Physics 8 Work, Energy, and Power (4 of 37) Compressing a Spring

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In this video I will show you how to find the potential energy gained when pushing against a spring.

[@HuyNguyen-vo2ss]

Love how you explain things so clearly. My professor just scribbles random equations and call it teaching

[@scotthoffman7491]

So true. My professor does the same except his scribbling is illegible...

[@soulblaster2639]

My professor does the same so i decided not to study from him and came here instead

[@historyisthebest5831]

Even my professor recommends his video as resources.

[@aktersalma279]

Yes

[@nofarmarom1306]

i swear this guy saved my grades in chemistry and physics! keep up the good work! dont know what I would do without your lectures!

[@MPmang-d1f]

this man explained 2 days worth of lecture to 5 min video. really amazing!

[@TheLastWizardOfTheCentury-u7o]

You, Sir, are my hero. Last year while I was a high school senior, I was required by my foreign dream university to pass AP Physics 1 and 2, which included some topics that aren't included in the high school curriculum in my country. This caused a lot of stress for me, until I came across your perfectly organized playlists of amazing videos! Not only I got a 5/5 in both exams, you helped me in my national high school final exam too: I was among 3 in the whole country who got a perfect score in it. And this september I just starded studying at my dream university. Thank you!

[@MichelvanBiezen]

That is fantastic! Keep up the hard work.

[@historyisthebest5831]

Wow congrats! I wish I can get a perfect score on my future SAT too. I love Physics a lot!

[@awa8650]

😁 he is really helping me too. I have to take all my courses in English, even if I am not fluent in this langage, I found his Playlist and I am learning a lot of things here 🙂 Sincerely, thank you so much 🙇‍♀️

[@salehahmed4139]

Materials are well organized. I can do without a text book if I go through all the videos, and it is so much better than the text book. Thank you.

[@renatofrancorosas1397]

beautifully explained. I actually had trouble understanding this from my professor, but now it is clear as water

[@MichelvanBiezen]

Great! Thank you for the comment.

[@pierregarcon3664]

For you it's agua Wi wi #pierreBurn

[@pierrefabela]

Pierre Garçon This Pierre approves

[@policepankaj4554]

You mean Cristal clear but where inside the brain or from brain

[@harsh909]

You have been the best Physics Instructor

[@pierregarcon3664]

You rock the Bow tie. Not many people can. kudos

[@BlueBunnyGamer]

For a second I was like why is he doing derivatives and integration 0.o and then I realized he was doing the proof! Very well explained sir!

[@thy7917]

you are the best. this is the core key of every physic students.

[@earyrockwell8030]

Sir, what happened to the constant of integration

[@aang7505]

amazing explanation, much better than Khan Academy! thank you!!

[@ahmedal-ebrashy3691]

Brilliant Brilliant Briliiant. I learned a lot. Small q thought. If the relationship between Fand x is linear and constant, why do we need calclus? Couldnt it be solved with linear equation line y-y1=m(x-x1)

[@MichelvanBiezen]

The rule is that if the force is not a constant, you will need to integrate to find the total work.

[@abdullahkhalid6937]

I hope u r so well i get what i need and more in this channel

[@MichelvanBiezen]

Glad you found our videos. (there are more than 9000 videos on this channel)

[@madscientist545]

Hi sir can you send me the example of the link in which the pulley has friction

[@zakirhussain-js9ku]

Displacement seems to a common denominator associated with work & energy.

[@MichelvanBiezen]

It is key, since the definition of work is defined as the dot product of the force and the displacement. (Can't have work without displacement).

[@EdwinFairchild]

so if it takes 200N to compress it one meter, and since the force is not contant, does that mean that the 200N value is the sum of all the different forces in the 1 meter interval? is 200N just how much is needed to get it started?

[@MichelvanBiezen]

If you apply 50 N the spring would be compressed 25 cm. If you apply a force of 100 N then the spring would be compressed 50 cm and when you apply a force of 200 N the spring is compressed 1 m. There is a linear relationship.

