The Physics Problem Students Keep Getting Wrong: Two Static Blocks Hung From a Spring Scale

This is a classic application of Newton's Laws. It makes a great demonstration of static force, equilibrium and Net Force.
Two masses are hung from opposite sides of a pulley. In between is a spring scale. What is the force reading on the scale?
Most people will report the answer to this physics problem wrong the first time through, thats ok, it's called learning!
This demonstration often comes up in introductory physics courses including AP Physics

[@RoyVanleeuwen-w1w]

Dude on reddit was right

[@pseudoplotinus]

but what if I added weight on the lead holding the spring-scale?? would that still be 100 N? (or 2 N in this case)

[@JJ-it3iq]

@@pseudoplotinus I assume you mean adding weight to the right-hand setup? If you add weight to, let's say the left arm, then that side will be heavier and the spring-scale will be moved to the left until it hits the wheel and if it gets stuck, it will act as if attached to a wall and behave like the setup in the middle.

[@rx326d]

yeah no shit. just imagine that the spring is attached to the wall. the spring would read 2N. Now imagine that same spring was attached to someone's finger, and they are pulling back at 2N of force to keep the weight up. The spring would still read 2N. now imagine the spring was tied to a 2 kilo weight being pulled down by gravity with 2N of force...the spring would still read 2N

[@yureinobbie68]

I was half expecting to be sent to a rickroll video. Just seeing the thumbnail made me remember basic physics again.

[@Brddvd]

answer for the picture is 200N on the video 100 and here is why In the video demonstration you're referring to, it seems like the person is showing a case where the tension in the middle of the rope equals the force on one side (in your example, 2 N), and the scale reads 2 N even though both sides have a force of 2 N. Here’s the explanation: The scale in the middle measures the tension in the rope. Tension is the force that is transmitted through the rope when forces are applied at both ends. In this setup, even though both sides of the rope pull with 2 N each, the tension in the rope is still 2 N. This is because the tension is the same throughout the rope if the system is in equilibrium and there is no acceleration. The confusion comes from thinking that the forces should be added together, but in reality, the tension is constant along the rope in such scenarios, and it equals the force on either side, not the sum of the forces. So, the scale shows 2 N because that's the force (or tension) experienced in the rope. The forces on both sides balance each other out, and the tension throughout the rope remains 2 N. This is different from the first image you showed, where the scenario is a little more about how tension in a single, straight rope system can appear depending on how it’s attached.

[@Binary_Omlet]

Dude is a FANTASTIC teacher. That was explained simply and concisely so that anyone can understand it.

[@INTEGRALPHYSICS]

quarter million people saw me wearing my white belt... wifes gonna be pissed.

[@RobertManzano]

@@INTEGRALPHYSICS Great now I can't even see the experiment over the blinding panache of that belt!

[@yannick_lisson]

@@INTEGRALPHYSICS guy is not just a great teacher, but hilarious too

[@tumblingartist]

Hahah great explanation and great sense of humor!

[@Rawing77]

Can not confirm, I didn't understand that at all.

[@MrOpenSeseme]

Checking in from Reddit.

[@fatgoolash]

Yup

[@ianb.6582]

@@fatgoolash Yup.

[@mystery-z]

theydidthemath really blew up this video lol

[@alkamino]

yup

[@whitespacenegative8527]

same

[@EvilMastermindOfDoom]

Also here from the dude on reddit. Went "OOOOoooohhHH!" out loud.

[@leonleszczynski3343]

Plot twist: Dude from Reddit is the dude in the video

[@TVideoupload]

Lmaooooo I came here to say same thing 🤣🙌

[@leonleszczynski3343]

@@TVideoupload 😂

[@JoshVangore]

He bamboozled us all for those juicy views

[@INTEGRALPHYSICS]

no, but it sure was nice to sit down in front of the computer to find an extra quarter of a million views rolled in this morning.

[@coloripple]

@@INTEGRALPHYSICS were there that many of us coming from dude on reddit?!

