Load force vs. Effort force

[edy]

My 9 year old is studying science and is on the section with fixed pulleys and movable pulleys. He got a handout to fill out with the questions and pictures, but both my wife and I (science university degrees) are either going crazy or something weird is going on. There are some simple definitions that I seem to have either lost my mind or they are too simplistic or something is not defined properly.

The handout says “The force needed to move the load is called the load force.”

In my mind, that’s not true… they mixed up load force and effort force. If you have a pulley system depending on the kind of mechanical advantage you have, it is the effort force that is what is needed to move the load. To me, the load force is the force exerted by the load on the main cable (absent any pulleys or at the point of connection to the machine)… i.e. the weight of the load itself. Or do they mean both are true? In that case yes load force is needed to move the load (without a simple machine) and effort force is also able to move the load (through the mechanical advantage of the simple machine). In that case the definition should point out that it is the machine that makes the effort force differ from the load force required to move the load. 

Then they say the following regarding a movable pulley… the kind that is anchored to the ceiling on one end, the cable “slings” down and up around the pulley like a “U”, and the centre of the pulley is attached to the actual load…

“The pulley is attached to the load, the rope attached to the structure, makes lifting load easier because rope attached to the structure takes half the weight of the load. You only use half the effort force that you would have needed with a fixed pulley”

Ok that makes sense, for a 100 N load force you essentially have 2-tethers on it (rope coming out from each side of pulley holding the load) each supporting 50 N. The structure takes 50 N (rope attached to ceiling) and you exert 50 N force to hold the other tether up. If it were attached to the ceiling as well, both ceiling hooks would feel 50 N.

However, I don’t like this explanation to kids as I’d rather they see generally that the force also is related to distance and really has to do with work conservation. The above is a static example of force distribution. However, ultimately the setup means that for every 10 cm you move the effort rope, the load only travels 5 cm against the load force. The mechanical advantage is that the distance x force is equal on both load and effort sides. You can make your effort less by moving a greater distance with less effort.

This analogy is better translated to many other examples including torque wrenches, levers, gears, ramps, and many other simple machines. The above explanation of the ceiling taking “half the weight” makes no sense to my 9 year old and ultimately nothing about the fact that the load is travelling a half the distance (for each pull of the “effort” rope) is mentioned anywhere.

So back to my kid’s science homework…
Questions are 1. What is a load force? 2. What is an effort force? 3. How much effort force is needed to lift 300 kg weight in fixed pulley system, 4. …movable pulley system? 5. In a movable pulley system, where does the other effort come from?

So for 3. and 4. it is 300 kg and 150 kg but I  am already cringing since they are mixing up mass and weight and force units. I am over-thinking this?

The 1. and 2. questions don’t seem to be properly addressed in the handout or switched/confusing definitions (see above). The effort force is what you put into the system to move the load. Imagine a black box where you have no idea what kind of mechanical advantage you have set up… all you have is a load on one end, and a place to apply effort force on the other end. The load force would be the direct amount of force the load applies to the machine or black box (first connection to the black box). Load force depends on the load alone (it’s weight), effort force is what you need to move the load, regardless of it’s weight as it depends on the machine (mechanical advantage) between the effort and the load.

Finally last question I am guessing they mean the “other effort” comes from the supporting structure? Your effort force is 50 N and the “other” ceiling effort of 50 N is what allows you to hold up a 100 N load force?

Thank you all for your thoughts on this primary school handout and please let me know if I am just over-thinking this or is this just going to confuse my kids and they will have to unlearn this so they can understand it properly later on? I want to teach it properly in a way that can be generalized to all types of machines and my kids understand the fundamentals properly, not just memorize a bunch of stupid examples that give half-arsed explanations that confuse them.

[IanB]

I think at a primary education level, things do tend to be oversimplified, and the people doing the teaching do not probably have physics degrees.

So things will be less accurate compared to a college level understanding, and to a degree, children are taught things that are not necessarily "correct". They will have to unlearn and re-learn things later. That's just part of growing up and understanding how the world works. It teaches children not to automatically believe everything they are told, and to be skeptical about "facts".