[@enriquesoler3150]

From my textbook, when talking about the formula with spring force this is it: Fs= -kx (Hooke's law), just want to know if that negative sign in the problem indicates that the force and displacement go in opposite directions, am i correct? If so, why didn't you that negative sign when doing your problem? If I'm wrong, why does my textbook include that negative sign?

[@MichelvanBiezen]

Negative signs are often misunderstood in physics. In principle they indicated direction when we use vectors. When we only calculate the magnitude of vectors, they can only be positive since the magnitude of a vector cannot be negative. In the case of Hooke's law, F represents the force OF THE SPRING. If you pull to the right, the spring will pull to the left. So if we calculate the force ON the spring, it will be positive when the displacement is positive.

[@MichelvanBiezen]

The F in Hooke's law is the force exerted by the spring. The force pulling on the spring will be positive.

[@hananibraheim994]

thank you so much I was really lost in this topic. Thank you

[@sublimeknight1754]

If a block of mass 'm' is suspended from a spring such that the string is streched, lets say 'x' (metres) due to the weight of the block and then a sharp impulse is given from below which gives the block an upward speed 'v'. Then how do we calculate how high the block will rise?

[@MichelvanBiezen]

The impulse will cause a change in momentum: I = delta p = m * delta v. That will give you the kinetic energy of the block, which will then be converted to the spring's potential energy. (Do NOT include gravitational potential energy, since the spring has negated that).

[@sublimeknight1754]

Michel van Biezen Thanks a lot!

[@jeelbambhroliya6287]

To learn work power and energy , from which lecture do I start , give link of that IMMEDIATELY, PLEASE.

[@MichelvanBiezen]

You can find all the videos easily from the home page of the channel. All the playlists are organized according to the topics. Here are the playlists on work and power: PHYSICS 8 WORK, ENERGY, AND POWER kzbin.info/www/bejne/gp6ahn9mjbpqarc PHYSICS 8.1 WORK ENERGY AND POWER EXAMPLES kzbin.info/www/bejne/ZoLIlWybgpuUo8U

[@hooman626]

you're saving my sanity, thanks

[@MichelvanBiezen]

Happy to help

[@مفكال]

can the force on a spring be constant for example 100 N ? and use the W= F . d

[@anilsharma-ev2my]

How much joules of energy required to winding up the ⏰ time piece Torsion spring mechanical properties ?

[@wisdomkeytraining700]

Spring force is restoring one and hence has to be written as F=-kx

[@MichelvanBiezen]

Only if you care about the direction. Force is a vector and if you are calculating the magnitude of the force, it must be positive. The magnitude of a vector cannot be negative.

[@_anusha_4091]

When you say the spring is not moving what does that mean? Since the spring has displacement doesn't that mean it's moving? Also, thank you very much for your videos! I'm studying for SAT 2 physics and don't have a teacher, so they are extremely helpful.

[@MichelvanBiezen]

KE = (1/2) m V^2 where v is the translational velocity. Since the spring does not have translational velocity the KE is considered zero. Any motion during the compression is very small and the KE related to that motion is so small that it is insignificant and ignored. (Good question).

[@metalloid6623]

@Andango I came here for the same reason!!! I'm taking the SAT 2 physics this October and have no teacher to teach me :( How about we study toghther? ya know skype and stuff?

[@_anusha_4091]

I'm taking the exam in October as well. Unfortunately I don't have a skype account, however if you need advice feel free to send me a message. Currently I'm using the Sparknotes guide and this youtube channel to study. Good luck!

[@metalloid6623]

DUDE MAKE A SKYPE ACCOUNT WE CAN HELP EACH OTHER ALOT !! why would we study all that alone :c And I've completely read the Sparknotes physics sat guide so you in a good company pal :3

[@anilsharma-ev2my]

Any app which gives mechanical properties of steel torsion spring ?

[@thy7917]

Please continue to upload videos.. Thank you

[@allrounder2367]

When will be the P.E will be positive and when it will be negative?

[@MichelvanBiezen]

When it comes to the PE of spring, it will be positive when compressed and positive when elongated.