[@scripted_rain]

anyone else from that reddit dude

[@nickcunningham6344]

Yeaaa

[@MrRazzio]

yep! that reddit dude fucks.

[@jacoMKW]

yep XD

[@nbakh16]

Welp xD

[@user-dj9ii1fs2w]

Nope

[@WxBuggin]

In case you're wondering where the heck we all came from on Reddit - there's a post on r/theydidthemath posing this scenario, and someone linked it. I'm glad they did! You're awesome at explaining all of this in a way that's straightforward and easy to understand...instead of clickbaity. My teen will appreciate your channel too ☺️

[@INTEGRALPHYSICS]

thanks

[@ptyptypty3]

physics RULES!! your demonstration is what teaches this principle very nicely... I think it was early on in my physics that it was all the Counter Intuitive revelations that Physics presented. Other examples are why a Bowling ball goes down a ramp faster than a Tennis ball, moments of inertia, or why a 20 ton Semi Truck will stop in the same distance as a Bicycle assuming they have the same coefficient of friction tires and starting speeds... etc etc... amazing.. Thanks again for your videos..

[@INTEGRALPHYSICS]

Its funny you bring up the bowling ball. I have a Ball Hoop and Disc video about precisely that topic.

[@Alphinell]

ty reddit for introducing me to this physics problem that ill never have to answer in my life

[@rymcmanus]

I think the root of people's confusion is that it's counterintuitive to say that a spring scale measuring 2 N has "a net force of 0". People assume the spring itself is responsible for counteracting the 2N of force in such a situation, rather than seeking an equilibrium to measure the external system.

[@TheKasimkage]

Yeah, the explanation makes sense, but my brain doesn’t like it.

[@INTEGRALPHYSICS]

Many people think the spring pulls on the string on one end, but forget that the spring has to be pulling on something at its other end, always.

[@TheKasimkage]

@@INTEGRALPHYSICS That actually helps! Thank you!

[@faredoondastur8114]

Thank you very much for this explanation. While doing a textbook question, I came across such a scenario, and was under the false impression that the forces would cancel out and the answer would be 0 N of force, but your explanation indeed cleared my incorrect thinking and confusion. Thanks once again!

[@INTEGRALPHYSICS]

Thank you! This problem was a really fun one to think through and present.

[@deathsinger1192]

imagine yourself holding 200 Kilograms on each side and then someone tells you‘re actually experiencing no force at all

[@umeshmidha7017]

Here after my physics classes, concepts further enhanced

[@INTEGRALPHYSICS]

That what we do here.

[@ChaoticD3sTroYeR]

Dude on Reddit just introduced me to a good teacher. W.

[@gregslingland3576]

This is useful, but highly counterintuitive. At least for me.

[@NicaneCreedX]

I had a really hard time with it, but then thought of it like tug of war against a person (the other 2 newtons) holding fast or a wall (the bracket) and it makes sense to me now.. I think lol

[@ZombieDiesel]

This guy is on another level. Placing the book in front of the right side was genius

[@aolar9099]

We are all here because of the reddit dude

[@Travisheksrh2024]

yep the linkurink guy

[@TobyC8104]

Another guy here from Reddit. I read the explanations on reddit and was still confused, but watching this, the problem makes so much sense now.

[@MrCrininer]

I'm here from Reddit, and you earned yourself a subscriber. Really well explained!

[@Mezog001]

Is this an artifact of how the spring scale is constructed? If it was just the spring the spring would double in length with double the load which means that the load is 4N. In the case here the answer is 2N because the scale is not moving but the total load on the scale is 4N but the string inside the scale is only measuring one of the loads. The other load is keeping it from moving.

[@INTEGRALPHYSICS]

Think of the spring scale as a substitute for a segment of string which connects both masses. If you replaced the spring scale with a length of string that had a tensile strength of 3N, it would not break.

[@jacobgrodman]

Crazy to see my high school physics teacher blowing up on a reddit thread 😂

[@INTEGRALPHYSICS]

for a good reason this time...

[@eZaFVulcan]

@@INTEGRALPHYSICS this time???