[IanB]

Also, when studying mechanics at a technical level there is a difference between statics and dynamics. If nothing is moving, then a static analysis using force balances is appropriate, and is what would be used in a professional engineering context (the design of bridges, structures, etc.).

[IanB]

I would also think that introducing the concept of conservation of work/energy at a primary education level would be a big stretch. What age group are we talking about here?

Edit: OK, 9 years old. Then really, don't even get involved. At 9 years old children just need to be able to remember what they are told and play it back. I think your job as a parent is to explain that it may or may not be the whole story, or even half the story, and they will learn it properly when they get older.

[eugene]

Edit: OK, 9 years old. Then really, don't even get involved. At 9 years old children just need to be able to remember what they are told and play it back. I think your job as a parent is to explain that it may or may not be the whole story, or even half the story, and they will learn it properly when they get older.

Ouch!!

"Parents: don't even get involved."
"9 year olds just need to be able remember what they are told and play it back"

Please, please, please, for the benefit of the children, don't ever become an elementary school teacher.

[bdunham7]

I am over-thinking this?

Yes. 

If I understand correctly, what they are trying to get the students to understand is simply the principle of force multiplication by simple machines.  In order to teach that to an elementary student, you have to oversimplify quite a bit.

[IanB]

Ouch!!

"Parents: don't even get involved."
"9 year olds just need to be able remember what they are told and play it back"

Please, please, please, for the benefit of the children, don't ever become an elementary school teacher.

I can see how you might react that way, but being serious, learning has to be pitched at the level of the student.

For example, when I was 10 years old, I observed by experiment that a loudspeaker had a lower volume when connected with thin wires than when connected with thick wires. I asked a teacher why that might be, and he told me that maybe electricity has a harder time flowing through the thin wires, and that maybe it gets impeded somehow and that's why the volume is lower? I remember not really buying that argument, because to me a wire was a wire, and the size of the wire shouldn't matter to the flow of electricity.

We have to remember that some things are not really easy to understand at 9 or 10 years old, and there is no point getting too technical before students have enough knowledge to appreciate the details.

[IanB]

To illustrate how complex this subject can be, let me offer an example.

Suppose we have a 1 kg weight resting on a table. We can say it is exerting a downward force on the table of 9.8 N. But at the same time, the table is pushing up on the weight with a force of 9.8 N. Since the two forces are equal and opposite, we can deduce that the net force on the weight is zero. We can verify that the net force is zero since we know that force equals mass times acceleration. Since the weight is clearly stationary and not accelerating, the net force on the weight must be zero.

Now let's suppose we lift the table very, very slowly through a height of 1 m. We could say that work was done on the weight, and it has gained a potential energy of 9.8 Nm (force times distance). But we also know the net force on the weight was zero, and we know that since we moved the table ever so slowly there was no appreciable acceleration. So if the net force on the weight was zero, and zero was moved through 1 m, how was any work done? Where did the potential energy come from?

Let's suppose we want to explain this to a child. How could we do that?

[eugene]

For example, when I was 10 years old, I observed by experiment that a loudspeaker had a lower volume when connected with thin wires than when connected with thick wires. I asked a teacher why that might be, and he told me that maybe electricity has a harder time flowing through the thin wires, and that maybe it gets impeded somehow and that's why the volume is lower? I remember not really buying that argument, because to me a wire was a wire, and the size of the wire shouldn't matter to the flow of electricity.

What I hear you saying is that you didn't "just memorize what you were told and play it back." It is not in the best interest of anyone of any age to treat them that way.

And anyone that tells parents to just not get involved in their kids education is a danger to parents and kids.

You seem to think that I'm unaware that kids need to have lessons framed in a way that they can digest. Everyone knows that. But humans of all ages, even infants, are capable of more than just memorizing and then waiting until they are older to understand. If that's the best you have to offer kids, then please stay away from mine. Actually, stay away from all of them!

[IanB]

And anyone that tells parents to just not get involved in their kids education is a danger to parents and kids.

Of course parents should get involved in their kids' education. That's not what I'm saying at all. What I'm saying is don't get involved in arguments with teachers about terminology.

