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Submitted URL: https://app.demandgen.ptc.com/e/er?utm_campaign=Mathcad_Newsletter_Mathcad%20Minute%20MAY%20Optimal_EM%201_FY23Q3_Multi%20Asse...
Effective URL: https://community.ptc.com/t5/Mathcad/Mathcad-Community-Challenge-May-2023-Optimize-Trajectory-for/m-p/872754?src=img1&utm_...
Submission: On May 14 via api from US — Scanned from CA
Effective URL: https://community.ptc.com/t5/Mathcad/Mathcad-Community-Challenge-May-2023-Optimize-Trajectory-for/m-p/872754?src=img1&utm_...
Submission: On May 14 via api from US — Scanned from CA
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MENU Ask a Question Search LogIn Enter a search word Turn off suggestions didn't see an answer to your question? post question Enter a search word Turn off suggestions didn't see an answer to your question? post question Enter a user name or rank Turn off suggestions Enter a search word Turn off suggestions Enter a search word Turn off suggestions didn't see an answer to your question? post question cancel Turn on suggestions Showing results for Search instead for Did you mean: All communityThis categoryThis boardKnowledgeUsers Enter a search word Turn off suggestions didn't see an answer to your question? post question Enter a search word Turn off suggestions didn't see an answer to your question? post question Enter a user name or rank Turn off suggestions Enter a search word Turn off suggestions Enter a search word Turn off suggestions didn't see an answer to your question? post question cancel Turn on suggestions Showing results for Search instead for Did you mean: Close X * Community * * Mathcad * * Mathcad * * Mathcad Community Challenge May 2023 - Optimize Tr... Options * Subscribe to RSS Feed * * Mark Topic as New * Mark Topic as Read * * Float this Topic for Current User * Bookmark * Subscribe * Mute * * Printer Friendly Page MATHCAD COMMUNITY CHALLENGE MAY 2023 - OPTIMIZE TRAJECTORY FOR MAXIMUM HORIZONTAL DISTANCE DaveMartin 16-Pearl May 01, 2023 04:13 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 01, 2023 04:13 PM MATHCAD COMMUNITY CHALLENGE MAY 2023 - OPTIMIZE TRAJECTORY FOR MAXIMUM HORIZONTAL DISTANCE A ball with a mass of 1 kilogram is at the top of a frictionless ramp 10 meters above the ground. The ball rolls down the incline and launches from a height of 2 meters and an angle of 30 degrees above the ground. (This picture was created in Creo.) 1. Create a function that calculates the horizontal distance as a function of initial height, launch height, and launch angle. 2. Calculate the horizontal distance the ball will land from the end of the ramp. 3. Solve for the angle that will optimize the horizontal distance. 4. How will the horizontal distance change if this were performed on the Moon instead of on the Earth’s surface? Assume the acceleration due to gravity on the Moon’s surface is 1/6 that of Earth. 5. Use the Chart Component to depict how the horizontal landing distance changes as a function of angle. 6. Use a 3D Plot to show how the horizontal landing distance changes as a function of ramp height and launch angle. Assume the ball starts at a height of 10 meters. The worksheet should contain sufficient documentation to stand on its own; someone unfamiliar with the initial problem should be able to understand what is being calculated. Find the Mathcad Community Challenge Guidelines here! Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com Labels: * Labels: * Puzzles Games * Tags: * Mathcad Community Challenge 1 Kudo Reply Notify Moderator * All forum topics * Previous Topic * Next Topic 24 REPLIES 24 Fred_Kohlhepp 23-Emerald I (To:DaveMartin) May 02, 2023 08:22 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 08:22 AM Can we assume that the ramp angle (from 10 meters) is also 30 degrees? (Otherwise the horizontal velocity requested in #1 is not fixed. Or do you want that discussed too? 0 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:Fred_Kohlhepp) May 02, 2023 10:24 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 10:24 AM The function should calculate horizontal distance, not velocity. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator Werner_E 24-Ruby V (To:DaveMartin) May 02, 2023 10:30 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 10:30 AM > -------------------------------------------------------------------------------- > > @DaveMartin wrote: > > > The function should calculate horizontal distance, not velocity. > > -------------------------------------------------------------------------------- Yes, that is clear, but the distance will probably depend on the speed reached. And this still does not answer the question whether the two legs of the ramp actually enclose a right angle, as one could assume on the basis of the drawing. So is the angle of the longer ramp 60 degree to the horizontal plane or should it be considered variable? 0 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:Werner_E) May 02, 2023 10:43 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 10:43 AM Here are a couple hints: potential energy gets converted to kinetic energy. The angle between the two legs of the ramp does not matter. I almost threw in the horizontal length of the ramp as a red herring, but I thought that might get people too caught up in the angles of the ramp. And even though I drew the angle between the two legs of the ramp at 90 degrees, it actually doesn't factor into the answer. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator Werner_E 24-Ruby V (To:DaveMartin) May 02, 2023 02:30 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 02:30 PM OK, but when the ball reaches zero height and is supposed to switch on to the 30° ramp, a part of the energy would be transformed into deformation and heat (even when you assume frictionless motion). How much depends on the angle of the first longer ramp. But I assume that you want us to neglect this as well and also assume a non-elastic ball with a diameter of zero so also the geometry where the two ramps meet is not of importance, right? 0 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:Werner_E) May 02, 2023 08:51 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 08:51 PM Yes, please ignore deformation, heat, and diameter/volume of the ball. Essentially it's a trajectory problem where the initial velocity comes from potential energy. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator ppal 17-Peridot (To:Fred_Kohlhepp) May 02, 2023 10:46 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 10:46 PM My Attempt May PTC Challenge.mcdx 1 Kudo Reply Notify Moderator ppal 17-Peridot (To:DaveMartin) May 02, 2023 08:15 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 08:15 PM So i get for the first iteration . Used Moment of inertia of hollow sphere . Anyone can confirm or dissent before I go further? 0 Kudos Reply Notify Moderator Werner_E 24-Ruby V (To:ppal) May 02, 2023 09:57 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 09:57 PM I have not spent much time on it so I may had made mistakes, but I ended up at approx, 17 meters The desired function would be or 1 Kudo Reply Notify Moderator ppal 17-Peridot (To:DaveMartin) May 02, 2023 10:38 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 02, 2023 10:38 PM Comments on my approach - Prime 9 attached May PTC Challenge.mcdx 1 Kudo Reply Notify Moderator Werner_E 24-Ruby V (To:ppal) May 03, 2023 05:53 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 05:53 PM Since the size of the sphere is not specified, I assume that it is simplified to be a point mass and things like rotational energy should not matter. @DaveMartin could go into more detail about this. EDIT: Ahh, I just noticed that he already wrote that the diameter of the ball should be ignored as well. So I guess that we should also assume that all kinetic energy is in translation and none in rotation. The ball is sliding down and up the ramp and not rolling, hmm... 0 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:Werner_E) May 03, 2023 06:26 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 06:26 PM Yes, please consider this a point mass. This problem was inspired by a high school physics problem cited by NASA in the 1960s. My intent was for people to consider the potential energy for the object at the top of the ramp and convert that into the kinetic energy as it comes off the ramp. That will give you the velocity of the object, and then you can plug that into trajectory equations like: https://www.physicsgoeasy.com/maximum-range-of-projectile-formula/?utm_content=expand_article For optimizing the distance in step 3, people should have an intuitive sense that the angle would be 45 degrees. I wanted to see how people would calculate that in Mathcad. The main point was to get to charts and 3D plots in steps 5 and 6. I should have probably used the word "slides" instead of "rolls" in the explanation of the problem. I will see if I can edit that. You can ignore friction, air resistance, rotational inertia, heat dissipation, or any other effects. I wasn't looking for anything beyond potential energy going into kinetic energy. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator Werner_E 24-Ruby V (To:DaveMartin) May 03, 2023 06:56 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 06:56 PM > -------------------------------------------------------------------------------- > > For optimizing the distance in step 3, people should have an intuitive sense > that the angle would be 45 degrees. Yeah, thats also what many may remember from school but it ignores the 2m ramp height above floor > -------------------------------------------------------------------------------- > > I should have probably used the word "slides" instead of "rolls" in the > explanation of the problem. > > -------------------------------------------------------------------------------- Would be unusual for a ball to be sliding instead of rolling So you would have to use a different point object which slides. But #1 needs clarification. Which "horizontal distance"? Probably you mean the horizontal distance from the end of the launch ramp depending on time (additionally to the asked for initial height, launch height, and launch angle). So a function with four arguments, not just three. But without friction, air resistance, etc. its just a simple function linear in time. If you meant in #1 a function for the landing distance, #2 would simply mean to evaluate that function for the given input values. 