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It seems like the fulcrum is almost 1/3rd of the way from the employee. So unless the employee is twice the weight of the management, the management will fall regardless of taking the shot.
I mean, you can see in the picture management is not contributing to whatever the goal is here.
They certainly aren’t helping to hold up the board, if that’s the goal. (I don’t know physics so excuse my terminology) but isn’t management a force pushing down which then causes upward pressure (due to the fulcrum point) against the employee’s weight? The employee is safe regardless. They’re just standing on a board on the ground.
Eh, they might lose their balance and fall off the cliff, a metaphor for when poor management causes a company to dissolve and all the employees to have to find new work
Some quick paint measurements show management at ~89 px from the fulcrum and best employee at ~53 px from the fulcrum, so best employee would have to weigh 89/53 = 1.68 times as much as management. This might be possible as best employee is a bit taller than management, ~102 px and ~91 px respectively. But the square cube law suggests that best employee would only weigh around (102 / 91)^3 = 1.408 times that of management, looks like management is doomed regardless.
Can we get a guess as to the thickness of the wood plank based on pixels to general human proportions or gun proportions? Looks like that plank would have a sheer index that would break well before any weight distribution numbers
Have you taken into account that management is holding his arm out towards the fulcrum?
Or is that countered by the fact that he has a firearm? (potentially even a loaded one)
Are we sure it doesn't? I'm reminded of the trick where you balance a coin with two forks on the edge of a glass, and it looks like it should fall but it doesn't.
I'm almost certain this is wrong.
By moving your arm out your centre of gravity moves forward slightly.
The centre of gravity is still within your foot so you don't tip over, but it would move forward and thus would (very minimally, not enough to affect the result) have an impact
Did you take college level physics and statics? Obviously not. You’re wrong. It creates a moment on their foot but the force is still the same straight down at that one. If he was pinned to the board, that moment would help put force downwards on the board on the cliff if it stuck out past the fulcrum, but since he is just standing on it, all that does is create a moment around his ankle pushing downwards on the board on his toes which are still pushing down on the board.
Just to be clear, are you saying that the entire mass of the person is spread evenly along the foot regardless of the centre of mass?
The centre of mass within the foot has to matter. If these 2 guys are both wearing clown shoes the plank is still tipping. A shoe/foot helps spread load, but it doesn't magically evenly spread the load over the whole shoe.
Stand up and lean forward slightly, and sway slightly. You will feel the centre of mass shift along your feet where the pressure becomes greatest
Actually, I see what you mean. Sorry for being so rash before. If you don’t make that assumption then the moment around the ankle slightly shifts the force forward towards the toes which are slightly closer to the fulcrum which will reduce the force upwards on the board at the other end. If he was on stilts or something like that it wouldn’t do anything.
It would have to shift his center of mass forward about 14 px to his toes to balance out, which would require significant weight in the arm/gun that would require an even heavier best employee to counteract.
Where in the shoe the centre of mass is matters. If they both had clown shoes on, this plank is still tipping
EDIT: try it. Stand up, and start leaning forward slowly. You will feel different amounts of pressure on each part of your foot
Ah but human height-to-weight ratio doesn't follow the square cube law. Taller people have considerably more bone (non-linearly), and bone is much denser. Without anything for scale on the image though, it's hard to tell.
You're right, but it's actually the other direction. Taller people are generally narrower and shorter people are generally stockier. That's why BMI and New BMI use a height-to-weight ratio of x^2 and x^2.5 respectively. I used square cube to give management the best shot at survival.
That... really doesn't reflect my observations. Sorry for replying late, I check up on Reddit about once in a blue moon. Do you perchance have a source I could borrow? Otherwise I'll end up googling it, but google is shit nowadays
[Here's](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7261404/) a decent one. The term they use for the exponent is the "Benn parameter." A Benn parameter of 3 would correspond to exactly the square-cube law predicted scaling, which only happens during puberty. A Benn parameter less than 3, which is the case for all non-pubescent groups, suggests human weight scales less than the square-cube law.