[@gamebuster800]

I’m 34 and I learned something today, thank you

[@RootedHat]

If only my physics teachers had been this eloquent

[@stevenkiss2371]

Looking forward to more videos in the future. These help a lot with my fundamental understanding of physics.

[@INTEGRALPHYSICS]

R.I.P. White Board.

[@Conceptofcandid4043]

Thanks for the audiovisual presentation

[@carloscampbellgiron7649]

I have a follow up question, what will the scale read immediately if one of the weights is bigger?, let's say the right weight is 3N and also if instead the left weight is 3N.

[@conanomalley8989]

It will read 2N while accelerating in the direction of the 3N weight

[@carloscampbellgiron7649]

@@conanomalley8989 so it will always read the lowest weight no matter if it is attached to the hook or the other side?

[@siddhantghildiyal1489]

​@@carloscampbellgiron7649no. It will measure the force that is being exerted by the block attached to the 'hook' side coz thats how spring balance work. It doesn't matter if that force is less or more or equal to the other (right side) coz the right side block isn't pulling the spring. It is just holding the spring balance.

[@INTEGRALPHYSICS]

It will read a value between 2N and 3N. Search for a 'hanging atwood' on my channel.

[@Cryodrakon464]

Very good scrumptious explanation

[@FlamaAce]

I never knew I needed this until that guy on reddit pointed out that scales can't read

[@mukeshsuman9306]

Thank you sir . 🙏 please continue the videos..... I am from India, a serious student of physics ....

[@INTEGRALPHYSICS]

Thank you, I will

[@bloomfilms]

We’re all from the one Reddit thread on r/TheyDidTheMath aren’t we 😂

[@xslayer88]

Also here from reddit...awesome explanation. Makes perfect sense now!

[@thegibusguy4969]

Very concise and informative, thank you!

[@Timothymukansi]

This was a very good explanation. Thank you.

[@KennyH1437]

thanks bro, many of my students still get this part wrong because they think it's the total force, instead of thinking because the dynamometer only measures the tension of the hanging rope.

[@nugab]

Question: if you take the middle sensor and reverse it's direction but leave the weight and the anchor as they are. What does the sensor read? So the force sensing side of the sensor is pointed at the anchor.

[@INTEGRALPHYSICS]

2N. The spring scale reads the tension in the spring that is the result of BOTH sides pulling on the scale.

[@jasonmurray8118]

Here because of Reddit; and got to learn something news. Thank you my physics guy.

[@senffabrik4903]

this thing is going viral. a guy from reddit lead me here

[@yky4986]

Well everyone is from reddit i guess

[@hadesogg7531]

I love when Reddit sites sources, congrats on getting all the views

[@morningstoke]

Half this videos views are probably from today from the Reddit post Anyways, this is a great explanation. Glad to have watched this

[@nomorenames5568]

This is just a trick question. no one would get this question wrong if they were allowed 10 seconds to examine the scale and pull on it. There are two sided spring scales that can measure the force pulling on both sides. The only reason people get confused by this is because they haven't ever seen or touched one of these scales so they don't know it only registers force on one side.

[@INTEGRALPHYSICS]

no. the force on each side of the scale is 2N. if you replaced the spring scale with a string that had a tensile strength of 3N, it wouldnt break.

[@nomorenames5568]

@@INTEGRALPHYSICS I edited my comment to remove the force a bit after commenting since it wasn't relevant. All this question is really about is asking someone how a scale they've never had their hands on works. It'd be just as confusing if you asked someone that's never used a bathroom scale what the scale would show with two weights on both sides. The answer is obvious if you've used a bathroom scale but if you have never used one and have nothing more than a sketch of one for reference it would be difficult to know

[@Ramone_JiuJitsu]

Here from Reddit! Excellent explanation! Super cool!

[@INTEGRALPHYSICS]

Awesome, thank you!

[@carposp7789]

"All right kids" as a 38 yo, that felt nice

[@Saboc44]

I really do love how many of us ended up here from that reddit post already. Also, great explanation! Subscribed

[@SirHarryOfKane]

Sir you prevented a Reddit nerd war. We thank you for your efforts.