[edy]

I wouldn’t necessarily argue with the teacher, but I would teach my kids that there are other ways to think about the problem. The main thing is to get the answer correct and make sure I can follow that their reasoning is correct. I can’t stand when they get some math homework and they are told to do things a certain way that doesn’t really teach them anything they can apply to anything else. The idea of learning fundamentals is that understanding that lets you construct all the more complicated systems that depend on it. If they learn some strange way to do something that they can’t reason from more fundamental building blocks then they are just robots doing things they can’t understand and will eventually get in trouble obtaining the correct answers when they hit some unexpected situation.

[edy]

To illustrate how complex this subject can be, let me offer an example.

Suppose we have a 1 kg weight resting on a table. We can say it is exerting a downward force on the table of 9.8 N. But at the same time, the table is pushing up on the weight with a force of 9.8 N. Since the two forces are equal and opposite, we can deduce that the net force on the weight is zero. We can verify that the net force is zero since we know that force equals mass times acceleration. Since the weight is clearly stationary and not accelerating, the net force on the weight must be zero.

Now let's suppose we lift the table very, very slowly through a height of 1 m. We could say that work was done on the weight, and it has gained a potential energy of 9.8 Nm (force times distance). But we also know the net force on the weight was zero, and we know that since we moved the table ever so slowly there was no appreciable acceleration. So if the net force on the weight was zero, and zero was moved through 1 m, how was any work done? Where did the potential energy come from?

Let's suppose we want to explain this to a child. How could we do that?

The net force on the weight is not zero because it is moving up. The force that the table exerts on the weight may be 9.80001 N, even though the weight on the table is 9.8 N. That differential means the weight translates vertically. By the time you stopped moving the table you are back to 9.8 N and it equals out the weight again so no movement, but you are 1 m higher than where you started. It was close to zero but not quite zero, and over time that small amount integrated itself to the full work done. Same if you drop the weight slowly, by moving table down you are supporting the weight by 9.7999999 N while it still pushes down with 9.8 N, so that 0.0000001 N differential is enough to make the weight drop.

Now I know at the beginning and ends of movement there is more and less force felt by the weight due to acceleration/deceleration but during steady state movement (most of the time) there is a stable force differential leading to steady translation at a fixed speed of the weight up and down. The acceleration/deceleration effects would cancel out and appear as the “limit” case in which almost no acceleration and deceleration occur and it is just moving…. Force x distance. At least that’s how I understand it. Is it too hard for a kid to understand this? Depends.

[IanB]

The net force on the weight is not zero because it is moving up. The force that the table exerts on the weight may be 9.80001 N, even though the weight on the table is 9.8 N. That differential means the weight translates vertically. By the time you stopped moving the table you are back to 9.8 N and it equals out the weight again so no movement, but you are 1 m higher than where you started. It was close to zero but not quite zero, and over time that small amount integrated itself to the full work done.

However, the formula for work done is the integral of force over distance, not the integral of force over time. If we have an infinitesimal force of 0.0001 N integrated over a distance of 1 m, that is 0.00001 joules not 9.8 joules.

Same if you drop the weight slowly, by moving table down you are supporting the weight by 9.7999999 N while it still pushes down with 9.8 N, so that 0.0000001 N differential is enough to make the weight drop.

Now I know at the beginning and ends of movement there is more and less force felt by the weight due to acceleration/deceleration but during steady state movement (most of the time) there is a stable force differential leading to steady translation at a fixed speed of the weight up and down.

But Newton's laws of motion say that a body moving at a constant velocity experiences no inertial forces, so in steady state movement the net force on the weight is zero.

The acceleration/deceleration effects would cancel out and appear as the “limit” case in which almost no acceleration and deceleration occur and it is just moving…. Force x distance. At least that’s how I understand it. Is it too hard for a kid to understand this? Depends.

Clearly gravity comes into play here, but now we have to deal with the physics of conservative fields and forces on bodies moving within those fields.

One can say the weight is experiencing a force due to gravity, but if that is the case, why isn't it accelerating? Why is it sitting in stationary fashion on the table?

Is there a force, or is there not a force?

To go back to the top of the thread, if I am pulling on the rope of a pulley, am I pulling down, or is the rope pulling up?

