Next speaker will be Dr. Peter Eubel. Peter is the MAG and Dennis McLehorn University Professor of Business, Public Policy, and Medicine at Duke University. Peter's research uses tools of decisional psychology and behavioral economics to investigate informed consent, shared decision making, and health care cost containment. Peter's has explored the role of values and preferences in health care decision making at the bedside and in policy. Some of his books that have commented in these areas are, one, critical decisions, how you and your doctor can make the right medical choices together. Another book is Free Market Madness, why human nature is at odds with economics and why it matters. Today, Peter will talk to us about the topic physician recommendations, Trump-patient preferences, but is that good or bad? Peter Eubel. Really love it. Getting very excited about the idea of patient empowerment. Even more excited about the idea of autonomy, because it was a fancier word. I thought I could impress the ladies with that. That didn't turn out to be true in practice, but in any case. Then somewhere in my training, I discovered behavioral economics and had some serious questions about just how well autonomy works in practice. And the kind of questions I had had to do with the psychology of decision making, famous example being people would think much better about a surgery with a 90% survival rate than they do about a surgery with a 10% mortality rate. And so these are just an example of the kind of unconscious thing, in this case framing something as a gain or a loss, influences choice. And I thought, wow, this is really cool. Really raises questions about whether just giving patients information and letting them be empowered to make decisions will work or not. So I started doing a whole bunch of experiments with colleagues like Brian Sockin-Fisher at Michigan, David Ash at Penn, George Loewenstein at Carnegie Mellon, where we tried to test different ways to present information to patients, find out what unconscious forces influence their decisions, and then ultimately use what we learned to fix the problem, to design decision aids, think of them like educational brochures on steroids. And we give decision aids to patients to really inform the heck out of them in a non-biasing way so they'd come into the doctor's office ready to go. Then I made the mistake of testing whether that actually worked in practice and realized that I pretty much wasted a couple decades of my life. So let me tell you a little bit about that. And it's in the context of early-stage prostate cancer. And I'll tell you why we studied that context and what happened when we informed patients about their alternatives and then they went and saw their doctor to discuss those alternatives. And I'm not seeing it down here, so I apologize. I'll have to look up a little more. Unless we can fix it here, it'd be great. So if you have early-stage prostate cancer or localized prostate cancer, a man has treatment choices here where the right choice depends on that man's individual preferences. He might face a choice between watchful waiting that's been rebranded as active surveillance, where you don't treat the cancer, you just watch it and you get tested regularly to see if it advances and then you do something only if it's showing signs of growing. And, or you could have surgery to remove your prostate gland and then you're definitely done with the cancer, but you have a chance of impotence or incontinence. You could get one or another form of radiation and that would, again, get rid of the cancer but give you these other nasty side effects. So for any given man, the choice really depends on how that person weighs the importance of they place on getting the cancer out of them and not having to worry that it's gonna grow in the six month interval between their checkups versus having definitive treatments that might make it impossible for them to make love to their wife. So we wanted to know, and this is a study led by Angie Fagerland at the University of Michigan, what would happen when we informed men about these treatment alternatives and tried to promote shared decision making. And in this case, we actually gave the men decision aids at the time that they got a biopsy before they knew whether that biopsy would show cancer or not. We gave them decision aids to help them understand their treatment choices should the biopsy show them to have cancer. We called them before the visit with the urologist to make sure they had reviewed that decision aid. Then when they came into the urology office, we tape recorded what happened. After they reviewed that decision aid, we, and they didn't know if they had cancer at this point, that's important. We said, now if it turns out you have early stage prostate cancer, where are you leaning in terms of what treatment you might want or not? And they could say, well, you know, I'm open to all of them or I'm like, just that watchful waiting thing looks good for me. So we had a sense of some of their early preferences. We even then also asked them very important questions that would determine what treatment might work, might be better for one patient versus another. Like, are you still sexually active and do you want to remain sexually active? If the answer to both of those questions is no, then one of the major side effects of surgery and radiation is not relevant. If it's like, yes, dang yes, that's important. Well, that's gonna be an important factor then to determine whether you want that aggressive treatment. Then we tape recorded the encounters and we looked at how physicians described the pros and cons of the treatment alternatives and I'll describe what we did with that in more detail. And then specifically, we looked at whether the surgeon recommended any of the treatments or recommended against them, like took an option off the table, like surgery is not an option for you or came right out and said, at your age, surgery is the best treatment. And so we had that ranging from a minus two scale, like taking an option off the table plus two, like this is the best choice. And of course, in between less strong preferences. Thank you for coming up and do that. So here's the demographic slide, which is typically pretty boring. I can just tell you that we definitely did not have many women in the study. Thank you very much. We measured a scale and shared decision-making scale that Clarence Braddock developed. Bad slide, but I'll show you more about each of these things, but it looks at the encounter to try to see, does that physician really share, get that meet the ideals of really informed consent and shared decision-making. Does he or she talk about the patient's role in the decision, tell them about their treatment alternatives and the pros and cons of those alternatives. In previous studies using that analysis in primary care settings, for example, physicians have done pretty abysmal on it. They don't even tell people all their alternatives and when they tell alternatives in those previous studies, they mainly say the good things about the alternatives and tend to under develop this discussion of the downsides of the alternatives. So we look to see what happened here. And I'll tell you this, the urologists in this study who are trainees at four VA sites across the country did much better than primary care attending physicians have done in previous studies. They didn't do perfectly. If they did perfectly, they'd get a score of 14. Whoops. But what we find is that decent amount of information and sharing that goes on in these decisions and in these encounters. And what you'll see especially here, white means they didn't ever touch anything. They didn't address any of this element. Black means they did a kick-ass job on it, graze in the middle. You see when it comes to discussing alternatives and risks and benefits, the bars are almost filled in. That means it was very hard to walk out of one of these encounters without hearing that you have a choice of active surveillance versus radiation versus surgery and even hearing the pros and cons of those three choices. That was routine. In many ways, the work we have done in this room to promote patient autonomy and inform the informed part of informed consent, we have done extraordinarily well. Even surgeons are following along. Okay. Just had to get that out there and there are lots of surgeons in the audience, right? The bad news is, first off, that thorough communication is not always good communication. So this way of saying, did they discuss all the pros and cons? We can say yes, they did. We also might say they did it in French. No, friends. No, they didn't. And usually they did it was in medical ease. So we saw a huge amount of jargon. We also found that they didn't take time to make sure people understood what they were saying, to absorb the emotional bad news. They just, the awful bad news they just got, they just found out they had cancer and they usually launch into it quickly. A very elegant or very detailed discussion of pros and cons of treatments, et cetera, while the patients just sitting there thinking, I have cancer, I have cancer, right? So there are real problems with the communication. The amount of jargon and undefined terminology was extraordinary. And so there are still huge problems. We need to train clinicians to communicate more clearly. That's not what I'm gonna talk about now. Instead, I'm gonna look more at how well these discussions promoted autonomous decision making. So before they found out they had cancer, but after they'd read our decision aid, remember they came in and we said, hey, what treatment might be leaning towards? Some said surveillance, only surveillance, that's the only one I'm thinking of. Some were like, it could be surveillance, could be an active treatment like surgery or radiation. And some were like, I just want one of those active things. I want it out of me, all right, I want it taken care of. So there's a variation of preference going in. And it's really hard to see that that had any impact on what treatment people actually got. So the preferences that came into before the urology appointment did not at all predict what they got after the urology appointment. Why did that happen? Well, okay, these are regression analysis, so I don't understand them, but I'll say them to you anyway, right? You find that prior to the visit, how anxious someone was did predict that they would get one of these active treatments. How interested they were in having sex did not.  So what about age and glesence? Now, a glesence score is a way of saying how bad this tumor looks under the microscope in the pathology office. And in all of our study, people either had glesence six, which is the lowest grade cancer possible. Anything less than glesence six, it's not a cancer. Or glesence seven, one step above it, so these are still, right? So whether someone had a glesence six or a glesence seven strongly predicted what treatment patients got. Whether they were young or old, strongly predicted what they got. What's going on? It's because it's largely explained, but not completely explained by the physician recommendation. What happened was, if you are a young guy with a glesence seven, so you're young and you have a slightly worse tumor, they said, watching this is not an option. You need to get radiation or surgery. And that option was taken off the table. Sometimes they say, now it's your choice, but it is not an option for you. So they respect autonomy. And then if you were old with a glesence six, they might really say, you know, yeah, you could have these surgeries and everything, but for you, it really makes the most sense to just watch it. And so that was what was shaping this. It was the physician recommendation based on age and glesence score. To give you a sense of just how that worked, this is the percent of people receiving active treatment. That's either radiation or surgery as a function of what the physician recommended. When the physician recommended surveillance, 20% of people got surgery. So you see it doesn't totally trump patient preferences. They're still pushed back. When there was no recommendation, only 20% got active treatment. And when they recommended the surgery, 80% got, or radiation, 80% got one of those active treatments. That's a big impact, right? And what's really interesting is I look back now at the guidelines from the urology professional associations. The American Urology Association says, for people that fit into our study, that had that kind of amount of tumor, it is a matter of patient preference that all of these three options should be on the table. But that was not the way physicians were acting. Now the national NCCN, whatever that stands for, right? Their guidelines are stronger. They say, young men with sevens, watch ratings, not an option. So the guideline actually incorporates, I think, a massive value judgment. And that seems to be what the physicians in the study were doing, where they were adopting that. And they weren't presenting this as a value judgment. Like now, given your young age, and that's at least in seven, you might wanna really think carefully. They would just say, that's not medically indicated. One example of a pushback was a guy who was young, 62. And he said, I cannot afford to miss work for one of these treatments. And I read that for sure. If could I at least wait three years till I retire before I think about getting surgery? And he had to push, push, push back for the physician. I said, yeah, okay, I guess that could be okay. And so value judgments that have become framed as medical judgments is huge. Here's just again to give you a feel for what happens with recommendations. So you come in, you're considering surgery. If surgery is recommended, very good chance to receive it, but not 100%. If it's taken off the table, almost no chance you will receive the surgery. When they say it's not an option for you, then they don't get it. And the same thing if you came in and consider surgery was not something you said you'd even consider, if it was recommended, there's still a two-thirds chance that you're going to get it. That you will choose to get it. So it's highly influential kind of recommendation. Now what comes first year? Maybe, and I've talked about this with some surgeons, they say, well yeah, but we are really good at knowing what people want and then we make recommendations that fit their preferences so that they feel more comfortable. I don't know why you're laughing at this. And so we looked at that. For example, we looked at discussions of sexual functioning. Two-thirds of the time they assessed whether the man could have an erection or not. Fair urologists, they definitely care about that, right? Only 12% of the time did they talk about how that's important in deciding what to do and only 13% of the time, I'm sorry. Yeah, sorry, only 12% did they ask them how important sexual function was to them and only 13% of the time did they say, and that's important in making the decision. So it really didn't seem like they were diagnosing preferences in the making recommendations accordingly. They were making these judgments based on age and gleason and sexual function and interest in sexual function was kind of a side thought. There are other some things that happen in these visits that are kind of interesting. I want to just quickly show you that show the challenge to try to really promote autonomy and informed consent. Three of the sites we had that we did the research in had robotic surgery available. One of them didn't. It's controversial whether the robot assisted procedures are better, but it turns out what you heard about the robot from the docs depended on whether you were at the site that did or didn't have the robot and this is VA medical centers where there was no financial incentive to use the robot, right? You find when the describing incisions, some people would say, you know, hey, it's just the same.  You have one big incision. It's the same, no difference. And other people would say, well, you know, here, we have it, it's a less invasive way of doing it. There's smaller incisions. So you can see the same information is spun differently depending, right? You'll see this with the impotence talk. Reactions afterwards are not any better. Definitive saying it's no better with other physicians saying we're probably doing a better job of sparing the nerves and therefore preserving function. And what we find out, no surprise, if you were one of those sites that had the robot, those interpretations of whether the robot was better or worse tended to be more pro-robot than if you're in the site where it wasn't available. So you don't get the same information depending on what position you go to. You get different information even when financial incentive has nothing to do with it. Finally, we looked at physicians' earnest efforts because of the influence of this place in trying to admit they're not perfect at helping patients make decisions. Physician admissions that they are biased. Previous research has shown, in fact, if you ask a biologist, what would you get if you had localized prostate cancer? What treatment would you get? They're like surgery. And then you ask radiation oncologists and they say, I would have a radiation treatment. And so we have our own specialty biases. We see the bad outcomes of the other person's treatment or we think of people who should have gotten our treatment and didn't, right? And that's human and that's fine. We know those things better. So one way to approach this problem that we can't ever get totally outside of our biases is to disclose them. And so we found an example of physicians coming out and saying, look, now I'm a surgeon so I'm biased in favor of surgery but let me tell you about radiation. And I think this is morally better except for what happens. So 26 of these visits, the physicians explicitly used the B word and said I'm biased in favor of surgery because I'm a surgeon. Those patients were more likely to have surgery than other patients even after you count for whether the physician recommended surgery or not, what their age, glee, and score was, et cetera. Why? Well, we ran a lab experiment on this. We took a bunch of healthy men and we showed them a video of a surgeon. We actually used quotes from our actual transcripts and had this guy reenact them. And then we spliced in an admission of bias in half of them. So people hear about this doctor describing the surgery. Half the people, they also see the doctor admitting just with that willing kind of one sentence thing saying, look, I'm a surgeon, I'm biased in favor of surgery. Those people thought that doctor was more biased so the admission of bias made people think you're biased which is what it should do. It also made them trust the doctor more and it made them more likely to recommend that hypothetical doctor to a friend. There's something disarming about admission and admitting our own bias. We do it for the right reasons but we don't necessarily understand the psychology that underlying what people will do when they respond to that kind of information. This is the kind of challenge that I think autonomy faces. So I think to finalize the patient empowerment revolution and whatnot, and I'm really eager to open up to comments and questions. We have to look at communication. We have to teach clinicians to communicate more effectively with patients. Not only to explain things more clearly because they don't, not only to have them better recognize patients' emotions, negative emotions, which they don't but also to have them better understand the difference between admitting, recognizing your own bias and disclosing that bias in a way that won't further bias your patients. And critically, it means we have to get clinicians to understand the difference between a medical judgment and a value judgment. Really eager to hear your thoughts and questions. Thanks. Yeah, that's what I'm here to do, yeah. Yeah. Peter, I really appreciated your thorough analysis of this. I mean, I think it's pretty clear that disclosure really does not help. And I think that has wide ranging implications, I mean with publication as well as research. And knowing that and plus knowing what you found here, it seems to me that the obvious sort of solution to this is that the people who actually do the therapy, who own the therapy should not be the people who are involved in the decision making about the therapy. That other people can learn the risks and benefits and understand that in a way and then present that to patients and discuss it with patients and then have the patients decide without the surgeons or the radiation oncologists involved. Yeah, so do you think you would want to receive a major surgical procedure without talking to the surgeon about whether that's a good thing to do or not? No, I think you could talk to them after you've made the decision. I think that's fine. I think I just can't imagine that most humans would think that way, right? I mean, I just think that you want to, and I'm not saying that this is always that they're savvy about what they should do or not, but I think people wanna know, they wanna see, they wanna get a sense of that person before they make a decision, because the decision to get the operation can kind of depend on what you think of this person who will be cutting into your body. So I totally, and so I'm not shutting down your idea at all. I think it's got a ton of merit. And I think maybe, but I think, I expect vast majority of people won't want that extreme of a way of doing it. Maybe getting a mandatory, getting multiple opinions more when there's multiple choices. I know I've seen, I've experienced with my own family situations where surgical decision was made before ever talking to a radiation oncologist and the radiation discussion could have very much informed whether the switch in what surgery was right. So we'd need to maybe broaden the pool of views that people get before they're making a major medical decision, but I'm not sure that most people would be comfortable pulling a major player out. I might be wrong, you know. Marshall. Hey Peter, Marshall Chen from Chicago. So I think your talk was a great talk of raising a lot of fundamental issues about shared decision making in the doctor-patient relationship. But I wonder if you've somewhat set up a straw man where it's almost like a subtle implicit tone of, well, if we had just the right decision aid or just the right process, then we should have an end result where the patient's truly informed and makes a great decision. Whereas what you're saying is that maybe there are tools that can be used or maybe there can be coaching and education on communication process, but ultimately it is the doctor's professionalism and the sense of working through the discussion. But it's so complicated and the values are so diverse that it's necessarily gonna be a process. And so no particular tool or no particular set way of doing things would lead to the right result.   So yeah, is it a straw man to think that a person with an important decision to make who's been well informed about their alternatives should be able to go into a provider and come out with an appropriate information that guided decision. So I think it was very reasonable to hope for something better than what we saw. And no, I didn't think like a decision that was gonna solve all the world's problems. I definitely remember not that naive and pretty naive, not that naive. I'll tell you, we've done a follow-up study, we're just analyzing the data now where we made a video where that was part of what this another study came out of was the video we made. But where we reenact encounters and have a narrator walk people through, here's what you can expect to happen if they tell you you have cancer. And notice how this patient's nodding along like they understand and they don't understand. And the patient in this video saying, yeah, I was really confused but I didn't wanna be rude and interrupt. It's not rude to interrupt your doctor. You should, it's your body. So we're trying to train people how to act when they're in this situation. Try to help them remodeling behavior and help them visualize it. So that's a much more aggressive tool. I'll tell you, it gave everybody great intentions to go into the doctor and do it and early evidence is it still didn't probably work as much as it ought to. We need to probably really go at training providers to do a better job knowing whether, and I'm really getting back to the original question when is the physician the right person to have what part of the conversation. I do think a lot of the informing can be done by people better able to communicate to patients about stuff, supplementing the clinician, et cetera. Yeah, it's not no easy fix. Don't imagine an easy one but I think it's a worth trying to fix. Yeah. Peter Angelos, University of Chicago. Herdia. I have to admit, I'm biased, I'm a surgeon. But no, it was a great talk, Peter and I always learn a lot from you. I think though that you may be sort of putting two things together that are somewhat separated. So one is the concept of the patient has the opportunity to make a decision and that informed consent involves disclosure of risk benefits and alternatives. And whether the patient then chooses to do what the surgeon or what the radiation oncologist recommends to me doesn't necessarily map with whether it was a good decision or not for that patient. And so I think I'm a pretty good communicator and I try to discuss risks and benefits and alternatives with my patients. Frequently my patients will say, well, doc, what do you recommend? Yeah. Right? And I don't think that's a bad thing. Yeah, so in the worst-selling book, Critical Decisions, yeah. I feel very strongly that recommendations are part of our role as clinicians but the recommendation has to be based on two things. One is remembering the difference between the medical judgment and the value judgment. And second is figuring out the patient's values so that you can make a recommendation that reflects them. If I had seen the recommendation have a huge impact because the physicians had carefully discussed what they cared about in life and said, you know, based on that, surgery wouldn't be good for you because you might have problems with erections or something like that. I would be like praising, you know, hallelujah for what had happened. Instead, we saw mindless kind of sticking to a couple clinical facts that determine what's right or wrong for someone without recognizing there's a heck of a lot more at stake than that. And that it's really reasonable for a young guy with a Gleason 7 tumor to say, I don't want you to do that surgery on me. And so I believe recommendations are a very important part of our job. They have to follow us diagnosing patient preferences. Thanks. Hey, Peter, Michael Green from Penn State. You just answered my question about, I was gonna raise the issue about recommendations but so I have a broader question, I guess. You seem to be implying that implicitly that having biases are a problem and that we should strive to be unbiased as possible. And I think that's possible and I'm not even sure it's desirable. You don't think striving is possible? I don't think it's possible to achieve. I agree. A lack of bias. I agree. And I think patients related to recommendations is people want the biases of those who are making the recommendations. But I guess my question really is about what's the alternative? I mean, if the best that we have right now are these decision aids or some sort of attempt to provide information and to couch them in a set of values and assumptions and attempts to understand what matters to other people and you put that in the form of a decision aid and it doesn't work