[@allrounder2367]

Sir, you wrote positive two times. I guess you want to say that we should treat it on x-axis, that is, when it is stretched then P.E will be +ive and when it is compressed then it will be -ive.

[@thut6619]

You explained so well! Bravo

[@thailandfutsal5508]

Why work that act in to the spring equal to energy in the spring

[@MichelvanBiezen]

That is assuming that no energy is lost. So we take the idealized situation with no energy lost during the process.

[@thailandfutsal5508]

Does formula that say u2-u1 = work done by conservative energy is the formula that describe this question.

[@MichelvanBiezen]

u2 - u1 gives you the difference in 2 energy states. It doesn't give you any specific detail

[@otte070]

Would you be willing to explain the integrals? I have never used them and am unfamiliar with integrals. Is there a way to go around the use of integrals? I am not sure what you do in the last steps of dW to the integral dW to W. Is this relevant or world W= 1/2kx^2 be enough to know? Thank you for the great tutorials!!!! Best,

[@MichelvanBiezen]

Dutchy070, If you don't understand the integrals I wouldn't worry about it. It is sufficient to know that W = change in energy = (1/2) k x^2

[@otte070]

Michel van Biezen Thank you, you are my internet super hero! One of the few people who understands teaching. May I ask where you are from originally? I am from the Netherlands and your name sounds very Dutch, however, I cannot place the accent. Belgium? Luxemburg? All the best, Dutchy

[@MichelvanBiezen]

Dutchy070 Dutchy, Good guess. I grew up in a small town just south of the Dutch border so I am Flemish.by birth.

[@OnlineToBrain]

Please give us some information about professor Michel. Also you can share his social profile link. I have learn so much from his tutorial but i don't know who is he actually.?????

[@soureachsak5027]

Hi sir, normally after we integrate the function, we add constant, but why we dont in this problem? Thank you!

[@MichelvanBiezen]

In the integral it was "understood" that we had limits from x=0 to x=x. Physicists tend to be "sloppy" when it comes to writing out those limits. That is why we didn't need the constant of integration. (Very good observation).

[@soureachsak5027]

Ok I have read your response and I quite understood, but I got one last question, Is the result (W=1/2kx^2) the AREA underneath the straight line you drew? and does that area represent the Work Done? Thank you!

[@MichelvanBiezen]

That is correct.

[@jayeffiong6340]

hello Michel pls can u do a video relating Poisson's ratio to shear and young modulus? can't seem to find it anywhere

[@gytisdramblewolfskis8521]

so dw=kxdx meaning d's are deleted by each other like dw/d=kxx so w=kxx. but you say its w=kxx/2 where does this /2 appear from ?

[@MichelvanBiezen]

It is not quite like that. When you integrate, you have to follow the rules of integration (and there are many of them depending on the function). The integral of dW is W . But the integral of x^n dx = x^(n+1) / (n+1), therefore the integral of kx dx = kx^(1+1) / (1+1). See the videos about integration on this channel. CALCULUS 2 CH 0 WHAT IS INTEGRATION? kzbin.info/aero/PLX2gX-ftPVXXVfuT3Fg_x1rtrivBLc7r2 and CALCULUS 2 CH 1 INTEGRATION BASICS kzbin.info/aero/PLX2gX-ftPVXU1rav_QOzn8Bgfgn7HfRra

[@gytisdramblewolfskis8521]

Michel van Biezen well i did not learn any of this in 11 classes so far and i'm at 11 right now and seeing how complicated all that is i don't have time to learn all of that any time soon. Though your videos are better than my physics teacher thanks!(at least for me knowing very little physics) i'll just learn your physics lessons for now.

[@angelicaraventeves6961]

Can someone help me? I cant solve this problem: the spring of a toy gun has a force constant of 500n/m. If it is compressed 0.05m and a ball of mass 0.01kg is placed in the barrel against a composed spring. Determine the velocity with which the ball leaves the velocity which the ball leaves the gun when released

[@MichelvanBiezen]

Set PE = KE (1/2) k x^2 = (1/2) m v^2 You can find lots of examples in this playlist: PHYSICS 8 WORK, ENERGY, AND POWER

[@iwontreveal6723]

yesss...that's it..keep it as simple as possible. you are the best. i am a new subscriber :-)

[@MichelvanBiezen]

Welcome to the channel.

[@xgerbil3586]

My professor seems to like to throw curve balls at us on the exams. Is there a way to calculate the velocity and acceleration after the spring is released? I thought we could use F = ma or W = Fd, but I'm not completely confidant in that.

[@MichelvanBiezen]

I would use the conservation of energy equation to solve that type of problem. There are lots of examples in these playlists.

[@ejazahmad4279]

Respect Sir

[@MichelvanBiezen]

Thanks!

[@jonathankim6013]

PH2A: Are you implicitly differentiating, or are you doing it with respect to x? Why can you differentiate everything except F? If it is with respect to x, shouldn't it be dw/dx?

[@jonathankim6013]

F and D are being multiplied, so wouldn't you differentiate that with the chain rule? Fdd+ddf?

[@jonathankim6013]

I mean product rule not chain rule.

[@jonathankim6013]

My calc is already a bit rusty so i probably didn't make a lot of sense. My main question is why can we differentiate everything except F?

[@sukinaikab3993]

Your amazing, thank you.

[@gboypoker]

Question: If i were to find the length of the compression (x) and with only the K is given how am i supposed to do that ?

[@MichelvanBiezen]

The length (x) can be found by: x = F / k where F is the force applied.

[@gboypoker]

Michel van Biezen thank you ^_^

[@sunfll]

so PE not means object do vertical moving upside down.....on i thought when object do horizental means there s only KE inside......OMG....confuse again...>

[@MichelvanBiezen]

There are multiple ways energy can be stored (PE = mgh). One way is to lift object against gravity, another way is to compress a spring (PE = (1/2) kx^2)

[@harsh909]

Thanks for your hard work and explaining everything so clearly with details that I started loving Physics

[@WildGoose2012]

If you leave a spring under compression over time does it lose potential energy? If so, What is the equation for the loss?

[@MichelvanBiezen]

+WildGoose2012 Theoretically the spring will maintain the potential energy. I real life, the spring could lose its stiffness and begin to lose energy. There are many factors that determine that.

[@nofarmarom1306]

+Michel van Biezen where does this energy go?

[@深夜-l9f]

+Nuphar Marom It might be heat due to friction

[@nabarajbaral2063]

Which factors does the power of a body depend on?

[@MichelvanBiezen]

The definition of power = rate of doing work = W/t or the rate of changing the energy = delta E'/t

[@pavankumarchellu334]

As force is varying then displacement also varying accordingly due to linear relationship, then why do we take only force as a constant value why not displacement?

[@MichelvanBiezen]

There is no linear relationship between force and displacement. There is a linear relationship between force and acceleration. (F = ma)

[@pavankumarchellu334]

I am talking about stiffness constant of the spring...as there is a linear relationship between force and stretching

[@MichelvanBiezen]

Yes, the spring constant = force / distance

[@MichelvanBiezen]

(btw. force was not taken as a constant value in this video)

[@azibodusiosain3762]

thanks alot , you ways make my day great

[@kyugreywolf6801]

Thanks again for the video, I had no idea that's how the equation [E = 1/2kx^2] was derived; I simply have a formula sheet with that written on it. Until now, there's not been a need to integrate equations [for me at least]; all the equations are given. Is it worth knowing how all these equations are derived and how to integrate them?

[@MichelvanBiezen]

It is OK not to know how the equation is derived while learning how to use it, but in the end it will give you better understanding to know how the equations are derived and in some cases to see the connection between the physical properties and dimensions and the equations.

[@kyugreywolf6801]

Michel van Biezen I see, I guess it wouldn't hurt to try and learn how equations are derived then; it would certainly be a huge help if I were to undertake physics at university or just generally when trying to deal with equations of a harder difficulty. Thanks

[@farzanamariyam4665]

So at the time of compressing spring, work done by external force is supposed to be negative right? But since external force and displacement is in the same direction how is that possible?

[@MichelvanBiezen]

Why would work done by an external force be "negative"? It is better to think about what negative and positive work means.

[@farzanamariyam4665]

@@MichelvanBiezen since work by spring at the time of releasing a compressed spring it is positive and work done by spring= (-) work done by external force. As in they are equal in magnitude but opposite in direction

[@MichelvanBiezen]

Work results in a change in energy. If the work done on an object increases its energy (KE or PE) then the work done is positive.

[@jonasakarlsson2036]

A wagen with the mass 5 kg is roling agianst a feather that is connected to a wall. The feather constant is 200N/m. When the wagen pushes against the feather it is compressed 5 cm. Determine "v" Is just that KE transforms to PE. So 1/2mv^2=1/2kx^2 mv^2=kx^2 v^2=kx^2/m v=... Or how can i solve a problem like this?

[@MichelvanBiezen]

+Jonasa Karlsson That looks correct to me. (assuming a feather acts in the same manner as a spring)

[@jonasakarlsson2036]

Yeah sorry, in my country we have the same word for feather from a bird and the thing u show in the video :p

[@ramneet-singh]

Why is the formula for work done kx^2/2 and not just kx^2. Where did the /2 come from?

[@MichelvanBiezen]

+Ramneet Singh Kumar When you integrate you add one to the exponent and divide by the new exponent.

[@j0mezzy]

Wait, how is it potential energy when there's change in height ? I thought it would be kinetic energy if it were being compressed horizontally? No?

[@MichelvanBiezen]

+Jomel Sagsagat Energy stored in a spring is also potential energy. PE = (1/2) k x^2

[@Peter_1986]

+Jomel Sagsagat Potential energy is the "ability" for something to do work - so if you compress (or stretch) a string then you can release that spring at a later time and have it do work. This is why you also have potential energy when you move something to a greater height - that object will then, relative to the lower height, be able to do work until it reaches the lower height and comes to rest (for example, you could tie it to a rope and have it give energy to a power generator or something). Professor Biezen has a bunch of interesting problems somewhere that involve both kinds of potential energies at the same time - they are definitely worth a look.

[@vikashraghuvanshi993]

simply great sir👌

[@johnw1234]

Why is the Force not constant?

[@MichelvanBiezen]

The force of a spring is proportional to how much the spring is compressed. If you compress the spring twice as much, the spring will push back with a force twice as much.

[@wiledorigin]

question: as an engineer without the exact numbers would multiple springs be better than 1 large spring to handle work linearly (in theory) could someone make/explain to me a graph to show it and where the load would be better stopped by 1 compared to 3 with less energy? exp Spring Large Single l~~~~~~~~~~~~l Spring mult. l~~~~l~~~l~~~~l

[@XXX-wt6jv]

this is great，so easy to understand

[@paperbag6707]

Does like 4 spring that look like same make it more powerful answer meeeeee

[@MichelvanBiezen]

If they are placed in parallel yes. If they are placed in series, then it has the opposite effect.

[@cloudyevening4524]

I sent Mr michel’s video to my physics sir ........ n told him that he explains very well just have a look......then after 10 mins my physics sir blocked me on Whatsapp...😅😅😋😞😁😉

[@analutzmarques480]

how are the lines he draws so damn straight?

[@oscarcastanedamunoz]

can someone help me? I have 1 liter of air at 1 atm and I'm compressing it to 0.045 liters and have a pressure of 39.476 atm. How much force is needed to compress the air? can someone just walk me through the math?

[@MichelvanBiezen]

+ocast evo The answer depends on the shape of the container, its dimensions, and the dimension of the piston. Do you have that information?

[@MichelvanBiezen]

+ocast evo The answer depends on the shape of the container, its dimensions, and the dimension of the piston. Do you have that information?

[@oscarcastanedamunoz]

Michel van Biezen yes the swept volume of the piston is .955 liters and is a cylinder with a height of 12.15 cm and a radius of 5 cm. The clearance chamber is also a cylinder with a volume of .045 liters. Its dimensions are 1 cm radius and a height of 14.5 cm.