[RJSV]

EDY:
   Immediately, THIS image popped into my head:
Suggest:. Place yet another 'U' shaped rope, attached the same way, so now you have Weight / 3 on each rope. But that in itself supports your argument, as that 'shared' weight is meaningless, by itself, and simply does not work, as that third rope with pulley becomes immediately separated, as you lift, and would just sit there. I suppose, maybe, that 'two handed pull' done by grabbing BOTH free ends and lifting, perhaps would be two-thirds perceived lifting, while the...yeah uh no...
I'm thinking, a second rope/pulley would not change any of the ratios ! They are, essentially in parallel.
(This is gonna bug me).
You're on the right track though, it's needing the distance covered, while pulling, to fill out the 'Work' calculation properly.

[Someone]

Questions are 1. What is a load force? 2. What is an effort force? 3. How much effort force is needed to lift 300 kg weight in fixed pulley system, 4. …movable pulley system? 5. In a movable pulley system, where does the other effort come from?

Is that verbatim? Perhaps a photo/scan of the exact question and any illustrations/images it has with it would help.

Based on precisely what you wrote: Answer 5) Effort /= Force

The terminology is consistent and commonplace:
https://www.engineeringtoolbox.com/pulleys-d_1297.html

We have to remember that some things are not really easy to understand at 9 or 10 years old, and there is no point getting too technical before students have enough knowledge to appreciate the details.

Some 10 year olds will happily grasp statics and vectors, but they're not concepts most would be able to understand. Hence the baby steps. I checked some physics texts, and they completely ignore statics/levers (leave that for the engineering texts) and start with dynamics instead.

Thank you all for your thoughts on this primary school handout and please let me know if I am just over-thinking this or is this just going to confuse my kids and they will have to unlearn this so they can understand it properly later on? I want to teach it properly in a way that can be generalized to all types of machines and my kids understand the fundamentals properly, not just memorize a bunch of stupid examples that give half-arsed explanations that confuse them.

You are over thinking it! A question is from it's defined assumptions/definitions (which we have not seen in full). Yes, using the word work or effort is muddling the water but only if you already associate specific technical definitions to those words, introduced much later in the education system. Its not practical to avoid all possibly technical words when explaining basic ideas to beginners.

I checked some texts here that label similar problems with simple letter designations, and talk about differentiating forces (for statics) based on applied/inherent external/internal acting/reacting.

[Someone]

I'm guessing this is the level of complexity they are trying to convey. You can walk through with the student how equal/opposite means you can split the system through any plane/cross-section and there must be a balance.

[SiliconWizard]

I'd be curious to see what kind of physics, even basic stuff, is being taught to 9-year olds anyway. I don't think I've ever been exposed to the concept of forces and pulleys until junior high school.
So if it's very basic stuff, I wouldn't worry about the exact terms anyway. As much as I don't like teachers messing up with terms, we need to remember those are just classes for 9-year old kids.

[edy]

I just realized I completely goofed up on that lifting table question by IanB. The truth is if I apply a 9.80001 N force continuously the 1 kg weight doesn’t just go up… it accelerates up! This is a better analogy…

Imagine a balance, perfect frictionless. A 1 kg weight on each side of the balance, each pushes down exactly by 9.8 N and the balance pushes up also by 9.8 N so things don’t move, they are stationary. If you want you can use a pulley with 2 weights, same idea. You come by and ever so slightly give a nudge to one side… say 0.00001 N for a split second, enough that it creates an acceleration, then you take your finger away… no more acceleration but the balance (or pulley system) is now moving at a constant rate of speed. One side of the balance goes up, other side goes down. Or if thinking pulley, like elevator and counter-weight.

Now it could take 1 year to move 1 meter, it doesn’t really matter. The point is that it took a tiny effort to get things in motion. The increase in potential energy on one weight is balanced by the loss of potential energy of the other weight.

Now imagine a 1 kg drone hovering and thrust of 9.8 N down. It is not moving. I come by and nudge it with my finger… it starts to move up. My finger produces an acceleration but the minute I remove my finger the drone has constant linear motion, constant speed, because force of gravity exactly cancelled by thrust force of 9.8 N. It will continue to move up until I stop it again with my finger. This could be 1 minute later or 1 hour later (I am of course not limiting the case by anything real here like battery life, wind, etc).