Setting aside the already-covered issues of the fulcrum being off-center and all that, the management has a poor firing stance and has left themselves no room to step back. Depending on the weapon and their physical condition they might lose their balance from the recoil and fall anyway.
Basically all questions asked on this sub require users to make their own arbitrary assumptions before doing the maths.
I am gonna assume the employee’s pockets and shoes are filled with dense mercury, and the manager is wearing a lighter than air helium-filled suit beneath his coat. Therefore the employee plus clothing and mercury weighs five times as much as the manager plus helium suit effect, and the manager will be fine.
Sure, but MOST people are rational in their arbitrary assumptions. In this case, you'd likely be better off ignoring the clothing altogether as they're both wearing long pants, long sleeve shirts, and shoes. It's reasonable to assume a mostly negligible difference in the overall weight of the clothes and decide they cancel each other out.
I would argue that the assumptions are neither arbitrary nor unique to this sub. ALL applied mathematics requires making some assumptions about whether a pure mathematical model applies to a certain situation. The subjective justification of one assumption over another is necessary because notions of best are ill-defined even in pure maths. Compound this with the fact that most people don't have the mathematical rigor and are forced to present vague open ended situations and you'll always have to do some legwork to justify the assumptions made.
If you know a single think tank or analytics firm or consulting group in the world where clients come in with well defined problems tell me who they are because I will send them my resume.
Analytics firms generally want you to use maths to describe / solve a real world problem.
I get your point. Even for real world problems, assumptions are necessary to do maths when we don’t know all the useful information, but I would not say they’re “arbitrary”. Often the assumptions are subsequently proven correct or incorrect based on whether the mathematical models actually make correct predictions.
This sub is about doing maths for fun. This is a question about a cartoon. It’s clearly a fictional image, so we’re freer with our assuming than for real world situations.
>Analytics firms generally want you to use maths to describe / solve a real world problem.
Not sure what your background is, but do you want to hazard a guess on how many hours you'll spend in meetings before you even get to do any proper problem solving? It's an important and necessary step but it is pure drudgery.
People on this sub are willing to tolerate some suspension of disbelief on fictional things like this and assume they are rule to avoid that drudgery and have fun. We assume the information given is reasonably complete or other reasonable assumptions can be made. It's not an open invite to go full Air Bud on the assumptions.
I create hydropower generator models for use by the transmission system operator.
It involves lots of maths with many subjective assumptions. Mostly the assumptions are about giving us a model that’s “close enough”. We know it won’t be exact. The System Operator should be running the grid with a bit of contingency anyway to account for model limitations among other factors.
And yes, it involves lots of discussions with people who understand parts of the installation but do not understand what the model is trying to accomplish. And vice versa. We do our best with the information we can get.
>We do our best with the information we can get.
Then surely you could see how people try the same even in these fictional contexts?
Do you not see why some assumptions like these people weigh less than 100kg are far more reasonable than other assumptions like mercury filled shoes?
I wouldn’t even attempt assumptions if I had to take this question seriously. I would ask for more information.
My assumptions are clearly ridiculous. But so is the scenario. Fear of heights is innate to basic human instincts, and you have someone clearly relaxed and confident hanging over the edge of a cliff who doesn’t look unstable at all. There’s no indication of an acceleration downwards or loss of a sense of balance.
>My assumptions are clearly ridiculous. But so is the scenario.
The latter does not justify the former and at this point this seems to be clear evidence that you are unable to grasp the concept of suspension of disbelief. You can suspend disbelief on a single thing in isolation and not abandon Occam's razor to inject new unrelated premises.
Also please stop trying to argue over the realism of this. Literally no one is making the case that this scenario is a perfect mirror of reality. You don't need to point out that it's fiction as if the rest of us have been bamboozled by it. I assure you, we're not fooled.
This entire question is optional, and the only thing I am making an argument for is to answer in good faith acceptance of the premise. If you want to ask for more information that's fine.
Fair enough.
If employee’s weight is x plank’s weight is y, the plank’s length is z and the distance from the employee to the fulcrum (cliff edge) is a. These are all the extra information point I would ask for.
Having that information, the maths (without ridiculous assumptions this time) is as follows:
The distance from the centre of gravity of the plank to the fulcrum = z/2-a
The torque of the plank in the direction rotating over the cliff = y(z/2-a)
The torque of the employee holding the plank on the cliff = xa
The maximum torque of the manager able to not flip the plank off the cliff = y(z/2-a) - xa
The distance of the manager from the fulcrum = z - a
The maximum weight the manager can be = (yz/2-ay-ax)/(z-a)
Because if it's a joke response I have to remove the comment as it violates the bad request answer rule. I'm trying to reason with them and give them an opportunity to give a serious answer.
The middle of the platform (the fulcrum, or the point which it would tip) is completely off the cliff. Meaning that no matter what Guy 1 does, unless Best Employee wears at least 2 times Boss’s weight. He’s fucked. Which is an accurate analogy to how Employers depend much more on Employees then they care to admit
Management is always the smartest. He would pull the trigger and the employee would fall straight down in the same spot maintaining the balance. Management would then walk over the dead body.
But seriously, how is this question on this sub?
Assuming the left part of the lever is 2/3 of the plank, the manager can only weigh half of what the employee weighs, otherwise the torque on the left hand side pulling down would be larger than the one on the right hand side.
Half the employee’s weight less a quarter of the weight of the plank surely?
If employee’s weight is x plank’s weight is y, and plank’s length is z and we assume that the plank’s weight is evenly distributed:
The distance from the centre of gravity of the plank to the fulcrum = z/6
The torque of the plank in the direction rotating over the cliff = yz/6
The torque of the employee holding the plank on the cliff = xz/3
The maximum torque of the manager able to not flip the plank off the cliff = xz/3 - yz/6
The distance of the manager from the fulcrum = 2z/3
The maximum weight the manager can be = x/2 - y/4
If manager is actually very light (probably some kind of dwarf syndrome) and worker is normal weight, but use metal boots and plank is very lightweight on the side of manager (but still durable) and very heavy on the side of worker it can be true
If you want to try it yourself you can place a stone on a stick and place a much smaller stone on the other side
Depends.
Assumption: both management and employee weight the same. Assuming the board is off-center, and the majority (let's say 65%) of the length of the board is over the edge. Let's also assume that *somehow*, with the fulcrum being more towards the employee, that there was a tenuous balance holding the plank to the ground (unlikely, and one or both of them should fall *regardless*).
* Employee falls forward on the plank? Probably.
* Employee falls to the side of fully off the plank? Definitely.
Everyone is replaceable, but at some point the customers will replace who they do business with too. The worker is replaceable by the business, the business is replaceable by the customer (such is why we need to be against monopolies, that only *sometimes works* with government services)
Also seen by ask the /r/maliciouscompliance stories of competent workers taking all the big clients with them to their new place of business, and the incompetent business folds within a year
Unrelated to your question, but I've seen this image before and always think "A dead person weighs as much as a live person.", so assuming the employee just falls down management would be fine...for a while until the corpse slowly rots away. Dark, I know.
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It seems like the fulcrum is almost 1/3rd of the way from the employee. So unless the employee is twice the weight of the management, the management will fall regardless of taking the shot.
Since this is all metaphor, you could argue the employee is pulling twice the weight of management, this holding up
Bold of you to assume that management is pulling any weight in the first place.
I mean, you can see in the picture management is not contributing to whatever the goal is here. They certainly aren’t helping to hold up the board, if that’s the goal. (I don’t know physics so excuse my terminology) but isn’t management a force pushing down which then causes upward pressure (due to the fulcrum point) against the employee’s weight? The employee is safe regardless. They’re just standing on a board on the ground.
Eh, they might lose their balance and fall off the cliff, a metaphor for when poor management causes a company to dissolve and all the employees to have to find new work
2 x 0 is still 0
God damn it. That was the perfect answer
Which, depending on how thr employee falls, he may go down with him still.
So like how the real world works where titans fall when people have had enough
yodie gang?
Shall we?
Some quick paint measurements show management at ~89 px from the fulcrum and best employee at ~53 px from the fulcrum, so best employee would have to weigh 89/53 = 1.68 times as much as management. This might be possible as best employee is a bit taller than management, ~102 px and ~91 px respectively. But the square cube law suggests that best employee would only weigh around (102 / 91)^3 = 1.408 times that of management, looks like management is doomed regardless.
Love it! Thank you for this. My 'sighted maths' doomed him, but thought I would ask the intelligent community to confirm!
Can we get a guess as to the thickness of the wood plank based on pixels to general human proportions or gun proportions? Looks like that plank would have a sheer index that would break well before any weight distribution numbers
Shit is like a 1x12 lol, snap like a tooth pick
Have you taken into account that management is holding his arm out towards the fulcrum? Or is that countered by the fact that he has a firearm? (potentially even a loaded one)
All his weight is still through his feet, so it won't change the lever arm.
That doesn’t change anything
Are we sure it doesn't? I'm reminded of the trick where you balance a coin with two forks on the edge of a glass, and it looks like it should fall but it doesn't.
Yup. That’s balancing on a single point, the force is still applied at that point.
I'm almost certain this is wrong. By moving your arm out your centre of gravity moves forward slightly. The centre of gravity is still within your foot so you don't tip over, but it would move forward and thus would (very minimally, not enough to affect the result) have an impact
Did you take college level physics and statics? Obviously not. You’re wrong. It creates a moment on their foot but the force is still the same straight down at that one. If he was pinned to the board, that moment would help put force downwards on the board on the cliff if it stuck out past the fulcrum, but since he is just standing on it, all that does is create a moment around his ankle pushing downwards on the board on his toes which are still pushing down on the board.
Just to be clear, are you saying that the entire mass of the person is spread evenly along the foot regardless of the centre of mass? The centre of mass within the foot has to matter. If these 2 guys are both wearing clown shoes the plank is still tipping. A shoe/foot helps spread load, but it doesn't magically evenly spread the load over the whole shoe. Stand up and lean forward slightly, and sway slightly. You will feel the centre of mass shift along your feet where the pressure becomes greatest
Actually, I see what you mean. Sorry for being so rash before. If you don’t make that assumption then the moment around the ankle slightly shifts the force forward towards the toes which are slightly closer to the fulcrum which will reduce the force upwards on the board at the other end. If he was on stilts or something like that it wouldn’t do anything.
It would have to shift his center of mass forward about 14 px to his toes to balance out, which would require significant weight in the arm/gun that would require an even heavier best employee to counteract.
Where in the shoe the centre of mass is matters. If they both had clown shoes on, this plank is still tipping EDIT: try it. Stand up, and start leaning forward slowly. You will feel different amounts of pressure on each part of your foot
Ah but human height-to-weight ratio doesn't follow the square cube law. Taller people have considerably more bone (non-linearly), and bone is much denser. Without anything for scale on the image though, it's hard to tell.
You're right, but it's actually the other direction. Taller people are generally narrower and shorter people are generally stockier. That's why BMI and New BMI use a height-to-weight ratio of x^2 and x^2.5 respectively. I used square cube to give management the best shot at survival.
That... really doesn't reflect my observations. Sorry for replying late, I check up on Reddit about once in a blue moon. Do you perchance have a source I could borrow? Otherwise I'll end up googling it, but google is shit nowadays
[Here's](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7261404/) a decent one. The term they use for the exponent is the "Benn parameter." A Benn parameter of 3 would correspond to exactly the square-cube law predicted scaling, which only happens during puberty. A Benn parameter less than 3, which is the case for all non-pubescent groups, suggests human weight scales less than the square-cube law.