[@samuelosagie-aruya8086]

Thank you so much I am understanding it.

[@fahimakhan2621]

i don't understand why the equation was divided by 2

[@tyagiaryan82]

fahima khan integrating xdx gives us x^2/2

[@cihangonen9746]

because when you integrate "x" the result is" x^2/2"

[@678JuliaC]

Very helpful videos! Thank you very much!

[@ayushishukla8642]

Amazing lecture.. thank you sir...

[@MichelvanBiezen]

Most welcome

[@eternalramen_]

Very well explained, thank you!

[@rashkabashka7641]

PE in this video is = 250 not 25 sir

[@MichelvanBiezen]

The video is correct. Thanks for checking.

[@rashkabashka7641]

Oh sorry sir.. I took k as a 2000

[@mjylove2]

great video

[@christinegraham9069]

wonderfully explained, thank you so much :)

[@HeyitsHaydee]

how did 50cm became 0.5m?

[@MichelvanBiezen]

There are 100 cm in 1 m thus 50 cm = 0.5 m = (1/2) m

[@mohitbadukiya5825]

WTF

[@drmohini712]

Did you go*

[@ronham12]

go bless you sir

[@omparghale]

are you dutch ?

[@MichelvanBiezen]

Close. I am Flemish.

[@maxlolo1411]

Why do professors love making simple things so complicated? Someone gotta tell'em that this is NOT a sign of Intelligent! This is STUPIDITY... Tank you very much Mr.Michel

[@TheTechyBird]

IKR!? They just wanna show off.

[@gytisdramblewolfskis8521]

then explain me about this video dw=kxdx meaning d's are deleted by each other like dw/d=kxx so w=kxx. but the teacher suddenly writes w=kxx/2 where does this /2 appear from ?

[@kcaro98]

He did not divide the (d) from both sides; dw means "change in w" and dx means "change in x." The reason why the (1/2) comes out is because of the power rule for integration. Check out the link I attached and a couple examples for a better understanding. www.mathsisfun.com/calculus/integration-rules.html

[@gabor6259]

MrMaxLolo1400, not being able to write isn't the sign of intelligence either.

[@zubayirhkazi9115]

gytis dramblewolfskis Its integration, a calculus concept, not basic division lol

[@ArchanaYadav-vf9sz]

Thank you sir

[@MichelvanBiezen]

Welcome

[@ZWGames]

thnx

[@johnmwebela2226]

From zambia

[@MichelvanBiezen]

Welcome to the channel! 🙂

[@rasabeyk5291]

go white boy go

[@AlhambraDream]

Bizim hocalarada anlat üstad bize böyle anlatan adam çıkmadı daha

[@gabriellesalaveria6319]

Did he just not use a calculator?😰

[@MichelvanBiezen]

Yes he does that a lot. He was schooled in Belgium, where they drilled school children on how-to-do-arithmetic-calculations-in-your-head. By the way, we have some videos on how-to-do-arithmetic-calculations-in-your-head videos under the titile Math Tricks.

[@Star-si9uc]

I usually love your videos, but this time, I felt too confused.

[@Sunitakumari-dj7em]

Cool😂😂😂

[@fizixx]

🥳

[@MichelvanBiezen]

You are systematically working through the work, energy, power playlist. Keep it going. 🙂

[@fizixx]

@@MichelvanBiezen 🙂

[@fizixx]

@@MichelvanBiezen 🙂

[@jazank2624]

He looks like murray

[@manishmahawar4854]

Hindi bolne me sharam aati a kya

[@fayiskk8695]

Why force is not taken as Kdx while calculating dw

[@MichelvanBiezen]

W = F x dW = F dx

[@fayiskk8695]

@@MichelvanBiezen Force applied for moving the spring for a distance x is F=kx Similarly force applied to move a distance dx , F=k.dx So small work done for a diplacement dx , dw=Fdx=Kdx.dx ( I know i am wrong but why it is not taken like that)

[@MichelvanBiezen]

A small amount of work done = the force at that location x the small distance traveled. You must have F to represent the force at that location. Note that the force a little farther will be different, so F must be a function of the position.