great, what's a better alternative? What I would hate to see is that we just say, oh, this doesn't work and let's throw it all out. I don't think people come to the doctors wanting their bias. I think they want their expertise. What's sad is when our expertise is that we aren't expert at knowing what should guide decisions. And so what I think we need to do is go back to the drawing board and how we train physicians and the future physicians about decision making. I think the ethics training emphasizes patient autonomy and self-determination, et cetera. There's a ton of language going out throughout these encounters of now, look, it's your decision to make, but, or, and then there are times where they're neutral and there's the point where the person's saying, well, what would you recommend? Like it's not for me to recommend and they're left hanging. So I mean, we haven't really figured out how to go from recognizing that patients have rights to knowing how to help empower them, how to share, how to work with them. And so I think that's where we go. Is we need, how we train people to understand what, that values play a role in decisions and how to elicit and get to those values. That's where I would emphasize. That's why I don't run experiments nearly as much anymore. I study communication and I'm trying to figure out how to fix it. So I wasted those years, yeah. My name is Irene Martinez from Strozier Hospital, Cook County, here. I have a question. Why you didn't include women in your study? Because as you mentioned, you took decision regarding your family's health without your family. And I think that, at least with the patients that I work, the post-effects of surgery, everybody, impotence is a big issue. And I don't know, I want to ask this question. Why you didn't include women if you think it's pertinent or give them time to discuss if they were married? And the second thing that I really appreciate that you keep talking about emphasizing communication, is communication lack of training or lack of communication or lack of time? Oh yeah, thank you. I think with good training, it doesn't take much time to communicate a lot better than people do. And in terms of women, we did not survey any of the partners, the female partners or male partners that were involved. And we certainly, a more thorough study would have done that. There were times when partners were in the room during the conversations. We certainly transcribed and heard what they had to say. And there were some fascinating things that happened. But it was primarily, you didn't hear much from the patient or the partner, you mean they heard from the surgeon. Okay, thank you. Thank you, thank you. Okay, two quickies, Caleb. Okay, I got lucky, Caleb, Alexander Hopkins. Great talk, and I like the emphasis on training. I'd be interested to know your thoughts as a behavioral economist, knowledgeable about traditional economic theory as well, about using incentives to better incent physicians to help patients reach the right decisions. So, I'm surprised that you put all your money on training alone, although I think it's, I'm all for overhauling medical education, but are you aware of or have you thought at all about ways that might use either the principles of behavioral economics or just plain old financial incentives to help improve patterns, you know, to help develop scalable interventions that could improve the quality of decision making for issues like this? Yeah, so just for the record, I'm not an economist or a behavioral economist. I only have a medical degree, I apologize. Yeah, I haven't thought a ton about financial incentives in this setting, number one, because the study didn't really involve financial incentives. I think the biggest problems we have are that the incentives are often just to do more procedures than are good for patients. And so the real, the biggest bias we have going on in here is that surgeons want to operate because that's how they make a living, and colleges want to radiate, and they ought to, and they should be paid for doing that. So that is a huge problem. I think it's really tricky to figure out how you would build incentives in that look in this kind of situation where there's no right or wrong choice for a given patient, except for knowing what their preferences are, and to incentivize that would mean tape recording, seeing if their discussion happened. It could be tricky, but I haven't thought it much, so it's definitely something to think about. Final question, thanks. Final question. I'm Maggie Moon also from Hopkins, and I just want to add a hopeful note here. We actually have a program there where we do a lot of training with the surgery interns about this very issue, about informed consent, and we use a standardized patient and tell them that the goal is to help this patient figure out which of the two options for breast cancer surgery meet her goals. And it's interesting and it's a struggle, but the great majority of our surgery interns figure it out and are able to do it, so they practice, they have a chance. But I think that what's critical is telling them that the goal is to bring out this patient's values. I mean, I think that's sort of the surprise, that that's actually part of their job. And I think it's a simpler, I mean, I think part of this is a very simple notion in the way that what we tell surgeons we expect of them. Thank you and I'm not hopeless at all about this. I think that is exactly the kind of training we need to do and I think at the right time during residency. So thank you very much. Appreciate it.