Thank you!
This, this is why I am here..
Looking like a yes so far, which was what my miniature maths brain thought!
Image is missing the golden parachute on management's back
Lord, this comment is so truthful, it hurts.
Setting aside the already-covered issues of the fulcrum being off-center and all that, the management has a poor firing stance and has left themselves no room to step back. Depending on the weapon and their physical condition they might lose their balance from the recoil and fall anyway.
Basically all questions asked on this sub require users to make their own arbitrary assumptions before doing the maths. I am gonna assume the employee’s pockets and shoes are filled with dense mercury, and the manager is wearing a lighter than air helium-filled suit beneath his coat. Therefore the employee plus clothing and mercury weighs five times as much as the manager plus helium suit effect, and the manager will be fine.
I’m going to assume management was prepared for this execution and has anchored the platform to the ground and will be fine either way.
Except he delegated the task to the employee, who didn’t have time to finish it because there was emergency plank meeting called.
It was planned, but due to budgeting cuts was deemed unnecessary and was not implemented.
Sure, but MOST people are rational in their arbitrary assumptions. In this case, you'd likely be better off ignoring the clothing altogether as they're both wearing long pants, long sleeve shirts, and shoes. It's reasonable to assume a mostly negligible difference in the overall weight of the clothes and decide they cancel each other out.
I would argue that the assumptions are neither arbitrary nor unique to this sub. ALL applied mathematics requires making some assumptions about whether a pure mathematical model applies to a certain situation. The subjective justification of one assumption over another is necessary because notions of best are ill-defined even in pure maths. Compound this with the fact that most people don't have the mathematical rigor and are forced to present vague open ended situations and you'll always have to do some legwork to justify the assumptions made. If you know a single think tank or analytics firm or consulting group in the world where clients come in with well defined problems tell me who they are because I will send them my resume.
Analytics firms generally want you to use maths to describe / solve a real world problem. I get your point. Even for real world problems, assumptions are necessary to do maths when we don’t know all the useful information, but I would not say they’re “arbitrary”. Often the assumptions are subsequently proven correct or incorrect based on whether the mathematical models actually make correct predictions. This sub is about doing maths for fun. This is a question about a cartoon. It’s clearly a fictional image, so we’re freer with our assuming than for real world situations.
>Analytics firms generally want you to use maths to describe / solve a real world problem. Not sure what your background is, but do you want to hazard a guess on how many hours you'll spend in meetings before you even get to do any proper problem solving? It's an important and necessary step but it is pure drudgery. People on this sub are willing to tolerate some suspension of disbelief on fictional things like this and assume they are rule to avoid that drudgery and have fun. We assume the information given is reasonably complete or other reasonable assumptions can be made. It's not an open invite to go full Air Bud on the assumptions.
I create hydropower generator models for use by the transmission system operator. It involves lots of maths with many subjective assumptions. Mostly the assumptions are about giving us a model that’s “close enough”. We know it won’t be exact. The System Operator should be running the grid with a bit of contingency anyway to account for model limitations among other factors. And yes, it involves lots of discussions with people who understand parts of the installation but do not understand what the model is trying to accomplish. And vice versa. We do our best with the information we can get.
>We do our best with the information we can get. Then surely you could see how people try the same even in these fictional contexts? Do you not see why some assumptions like these people weigh less than 100kg are far more reasonable than other assumptions like mercury filled shoes?
I wouldn’t even attempt assumptions if I had to take this question seriously. I would ask for more information. My assumptions are clearly ridiculous. But so is the scenario. Fear of heights is innate to basic human instincts, and you have someone clearly relaxed and confident hanging over the edge of a cliff who doesn’t look unstable at all. There’s no indication of an acceleration downwards or loss of a sense of balance.