Whether it takes 1 minute or 1 hour, if the drone moves up by 1 meter in each case we have the same situation of increase in potential energy (relative to the gravity well of Earth).. Sure we used 60x more battery energy to keep it hovering against gravity for 1 hour vs 1 minute, but the initial “nudge” that kicked the drone up ever so slightly was what actually moved the drone. So again this is an integration of net force vectors over time which produces the F=ma that then affects position of drone/weight. Sounds like accelerometer-based movement tracking.

Anyways thanks for all the input… you know the saying, the “teacher learns more from the student”. Having another look at this stuff years later I appreciate even more of the nuances that I probably glossed over while going through it.

[RJSV]

Yeah... Just like you (,just did), GLOSSED OVER, the concept...FRICTION.
YEAH, NO, virtually none of that is going to happen.

   I'm now 'nudging' myself, to move, ever so slowly, I'm declaring it doesn't matter how slow...
I'm just moving away, ...and will STILL be moving, from that NUDGE, like, wasn't that like 6 hours ago ?

[james_s]

I can see how you might react that way, but being serious, learning has to be pitched at the level of the student.

For example, when I was 10 years old, I observed by experiment that a loudspeaker had a lower volume when connected with thin wires than when connected with thick wires. I asked a teacher why that might be, and he told me that maybe electricity has a harder time flowing through the thin wires, and that maybe it gets impeded somehow and that's why the volume is lower? I remember not really buying that argument, because to me a wire was a wire, and the size of the wire shouldn't matter to the flow of electricity.

We have to remember that some things are not really easy to understand at 9 or 10 years old, and there is no point getting too technical before students have enough knowledge to appreciate the details.

I certainly had a stronger understanding than that when I was 10. I didn't know the math, but I did understand the concept of resistance and higher current requiring a heavier wire. It was very intuitive to me, a garden hose could move a lot more water than a drinking straw. I was also familiar with the idea that you can't get more energy out of a system than you put in. My dad was an engineer and my uncle an electrician and I was fascinated with that stuff.

[james_s]

If I understand correctly, what they are trying to get the students to understand is simply the principle of force multiplication by simple machines.  In order to teach that to an elementary student, you have to oversimplify quite a bit.

The best way to teach that is to do it. I remember going to a science museum when I was a kid and they had an exhibit with pulley systems. A bunch of identical weights were attached to single and multiple pulley arrangements. With the single pulley you could barely lift the weight but with multiple pulleys it was easy to lift but you had to pull a lot more rope.

[IanB]

However, I don’t like this explanation to kids as I’d rather they see generally that the force also is related to distance and really has to do with work conservation. The above is a static example of force distribution. However, ultimately the setup means that for every 10 cm you move the effort rope, the load only travels 5 cm against the load force. The mechanical advantage is that the distance x force is equal on both load and effort sides. You can make your effort less by moving a greater distance with less effort.

This analogy is better translated to many other examples including torque wrenches, levers, gears, ramps, and many other simple machines. The above explanation of the ceiling taking “half the weight” makes no sense to my 9 year old and ultimately nothing about the fact that the load is travelling a half the distance (for each pull of the “effort” rope) is mentioned anywhere.

Here's a counter-example to that (work conservation rather than static force distribution).

In the setup pictured below, the blue rope is taut and the red and green ropes each have about one inch of slack.

If we cut the blue rope, how far will the weight fall before it reaches a new equilibrium?

[edy]

This is interesting…. One would at first think the weight falls. But if you look at the situation you first have 2 springs sharing the load and stretching by a certain amount each (half the load “yield”). It is as if you have one long spring really (you can ignore the blue rope or pretend it is at the bottom or top, not in the middle). After you cut the blue rope, you still have 2 springs but now they are in parallel, not serial. In effect their modulus is half, since each spring will stretch less as the weight tension is distributed between them… so counter-intuitively the weight will not drop and will probably go up!

[IanB]

Yes, that is indeed what happens: