Work Problems | Calculus 2 Lesson 8 - JK Math

How to Solve Work Problems (Calculus 2 Lesson 8)
In this video we look at how to solve work problems using calculus. First we look at work done by a constant force which does not require calculus, but then we look at work done by a variable force, which does require calculus. There are a variety of different types of work problems that involve variable forces that can be solved using calculus, so we take an in-depth look at the most common types of problems. This includes spring problems, propulsion problems, lifting problems, and pumping problems. We discuss each type of problem individually and solve at least one example for each as well.
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This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Work Done by a Constant Force Intro
1:17 Constant Force Example 1
4:15 Constant Force Example 2
6:04 Units of Work
6:42 Work Done by a Variable Force Intro
7:54 Types of Work Problems
8:56 Spring Problems Intro
10:59 Spring Problem Example 1
15:32 Spring Problem Example 2
21:57 Propulsion Problems Intro
22:58 Propulsion Problem Example
30:56 Lifting Problems Intro
32:46 Lifting Problem Example 1
36:52 Lifting Problem Example 2
41:45 Pumping Problems Intro
46:59 Pumping Problem Example
56:28 Outro
📝 Examples Video: • Work Problems Examples...
⏩ Next Lesson: • Moments, Centers of Ma...
📺 Calculus 2 Playlist: • Calculus 2
📺 Calculus 1 Playlist: • Calculus 1
📺 Extra Work Problem: • Work - Pumping Problem...
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-Josh from JK Math
#calculus
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[@gramsta836]

this is simply a fantastic video. I might even say better than organic chemistry tutor.

[@nathanielgarcia6909]

Without watching the video I would say you're wrong, but yes this is a great video

[@gramsta836]

@@nathanielgarcia6909 watch the video then and see why im right :)

[@aaronrhena7515]

The best work video EVER.

[@lokeshgnanasekar]

This guy is very under rated! Please post more videos or instead post different videos of the same topic instead of compiling it. This will definitely improve your views and subscribers count for sure. Just cut the same video and compile them under a playlist, that would be a better way. Thank you for the explanations

[@JKMath]

I appreciate the kind words and feedback! I do try to split up topics with my newer lesson videos where possible. If I were to make this specific video again, I would definitely consider splitting it into separate videos for each type of work problem to give each the spotlight rather than the all-in-one approach I did here, although I believe it’s still effective regardless. There’s a couple Calc 2 lessons I made where looking back I believe I could have split it up into two or three lessons. It’s something I’m more aware of when making new videos today. I’m always trying to find ways to improve my videos! Thanks again! :)

[@lokeshgnanasekar]

You can follow the same step as you did here, but you shall split the video where the topic gets more advanced. 99% of the viewers watch maths videos due to compulsion and they may feel overwhelming even before watching the entire video! What I personally suggest is, have two versions of the video one as such this and another one split up (if its possible). You have one of the BEST contents in youtube, you just need to improve the viewers and some presentation. In presentation i have seen some channels continuing the calculations step by step while they just keep zooming in to the working part and leaving behind without erasing, idk may be you sell them as templates digitally. Thank you for your wonderful videos, you are doing great!

[@Eng586]

Best video I’ve found on work, thanks

[@Amoeba_Podre]

This is something that I dont think enough channels do, using calculus to revisit old ideas

[@thondur2194]

This video was genuinely one of the best videos I have seen. This topic was making no sense to me until you explained it. I have a big test on this topic coming soon. This was immeasurably helpful. I actually feel like I can do these problems now. Thank you so much!

[@JKMath]

Awesome! Thanks for sharing this, I'm glad to know that this video was able to give you some confidence in solving these types of problems. They certainly are not easy! Best of luck on your test!

[@pestifygaminghacks4713]

Thank You so much for making this video sir. You are of great help for us students who struggle with these problems! Much love sir.

[@JKMath]

You're welcome! Glad to help :)

[@ale4462]

Incredible video just covers everything man

[@vikramsaldanha2001]

You deserve an Oscar for this :)

[@JKMath]

Thank you, that is very kind of you to say :) Glad this video was able to help you!

[@bhaveerathod2373]

BEST VIDEO EVER MAN!! I would run for president if I had a brain as big as yours

[@karlahonorato677]

thank you so much! you're a life saver! Definitely will tell my friends about this channel

[@JKMath]

You're welcome! Glad I could help :) And thank you in advance for sharing my channel with others, that is very much appreciated!

[@ChainsGame]

Thank you so much for this! Spreading the word about your channel :)

[@JKMath]

You’re welcome! And thank you, I appreciate it!

[@malekabbr]

Thanks for making this video. I can't calculate the (work) you put on your videos but after this video I can. :)

[@JKMath]

You're welcome! So glad I could help you :)

[@madelineparker4647]

thank you so much this saved my grade! I completely did not understand propulsion problems and this explained them so well.

[@JKMath]

You’re welcome! Thank you for sharing, I’m glad that this video was able to help you :)

[@hystericalnigga12345]

Thank you for explaining these concepts so clearly

[@JKMath]

You're welcome! Glad to help :)

[@rozeisensei1380]

this is a great video idk why but I think it is from the ambience from your voice

[@abdiabdirahman6600]

goat

[@samirashams1304]

19:54 I can't understand why lower & upper bound is respectively 3cm & 8cm :d

[@JKMath]

I go on to explain that the lower and upper bounds are always measurements from the natural length of the spring. In this case, the natural length is 10cm, or 0.1 meters. The natural length meaning that the spring is 10cm long when it is not being stretched or compressed. So, when the spring is stretched from 13cm to 18cm, we want to know the work done when it is being stretched from 3cm past the natural length to 8cm past the natural length (13-10=3 and 18-10=8). That is .03 meters and .08 meters respectively. Does that make sense? You always want to be thinking in terms of how far from the spring's natural length it is being stretched or compressed. Let me know if this helps!

[@samirashams1304]

@@JKMath Ohhh I get it now thanks a lott :D