Particle equilibrium with springs Proposed Experiment
Summary
TLDRIn this lecture, the instructor introduces a common physics problem involving springs and their constants. While explaining Hookeβs 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
- π The speaker introduces a common problem involving springs and how students often struggle with it.
- π‘ The focus is on understanding spring constants and solving problems related to spring elongation.
- π The speaker explains that solving the problem involves using geometry, summation of forces, and Free Body Diagrams.
- π Instead of solving the problem directly, the speaker suggests modeling the problem using physical springs or rubber bands.
- π Rubber bands can be used as a substitute for springs, with multiple bands increasing the spring constant.
- π The process for determining spring constants involves using Hooke's Law and measuring elongation under different forces.
- π The speaker emphasizes the importance of accurately measuring the elongation and selecting rubber bands with similar properties.
- β Weights, such as a bottle of water, can be used to measure forces when performing the experiment.
- π A trendline on a force vs. elongation graph can help calculate the spring constant, with errors expected due to material imperfections.
- π 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
π€ 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.
π οΈ 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.
π 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.
π 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.
Mindmap
Keywords
π‘Springs
π‘Hooke's Law
π‘Spring Constant
π‘Equilibrium Position
π‘Freebody Diagram
π‘Rubber Bands
π‘Stretch Length
π‘Force
π‘Elongation
π‘Experimentation
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.
Hookeβs 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
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