[@sebastiansanchezmendoza7523]

He did the math

[@jayeshametha]

Let each weight pull down by x. Then the P.E they lose = mgx + mgx = 2mgx The energy stored in spring = 1/2k(2x)^2 = 2kx^2. So kx = mgx. But the total force on the spring is k(2x), so it should be 2mgx. What it reads is nonsense because the dial dows not see the full stretch

[@evolove3602]

Damn, that guy on Reddit was right, thanks for the explanation!

[@gnux1]

So is the force exerted on the spring actually 4N in total (2N from the weight and 2N from the bracket) but the scale's purpose is measuring the force exerted on one side? or is the total force exerted on the spring actually 4N (not the number shown on the scale)

[@siddhantghildiyal1489]

The force exerted on spring is 2N in any case. Even if u attach a 1000N weight on the other side (bracket side) This problem is unnecessarily dodgey and has nothing to do with Force or weight but it is about how spring balance work. The spring inside the balance is actually pulled on one side only. The other side is just a support. Here the left side is the pulling side and the spring will only measure whatever is attached to that side. The right side (bracket side) doesn't pull the 'spring' inside the balance. It is attached to the outer body of the balance which has no bearing on the spring inside.

[@mike2106]

This explanation helped a lot. Thank you!

[@wibu_doge]

I'm from reddit :)

[@sethmarcell1131]

Very well explained, thanks!

[@JerGol]

Looks like they did the math.

[@mudrunner1990]

Also checking in from reddit.

[@siobhanhunt1749]

What happens if the counter weight (replacing the bracket) is lighter than or heavier than the weight being measured?

[@davebigman240]

Great vid! I was thinking it must be just the normal reading on the spring because when I'm lifting my luggage to check its weight before hitting the airport, it doesn't make a difference to the reading whether I'm struggling to pick it up manually or whatever

[@Xeit]

Hi, we come in peace, thank you for nice explanation!

[@vygandasjurkaitis1274]

What will show Spring scale if one side is pulling by 3N and Another 2N

[@INTEGRALPHYSICS]

in a static situation the two forces must be equal. If the spring scale is pulled harder in one direction than the other, then the spring scale will accelerate.

[@duskmare0000]

@@INTEGRALPHYSICS But while it's accelerating, what will it read as?

[@AgStarRay]

@@duskmare0000 I imagine it would read 2.5 N since it's the average of the two forces, but there'd be a bunch of interference while trying to read it

[@TheWinjin]

Let's drive the algo the way of that nice channel with excellent vids

[@SimplyUsefulChannel]

Checking in from Threads.

[@qgame4941]

They did indeed do the math

[@deephorizon1365]

Once he covered the other weight, everything clicked

[@priyank5161]

Redditors, assemble!!

[@polaroller]

Does the spring itself experience 4 newtons in all 3 situations? Is the spring scale designed to show half the force applied to the spring?

[@dinalijayasuriya3196]

In all 3 situations, the newton meter experiences a force of 2N in one direction and 2N in the other and it's stationary. But the measurement on the newton meter is only based on how much mass hangs from the spring at the bottom, which is 2N in all scenarios. (At least that's what I got from the video)

[@JJ-it3iq]

@@dinalijayasuriya3196 Newton's 3rd law means that there is no such thing as a lone force. Any force you feel will always have an opposite. If you hang 2N on a spring, it will move towards that weight because of Newton's 2nd. For the scale to measure a tuck of 2N, there has to be something holding it in place by an equal force in the opposite direction. Whether that something is a wall (that pulls with 2N of force) or a weight (that does the same) is irrelevant.

[@dinalijayasuriya3196]

@@JJ-it3iq Yep I already understood that, but thank you for the clarification :)

[@condad503]

@@JJ-it3iqThis is the clarification I needed. The top end isn’t connected to the spring itself it’s simply holding up the scale to counteract the other weight.

[@stonedyeet2675]

Tbh I knew the Reddit dude was right, I just need to know why he was.

