Related rates piston

Hot Threads. Featured Threads. Log in Register.

Calculus Related Rates

Search titles only. Search Advanced search…. Log in. Contact us. Close Menu. Support PF! Buy your school textbooks, materials and every day products Here! JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding. Related rates problem involving a piston simple. Thread starter stf Start date Feb 25, What is the rate of change of the volume of the cylinder when the piston is 2cm from the base of the chamber?

SammyS Staff Emeritus. Science Advisor. Homework Helper. Gold Member. It's almost right. What are units for volume? SammyS said:. The base is uniform for a cylinder. BTW: the "2 cm form bottom" is unimportant for this problem. You must log in or register to reply here. Last Post Jan 2, Replies 2 Views 2K. Related rates problem involving a cone.

Subscribe to RSS

Last Post Oct 26, Replies 3 Views 4K. Related Rates problem involving triangle. Last Post Mar 12, Replies 4 Views 3K. Related Rate Problem Involving Trig.

Last Post May 15, Replies 2 Views 1K. Related Rate Problem involving Theta.If you're seeing this message, it means we're having trouble loading external resources on our website.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Donate Login Sign up Search for courses, skills, and videos. Related rates intro. Analyzing problems involving related rates. Analyzing related rates problems: expressions. Practice: Analyzing related rates problems: expressions.

Analyzing related rates problems: equations Pythagoras. Analyzing related rates problems: equations trig. Practice: Analyzing related rates problems: equations. Differentiating related functions intro.

Related rates intro - Applications of derivatives - AP Calculus AB - Khan Academy

Worked example: Differentiating related functions. Practice: Differentiate related functions. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter.

Video transcript So let's say that we've got a pool of water and I drop a rock into the middle of that pool of water. And a little while later, a little wave, a ripple has formed that is moving radially outward from where I dropped the rock.

So let's see how well I can draw that. So it's moving radially outwards. So that is the ripple that is formed from me dropping the rock into the water. So it's a circle centered at where the rock initially hit the water. And let's say right at this moment the radius of the circle is equal to 3 centimeters. And we also know that the radius is increasing at a rate of 1 centimeter per second.

So radius growing at rate of 1 centimeter per second. So given this, right now our circle, our ripple circle has a radius of 3 centimeters. And we know that the radius is growing at 1 centimeter per second. Given that, at what rate is the area growing? At what rate is area of circle growing? So let's think about what we know and then what we don't know, what we're trying to figure out.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. I just finished teaching a freshman calculus course at an American state universityand one standard topic in the curriculum is related rates. I taught my students to answer questions such as the following taken, more or less, from the textbook :.

How fast are they moving apart when the woman has been walking for ten seconds? How fast is the distance between the tip of his shadow and the top of the post changing when he is 40' away? How fast are they approaching each other after one second? My students do, but only because they know these questions will appear on their exams.

The baseball question or something very similar is actually an exercise in Stewart, and I struggled in vain to imagine a situation in which the manager of a baseball team would need to know the answer. This is in stark contrast to many other topics addressed in first-year calculus -- optimization, basic differential equations, etc.

Basically, all the related rates questions seemed to be cooked up in response to the fact that calculus students now knew a method to solve them. My question is in the title. Can anyone share any related rates questions which don't seem quite as contrived, and which might naturally seem interesting and motivated to a typical class of college freshmen?

The main reason that related rates problems feel so contrived is that calculus books do not want to assume that the students are familiar with any of the equations of science or economics. Every related rates problem inherently involves differentiating a known equation, and the only equations that the calculus book assumes are the equations of geometry.

Thus, you can find related rates problems involving various area and volume formulas, related rates problems involving the Pythagorean Theorem or similar triangles, related rates problems involving triangle trigonometry, and so forth.

related rates piston

A few of these problems are compelling -- for example, computing the speed of an airplane based on ground observations of its altitude and apparent angular velocity -- but most of them do feel a bit contrived. The reality, of course, is that students are familiar with many of the basic equations and concepts of science and economics, and there's no rule against using these in problems.

For example, you can make up all sorts of compelling related rates problems by starting with any physics or chemistry equation and imagining a situation where you might want to take its derivative:.

related rates piston

Give the rate at which the temperature and volume of the gas are increasing, and then ask about the rate of change in pressure when the volume and temperature reach certain amounts. Note that, by convention, brighter stars have lower magnitude. It's easy to make these up: just think of any equation in science or economics whose derivative might be interesting.

Edit: I have compiled a list of these problems in the form that I use them in my classes, and posted them on my professional web page. Doppler radar measures the rate of change of the distance from an object to the observer. What is the car's actual speed? Some students may even say that from their experience or physical intuition this actually makes sense, which raises the question of whether this is truly a physical phenomenon or a purely mathematical one that has been revealed from calculus.

It's perhaps worth first discussing a situation where such intuition is right, namely where the sum of two variables is fixed, rather than the product. But when the product is constant this is completely incorrect.

related rates piston

When I was in high school, I'd see water running out of a faucet growing narrower, and wonder if I could figure out what determines that curve. I found it was rather easy to do. I didn't have to do it; it wasn't important for the future of science; somebody else had already done it. That didn't make any difference. I'd invent things and play with things for my own entertainment. Assume a constant flow rate, and see whether your students can be guided to a solution.

You might try a warm-up problem, where you pour water into a non-cylindrical glass a martini glass, or something more weirdly shaped and try to determine how quickly the level rises, as a function of cross-sectional area. The following example is contrived, but I created it with the same frustration at the boring and repetitive nature of most related rates problems. Since I found this MO question by doing a google search for a "really interesting related rates problem," I'm recording this here for other instructors looking for juicier problems.

Related rates - a piston turns a wheel.

Question: What is the rate of change of the width of a shadow as you walk away from a street lamp considered as a point light source which is higher than your head? You can model yourself as a rectangle is you'd like!The problem was something like this:.

A cylinder filled with water has a 3. It is drained such that the depth of the water is decreasing at 0. How fast is the water draining from the tank? Here, the problem tells you that the water level is falling at 0. In an earlier postwe developed a 4-Step Strategy to solve almost any Related Rates problem. Take the derivative with respect to time of both sides of your equation. Remember the Chain Rule.

Draw a picture of the physical situation. See the figure. When a quantity is decreasing, we have to make the rate negative. To develop your equation, you will probably use. Remember the chain rule. Another very common Related Rates problem examines water draining from a cone, instead of from a cylinder. You can learn how to solve that in this blog post. Reading our solution may be a great start to learn how to solve Related Rates problems, but to be ready for your test you need to practice for yourself, pencil in your hand.

We have lots of problems for you to tryeach with a complete step-by-step solution. For more example problems with complete solutions, please visit our free Related Rates page! Over to you: What tips do you have to share about solving Related Rates problems? What questions do you have? Please comment below! Head over to our partners at Chegg Study and gain 1 immediate access to step-by-step solutions to most textbook problems, probably including yours; 2 answers from a math expert about specific questions you have; AND 3 30 minutes of free online tutoring.

Please visit Chegg Study now. Sucks how school speeds through subjects like a bat outta hell and covers topics in a manner that is more shallow than a puddle. I really learn from this site. I also have a problem set which im not really sure with the way i solve it. The problem is: An open top cylindrical water tank containing a certain volume of water with its depth and given area of its hole at the bottom of the container.

Find the time rate of the cylindrical water tank will be drained.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. There is another way to solve this problem, though you will still ultimately substitute the known value of the radius. Implicitly differentiate the equation with respect to time remembering to apply the product rule :. However, substituting the known, constant value into the equation early allows you to avoid application of the product rule.

This is why you want to substitute known constants into the equation before you differentiate. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 5 years, 8 months ago. Active 1 year, 7 months ago. Viewed 28k times.

Therefore, r would be cm. Active Oldest Votes. Varun Iyer Varun Iyer 5, 10 10 silver badges 27 27 bronze badges. Randall Blake Randall Blake 1 1 silver badge 9 9 bronze badges. Here's a link to a site that shows a pretty in depth explanation of solving this problem this way: jakesmathlessons. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown.

The Overflow Blog. Socializing with co-workers while social distancing. Featured on Meta. Feedback on Q2 Community Roadmap. Question to the community on a problem.

Autofilters for Hot Network Questions. Related 2. Hot Network Questions. Question feed. Mathematics Stack Exchange works best with JavaScript enabled.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields.

It only takes a minute to sign up. Calculate the piston speed when. I have absolutely no knowledge whatsoever about engines or pistons. So I am far outside my comfort zone. Then taking the derivative and plugging in the expression given in the question. Perhaps the law of cosines will give us something:. However, I am not able to get it to go anywhere from here.

I am doubtful that I have even gotten the basic idea of the question right. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Implicit differentiation and piston engine speed Ask Question. Asked 3 years, 8 months ago. Active 9 months ago. Viewed times. I am looking to finish this question off using a calculus-based answer. MathInferno MathInferno 1, 7 7 silver badges 12 12 bronze badges.

Aug 1 '16 at However, for this particular problem, you can skip the calculus. I have awarded the bounty to the first answer that fulfilled the bounty, which was yours. Active Oldest Votes. Yves Daoust Yves Daoust k 14 14 gold badges 97 97 silver badges bronze badges.

Aretino Aretino G Cab G Cab Sign up or log in Sign up using Google.Favorites Homepage Subscriptions sitemap. Related rates, piston problem. But I cant get anywhere.

Any Help is appreciated I really cant figure this out.

Related rates - a piston turns a wheel.

This is what the figure looks like. In this question we study how the two rates - rat at which piston moves back and forth and the rate at which the wheel turns are related to each other. For part a, I know I am suppose to use the law of cosines to somehow prove it. But I can't get anywhere. Any Help is appreciated I really can't figure this out. The first part is just a statement of Pythagoras' theory.

New What happens when the skydiver opens. If Darwin is the father of evolution. Which one is greater x or -2 What is the axis of symmetry of the.

Compute the Gauss curvature of the e. What do astronomers do day to day Weather help, how high is mb. Group theory question 0. Need Help on Chemistry homework Need help with proving onto function. Write equation with undefined point Oxidation states of Calculus problem about related rates.

Based on the first and fourth sketch. What is the label for this orbital t. Determine the number of bonding elec.