We've looked a little bit at some equilibrium problems, so let's come back and look at the more general case where we have non-equilibrium. So in that case, what we know is that the acceleration is not equal to 0. We're going to have an acceleration. And that's because the vector sum of the forces is not equal to 0. Now, it doesn't really tell us immediately just by saying it's non-equilibrium what we have in terms of fx and fy. There could be equilibrium in one of these two, but there isn't equilibrium in both of them. So in general, there will be an ax and an ay. But it's possible that one of those cases might be 0. So let's look at a problem here where we have our forces and we're figuring out what the acceleration is going to be. If I've got a basic diagram where let's just say I've got two forces, let's use some vertical ones this time just to sort of shake things up, I'm going to call it f1 and f2. Well, the sum of the forces in y is equal to minus f1 plus f2. And in general, that's going to be equal to sum may. Well, if I've got actual numbers, I can start solving for different things. There's four different unknowns, so if this is the only equation I'm working with, I need to have three of these things in order to be able to solve the problem. And it could be any of these three things that you're given. In this case, let's say we know that f1 is equal to 20 newtons. f2 is equal to 30 newtons. And the mass is equal to 2 kilograms. If we come through and work out this equation, well, what are we then solving for? Well, we're trying to find out what is my acceleration. One method is to come in and plug in all my numbers first. The other method is to do all my algebra first. In this case, since the equation's laid out pretty well, I'm going to go ahead and plug my numbers in.  As I'm working on this, then, what I can see is I do the addition subtraction here. And that gives me 10 newtons equals 2 kilograms times my unknown Ay. Since these two things are multiplied together, in order to separate them, I'd have to divide through by my 2 kilograms. And I see that 5 newtons per kilogram is equal to my acceleration. Now, the units look a little weird at first until we remember that a newton is equal to a kilogram meter per second squared. So a newton per kilogram would have those 2 kilograms cancel each other off. And this is really just 5 meters per second squared for my acceleration in the y direction. So in this case, we knew all the forces, and we were trying to find the acceleration. Let's take a look at a similar situation, but where I'm trying to find one of the forces. So I might have a problem where, again, I've got an object, mass 1. That mass 1 might be 4 kilograms this time. And let's say I've got forces acting on it, a weight and a tension. So this is an object which is hanging from a rope, perhaps. Now, let's say I'm actually told that this box hanging from this rope is moving downwards. And not only is it moving downwards, it has an acceleration downwards of 2 meters per second. Well, I've got to figure out how to draw my diagram. Well, no, I've got my diagram. How do I construct my equations from this so I can start solving different things? This is a little bit trickier equation because we're actually bringing into place several things here. Let's start with our equation, though. Some of the forces in the x, for this particular case, is 0. There's nothing in that direction. I don't have to worry about that. Some of the forces in y is equal to plus t minus weight equals m Ay. I'm going to write this equation one more time just to kind of clarify some things. One thing I'm going to remind you of is that weight is equal to mg. And g is equal to 9.8 meters per second squared. So I can actually find my weight here. I've got plus t minus mg. And that's going to be equal to m. But notice I've got an acceleration that's going downwards. Well, I can handle this in two ways. I can either say my acceleration is negative 2 or I could say my acceleration is in the downward direction with a value of a. You can work this either way and just make sure that you're being very careful on how you're treating your signs. If I had to do the algebra on this particular equation, I would say that my tension is then equal to mg minus ma. And I can plug in my exact values here.  And if I actually plug my numbers in at this point, now I haven't left myself much room, so I'm going to slip over to a different sheet here. That means my tension is equal to 4 kilograms 9.8 meters per second squared minus 2 meters per second squared. I wasn't being careful up here at the top, but I caught myself. I said my acceleration was 2 meters per second. That's got to be 2 meters per second squared. I can't have an acceleration that has units of meters per second. Simplify my algebra a little bit here, and then I have to actually come and plug this into the calculator. 4 times 7.8, that tells me. Now, if we want to actually compare this to a broader problem, I could have actually figured out what is my weight up here at the top? My 4 kilograms times 9.8 meters per second squared and see that I've got 4 times 9.8, that would give me a weight of 39.2 newtons. So as a check back here to reality, what I'm saying is if my object is accelerating downwards as it's being held up by the rope, the tension of the rope doesn't have to support the entire weight, as would be the case if it was in equilibrium. Instead, the tension only has to support part of the weight, and the other part of the weight is causing a downward acceleration.


You may cast millionaires out here man. A lot of us can't say that. It's even more deeper from his standpoint because he was an artist. A lot of motherfuckers ain't an artist so they don't have that ego to push to the side.