[@sebidobre5018]

I still have a problem with visualing the sum of those forces in the system... Maybe i need a drawing on the blackboard😅 So the weight on the left pulls with X newtons, compressing the spring, the spring acts with a force on the weight and on the casing of the scale, right? So the whole system would move left with a force of X N acting on it, but the force on the right would stop the system in place for a net force of 0N, so the casing want to go left but the weight on the right cancels it, so the reading is the initial stretch in the spring, right?😅

[@tcblob4837]

Thanks for the info, dude from Reddit

[@anthonyshearer2657]

"Alright, kids" .. hey, I'm not a kid! Hmmm.. okay, please explain like I'm five, sorry for interrupting :) great video

[@Reclaimer01]

Covering the reason with physics.

[@almo2001]

Another reddit visit! Great explanation.

[@Ravvsss]

A curious visitor from reddit as well, really cool stuff

[@Mindrier]

Does this still hold if the two weights are not equal? Also here from Reddit 😅

[@vitorsousa8172]

Okay, it makes senses. Cheers

[@thomasleonards8660]

Yes! I love telling people that sometimes 2+2=2!

[@Pendragon667]

Once again we have gathered to heed the call of the great and almighty Reddit.

[@mimirovitch2792]

And that's the difference between mass and weight, this spring does not mesure any mass, it mesures the force pulling on one side that is cancelled by the other side

[@kylespringer7905]

Didn't click for me. If you hung the spring scale upside down, would the spring scale measure zero? If you attach the hook to the bracket and the weights to the other end would it read zero? Maybe I don't understand spring scales.

[@AjWentz23]

It's been a very long time since I've taken a physics course. But if you change the weight, specifically on the backend where the book covered, that doesn't make any difference does it?

[@Someone-ui5uk]

Thank you Reddit

[@frankjames4743]

This is a conspiracy theory to force Americans away from the Imperial system to the Metric system and to whatever unit a 'Newton' might represent. Can you Mr Physics guy explain what size socket/wrench is needed to remove a 5/8" bolt head, and why so complicated? Thank you. Subbed and liked. From reddit also

[@funnyguywithafro]

"why are the suddenly 100 new comments on a video I posted a year ago??"

[@INTEGRALPHYSICS]

^^This

[@lukehudson5674]

What would it read if the weight on the right hand side was 3N? Would the spring still say 2N because that's what's pulling? Or would rolls be reversed and it would say 3N?

[@INTEGRALPHYSICS]

the forces are imbalanced so the spring scale would get pulled/move right.

[@archibaldaddelton4432]

What would the scale read with R-2n and L-4n ?

[@abhijithharimenon9916]

I love how there's sudden activity from redditors here 1 year after the video was posted

[@priyank5161]

And just like that, this video grew from 10-20k to 500k All due to reddit

[@borisquezadaa]

Is correct to asume that the scale reads 2[N] + a small amount of [N] from the scale own weigth?

[@dieterrosswag933]

So if I'm lifting 100kg I'm actually using force about 200 kg (+body)? Since my legs are pressing the opposite direction. But it only counts 100kg?

[@chriswiltz6860]

Force = Mass x Acceleration so the force (newtons) needed would depend on the amount of acceleration you applied to the weight. Lifting a weight faster (e.g., power lifting) requires more force. The force needed at bare minimum to lift a 1kg weight off the ground is 9.8 newtons (because the pull of gravity is 9.8 m/s). So to lift a 100kg weight you need to generate at least 980 newtons or roughly 100 kg of force.

[@dieterrosswag933]

@chriswiltz6860 if i attach 100 kg separately on each ends (similar to the video) on a kg scale measure device....how much will it show? 100 or 200 kg? If it's only 100, then how comes than if lift the whole device with my hands it weights 200kg Edit: i think know i get it. The opposite weight is pushing in the opposite side. It's actually a mechanical issue, not a gravitational

[@chriswiltz6860]

​@@dieterrosswag933Yes you're correct. A key thing to understand is that the spring scale isn't measuring the weight of the object, it's measuring the force being applied to the spring. It becomes confusing because a hanging weight is only exerting the amount of force gravity is putting on it so the weight and the force are the same. If you pulled down on the 100kg weight (added more force) the scale would read higher than 100, but the 100kg weight still weighs the same.

