber bands hanging from

here I'm gonna just have some weight and

you say okay I don't have a weight of

course you have weight you have it

skills at home on even if you don't have

it skins at home I don't know there are

certain things that you know the weight

or they're very very approximate nice

weight which is for example a bottle of

water and you know that's a pound so you

can start thinking of those quantities

now be careful with something because

the way you do this is that first you

put your rubberband like that and you

draw the baseline for that that's gonna

be the initial length and then you get a

known weight and you hang that no way

from that and then you measure that

distance how do you measure that

distance with the ruler mention that in

centimeters I marked a point there and

this is approximately like 4.5

centimeters or so for that one now be

really careful because I'm pretty sure

that if you just get a bunch of rubber

bands and you start trying the rubber

bands you're gonna mess up why and then

I show you look at that rubber band over

there I'm gonna put another rubber band

from the same box here now look at the

location the elongation is like one

point x the other one so the first thing

the other one was 4.5 and this one up to

this point it's almost eight so what do

you what do you should do from the

beginning is just selecting a bunch of

rubber bands with similar elongations

and it's easy to do but it's highly

necessary so you do that for the three

of them and then you put the two rubber

bands which I already try and then you

put the second one and then you mark a

point and then you do it as you are

adding rubber bands it's gonna be more

difficult so you can add more weight to

that and you have a bigger a better

solution for this one for example I

already did the calculation

and I measure them so for the second

rubber band this year if you see

coincide kind of almost to a scary crazy

with the first one but the reason is

because I already selected the same type

of rubber bands within the back so is

the same the same elongation for double

blade with two rubber bands and then you

do the same thing with different weights

and with different situations and then

you do the same thing for the with three

rubber bands and whenever you have the

three rubber bands here and you measure

it this is like to point you have to

mark the points exactly there you are

supposed to put a label of a terrible

labor or something but it is like to

point A to point seven to point a

something like that for three rubber

bands and you can do the same thing for

different ways so you can put one weight

that you know another way etc in my case

I'm adding these because I had those you

don't have to have these each one of

these is 5 Newton so I'm adding 2 or 5

Newtons and then I have 2 extra more

than a body or one extra more of to

Newtons okay let me go back to the Anna

let me come back here so once you have

the rubber bands

the idea is to reproduce the experiment

that we had before so I get something

like these this is just a ring from the

keychain and that's gonna be the bottom

part of that where I'm gonna hang they

wait in that part and then I have these

two rubber bands are gonna simulate one

of the springs in one direction let me

try to make quick here

first just be sure also you don't damage

your Springs by doing that and I'm

showing this at this level because I

always receive a concerns and oh I have

to buy a lot of I have to spend a lot of

money by doing this no you don't have to

spend a lot of money

rubber bands are everywhere so I had the

other one now if you remember the

problem this is just a hook here you can

use paper clips either paper clips are

sufficiently strong to hold it

you put one rubber band here you put two

rubber bands at this point two of them

and then you're gonna hang the weight at

this point when you hang the wave here

there you go be sure that this is not

touching the directly the board that you

were put in there because otherwise is

gonna be friction here so it has to be

vertical but it has to be somehow hang

in there you see the shape this is

exactly the same shape that you saw in

the product kind of because I just I

realized there is a problem without

drawing but it doesn't matter this is

what I want you to do once you do that

then you're gonna come here and make

sure the physical distances for the

weight that you know and the spring

constant that you should know now how do

you calculate the spring constants let

me go back here let me show you how to

calculate this me constants really easy

so if you come here okay you can you can

go and I'm just going to show you really

quick for this example how to do it are

you looking for

you can use this one okay so I'm gonna

I'm gonna show you the resource and I

got for the spring to PPT plus webcam

okay perfect here I have myself page

here and this is the stretching that I

measure for the spring - which is not a

spring you know that I'd write this just

two rubber bands so for a force or five

Newton I got a stretching of two point

three centimeters for the fourth of

seven you know tone I go three point two

centimeters and for a force of 10

Newtons new toes I got four point four

centimeters you get these here you mark

them in Excel you say it insert we're

gonna go to the scatterplot and I want

to select these which are only a point

markers because the points are not gonna

coincide and that's good that's normal

that means as use the material is not

perfect but they what you're gonna do

you're gonna add a trendline here

trade line and the trend line that

you're adding you are saying to show on

display I'm sorry the equation on the

chart if you want to you can also do it

by hand and draw they the more

approximate line that you can you can