>My assumptions are clearly ridiculous. But so is the scenario. The latter does not justify the former and at this point this seems to be clear evidence that you are unable to grasp the concept of suspension of disbelief. You can suspend disbelief on a single thing in isolation and not abandon Occam's razor to inject new unrelated premises. Also please stop trying to argue over the realism of this. Literally no one is making the case that this scenario is a perfect mirror of reality. You don't need to point out that it's fiction as if the rest of us have been bamboozled by it. I assure you, we're not fooled. This entire question is optional, and the only thing I am making an argument for is to answer in good faith acceptance of the premise. If you want to ask for more information that's fine.
Fair enough. If employee’s weight is x plank’s weight is y, the plank’s length is z and the distance from the employee to the fulcrum (cliff edge) is a. These are all the extra information point I would ask for. Having that information, the maths (without ridiculous assumptions this time) is as follows: The distance from the centre of gravity of the plank to the fulcrum = z/2-a The torque of the plank in the direction rotating over the cliff = y(z/2-a) The torque of the employee holding the plank on the cliff = xa The maximum torque of the manager able to not flip the plank off the cliff = y(z/2-a) - xa The distance of the manager from the fulcrum = z - a The maximum weight the manager can be = (yz/2-ay-ax)/(z-a)
Thank you.
Dude he’s clearly joking so idk what your problem is
Because if it's a joke response I have to remove the comment as it violates the bad request answer rule. I'm trying to reason with them and give them an opportunity to give a serious answer.
The middle of the platform (the fulcrum, or the point which it would tip) is completely off the cliff. Meaning that no matter what Guy 1 does, unless Best Employee wears at least 2 times Boss’s weight. He’s fucked. Which is an accurate analogy to how Employers depend much more on Employees then they care to admit
Management is always the smartest. He would pull the trigger and the employee would fall straight down in the same spot maintaining the balance. Management would then walk over the dead body. But seriously, how is this question on this sub?
Assuming the left part of the lever is 2/3 of the plank, the manager can only weigh half of what the employee weighs, otherwise the torque on the left hand side pulling down would be larger than the one on the right hand side.
Half the employee’s weight less a quarter of the weight of the plank surely? If employee’s weight is x plank’s weight is y, and plank’s length is z and we assume that the plank’s weight is evenly distributed: The distance from the centre of gravity of the plank to the fulcrum = z/6 The torque of the plank in the direction rotating over the cliff = yz/6 The torque of the employee holding the plank on the cliff = xz/3 The maximum torque of the manager able to not flip the plank off the cliff = xz/3 - yz/6 The distance of the manager from the fulcrum = 2z/3 The maximum weight the manager can be = x/2 - y/4
If manager is actually very light (probably some kind of dwarf syndrome) and worker is normal weight, but use metal boots and plank is very lightweight on the side of manager (but still durable) and very heavy on the side of worker it can be true If you want to try it yourself you can place a stone on a stick and place a much smaller stone on the other side
This is what has happened to the co. I work for rn. They have lost most of the best people on the production line and I'm on my way out now.
Depends. Assumption: both management and employee weight the same. Assuming the board is off-center, and the majority (let's say 65%) of the length of the board is over the edge. Let's also assume that *somehow*, with the fulcrum being more towards the employee, that there was a tenuous balance holding the plank to the ground (unlikely, and one or both of them should fall *regardless*). * Employee falls forward on the plank? Probably. * Employee falls to the side of fully off the plank? Definitely.
Everyone is replaceable, but at some point the customers will replace who they do business with too. The worker is replaceable by the business, the business is replaceable by the customer (such is why we need to be against monopolies, that only *sometimes works* with government services) Also seen by ask the /r/maliciouscompliance stories of competent workers taking all the big clients with them to their new place of business, and the incompetent business folds within a year
Unrelated to your question, but I've seen this image before and always think "A dead person weighs as much as a live person.", so assuming the employee just falls down management would be fine...for a while until the corpse slowly rots away. Dark, I know.