[@dieterrosswag933]

@@chriswiltz6860 thanks

[@mamedvu8770]

I wonder how many views this video had before the Reddit people showed up

[@Agrim_VM]

love you man

[@matthewstanulet1441]

He’s going to be confused seeing a spike in views all of a sudden

[@ThBlindElephant]

So if Spiderman were holding up two buses from the middle of a bridge, it would equal the weight of Spiderman pulling up 1 bus from the side of a building?

[@roberti2755]

The weight would be double but the force would be the same. Imagine you are carrying a bucket of water in one hand and a buncket of water in the other, the weight is 30lbs per bucket so a total of 60lbs. Now imagine you have to carry the same 2 buckets in one hand, its still the same amount of water but it will require much more force on your one hand as the weight is not equalized.

[@Coolbeans_1999]

But there the force vector is the same in that example, aren’t the directions of force here horizontal in opposite directions because of the pullies. Like the pullies transfer the vertical force into a horizontal force right?

[@aya-chan2371]

Idk anything about physics, so i have a silly question. So what happens if you have 2 newton on one side, and then 4 newton on one side? What will the scale says? Will it be 2 newton then?

[@OdekoMoon]

It will still say 2 newtons, but also the scale will slide towards the unbalanced side because it's pulling with more force. If the scale gets pulled so far that it hits the pully and stops, now the pully is holding the scale in a fixed place, making it identical to the middle example in the video where a bracket holds the scale in place. It will still say 2 newtons while at rest in this position as well.

[@INTEGRALPHYSICS]

More than 2, less than 4. See link. kzbin.info/www/bejne/l5TWh5-srcljibs

[@danielsdefense1635]

Battle field from Reddit comment section got me here.

[@sumthingsup098]

Well explained. Thank you

[@RitusG]

What happens when you hook two scales together. First, in series, and then facing the opposite direction.

[@hutxhy4071]

Would it still read 2 N if the "anchored" side of the spring weight was attached to a 3 N weight?

[@rodneylong2493]

I am still confused by this. At one point, it is stated that 'the net force on this weight right here is zero'. So does the confusion over how to answer this given physics problem a misunderstanding of what a spring scale measures? I am assuming it only measures that forces applied to any given side (as long as there is a counter-balance to prevent acceleration) and is not measuring the net force of a system.

[@ericjackson9462]

Whenever you see something stationary, you can be confident that the net force on that thing is zero. Otherwise, the net force would start moving the thing. You can see this in Newton's 2nd law -- F=ma. Since net acceleration is zero, net force is certainly zero. That's all that is meant by "the net force on this weight right here is zero". The spring scale is measuring tension for one part of the system. It's one of the internal forces. But it's not the whole story.

[@luisrogelio98]

The spring read 2 newtons because in both case is held in place by the same amount of force, if in the 2 weight version you remove one what will happen is that the spring will fall to the ground cause there is nothing holding it in place. If held in place with a force of 2 newtons will experiment the same regardless if it is static object or a different 2 newtons.

[@DavoBrawn]

What happens if we lie spring scales in series? Or parallel?

[@INTEGRALPHYSICS]

Series: Each spring scale has a reading that shows the total load. Parallel: All of the spring scales readings added together equal the total load.

[@adigraydi1381]

Thanks a lot mate

[@legendrags]

I can confirm more than 300K views were from reddit statistics: essef said it was 180K 20 hours ago and Im pretty sure its around 550K now dude on reddit was definitely right

[@INTEGRALPHYSICS]

this vid had 9k views two days ago...

[@legendrags]

@@INTEGRALPHYSICS Holy cow thats a lot of views from dude on reddit

[@KILLER_BOT_3.5]

R for REDDIT

[@facs27]

Dude on Reddit making this video go viral