you can do it like this so you don't

have to do it exactly just like that

really quick and do the drawing and we

put the measurements later so I say that

you can also feel it by hand and measure

the slope now remember that your look at

the chart that you have you see this is

a chart and these here is a slope now

forget about this term because this term

I'm starting not from zero even though

it's really close to zero I didn't

started from zero because when I did

this experiment I started from the

baseline this baseline that you see well

you don't see here but you you see it

over there basically the baseline that

I'm starting it was just to keep the

rubberband to keep it

for a first position stretch and that's

why the y-intercept would represent the

original deformation forget about that

but think of this is low this is slope

here it's going to tell you actually

what is the force which is why this is

the force divided by the elongation so

you have force divided by elongation

when you plot the force the y-axis

divided by the elongation here is going

to give you the spring constant which is

for the spring to about 2.4 now I did

the same thing for the other Springs and

I'm going to show you what the results

are results are for the other Springs

which to.com cross web cam here these

are the results that I got for the three

Springs actually this is a spring one

this is a spring water put two times the

spring oh that's so smart but I assure

you a spring - so a spring - I'm doing

this life so guys a errors happen in the

best families so let me see what I see

it's a sprint - you are the one that I

need copy spring to come back here you

know this is going to show you that this

is your production that is on

no pre-recorded not edited not anything

and then I'm gonna here and I'm gonna

paste it here

voila there you go and I'm gonna print a

new sheet five print prints a current

slide there you go

friends now we have it here

okay rewind that forget about that this

is the one spring one spring - spring

three look at the constant this is the

constant for the spring one this is a

constant for the spring - and this is a

constant for the spring three this is

kind of one point one point one for this

is two point three nine and this is

three point five a look at these values

we are basically trying to work with a

value a constant of one point two for

the first one two point four for the

second one and three point six for the

third one so once we had that I'm going

to show you the dimensions in the

drawing we were preparing here only

webcam there you go this is the way it

looks like so what we are doing here now

is where is the merger any marker here

you can basically take these out because

the cable I'm gonna put the cable in

yeah same color doesn't matter so the

cable should come somewhere here and

somewhere here

raining here then you have the other

cable coming from here now if you take

this out you take that out do you have

the problem you see this is a problem

these are the real the real measurements

and you have here team 10 Newton so you

have ten Newton of force over there and

then you have the dimensions here now

what you do and what you can do to see

if what you did was correct yes you come

back to your original drawing which I

have somewhere in this mess I have here

let me show you again you have it here

and then this is the problem that I show

you before but there is no there are no

values here and then you go and you

proceed

what do you proceed you say oh this

instance here experimental distance is

14 centimeters these are the distance is

X centimeters this constant I say that

for this spring was only one rubber band

so that constant was one point to

remember the units the units are Newton

per centimeter because that's what I use

this is 2.4 newton per centimeter and

this is 3.6 newton per centimeters this

weight here is 10 Newton the vertical

distance that I got from my result here

from here to here is 10 point five

centimeters and now you go and so these

are you gonna have errors yes are you

gonna have these crepin sees between

what the theory should say and the

practice the practical experiment that

we are doing is yes of course and those

are expected but you know something

that's what experimentation is about

these rubber bands as I show you they

are different they have different

thickness different stiffness different

everything if you have something from

this rubber band and you over stretch it

forget it it went to the plastic range

so or they last to practice a plastic

range is going to go back and you're

going to say oh it's the same one no

it's not the same one you have a

residual deformation there and if you go

to mechanics of material materials after

these you will learn

what is happening now what I expect you

to do go through that problem and solve

that problem in the way that I told you

and try to come out with some results to

see if they are you can just forget

about this wait for now

and say oh if I have this situation like

that what is the original a what is the

way that is here and you can have a day

a also the unstretched length because I

was one of the values how much is a the

length of one of these rubber bands

original length measure is there please

the original length region spring lamb

what nine point five centimeters nine

point five nine point four centimeters

somewhere around that point okay it is

the original length of the springs and

you can come with the solution and try

to solve that problem do it because you

have no idea how much that can help you

to understand the whole process and

solving a problem in paper yeah nice

seeing it like that and trying to solve

it priceless for everything else you

know what car you use see you next

lecture guys I hope you like