0 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:Werner_E) May 03, 2023 10:42 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 10:42 PM Yes, it's not exactly 45 degrees as I altered the original problem. I changed it slightly so that the ground is not level with the end of the ramp, as shown in this problem: https://homework.study.com/explanation/a-block-slides-down-a-frictionless-incline-that-terminates-in... Let's please keep it simple. I wasn't going for anything tricky or complex. In #1, I mean the horizontal distance from the end of the ramp when the ball lands. Yes, a ball rolls, it doesn't slide. But I had a nice model for a ball in Creo that I could use to make the image, so I did. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator Werner_E 24-Ruby V (To:DaveMartin) May 03, 2023 10:14 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 10:14 PM So anyway here is my entry - out of competition as it was created in Mathcad 15. But this version allows a much quicker and faster workflow and is significantly more convenient to use. Quite apart from the fact that it is also more powerful in terms of functionality. I briefly tried converting the file to Prime 9, but despite the fact that it would have required a lot of reformatting to make it look anything like the same, I also had to refuseto put up with the many shortcomings of Prime and the converter to bang around. The well known auto-label bug has struck again - h has become a constant, g an undefined variable without a way to change it. And Prime's inability to deal with incomplete functions would have required a workaround in calculating the optimal angle. I didn't even get as far as the plots then. I quickly gave up trying to create a Prime Worksheet, very disgusted, and instead attached a PDF Print in addition to the Mathcad file. Have fun! Here the pics of the two pages WE_20230504_May Challenge.xmcdz WE_20230504_May Challenge.pdf 485 KB 2 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:Werner_E) May 03, 2023 11:00 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 11:00 PM Looks like you got the trick answer to #4. The acceleration due to gravity falls out of the equation. So it doesn't matter if you're doing it on the Earth, the Moon, or Pluto. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator Fred_Kohlhepp 23-Emerald I (To:DaveMartin) May 03, 2023 10:49 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 03, 2023 10:49 PM Solution attached, Prime 4.0 Express challenge 5_23 chgedA.mcdx 2 Kudos Reply Notify Moderator JeffH1 13-Aquamarine (To:DaveMartin) May 05, 2023 07:23 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 05, 2023 07:23 AM My submission in Prime 9.0 format. Challenge May 2023 - JPH.mcdx 2 Kudos Reply Notify Moderator ttokoro 19-Tanzanite (To:DaveMartin) May 05, 2023 07:41 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 05, 2023 07:41 PM Ignore rotational kinetic energy. Prime 9. No Chart Component but x-y plot. Without units to solve. May2023 PTC Challenge.mcdx 1 Kudo Reply Notify Moderator AlanStevens 16-Pearl (To:DaveMartin) May 08, 2023 08:01 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 08, 2023 08:01 AM Here's my limited attempt with Prime 8 Express: MayChallenge.mcdx 1 Kudo Reply Notify Moderator JE_9022802 2-Guest (To:DaveMartin) May 08, 2023 09:40 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 08, 2023 09:40 AM If it's a ball, why does the incline need to be frictionless? The intent of a ball is to have it rotate. For that to occur, you need nominal friction. 0 Kudos Reply Notify Moderator DaveMartin 16-Pearl (To:JE_9022802) May 08, 2023 09:54 AM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 08, 2023 09:54 AM If you want the incline to have friction, add friction. If you want to incorporate that and rotational inertia, have at it. I will repeat my original intent. I modified an old high school problem, where the intent was for people to use the potential energy to find the initial velocity to calculate a trajectory. Anything else you want to add to the problem is up to you. As with the previous Mathcad Challenges, the point isn't the answer you get, but how you choose to approach the problem with the tools in Mathcad. Dave Martin - dmartin@creowindchill.com - https://www.creowindchill.com 0 Kudos Reply Notify Moderator JeffH1 13-Aquamarine (To:JE_9022802) May 08, 2023 11:07 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 08, 2023 11:07 PM @JE_9022802 - I'm with you. As much as 30% of the kinetic energy goes into rotational inertia. Without it, the problem is non-physical and sets a bad precedent, even for high schoolers. It is workable with the rotational component. Give it a go. 0 Kudos Reply Notify Moderator ppal 17-Peridot (To:DaveMartin) May 09, 2023 11:14 PM * Mark as New * Bookmark * Subscribe * Mute * * Subscribe to RSS Feed * * Permalink * Print * * Notify Moderator May 09, 2023 11:14 PM Prime 9 file PP_ May PTC Challenge..mcdx PP_ May PTC Challenge.pdf 758 KB 2 Kudos Reply Notify Moderator Post Reply Announcements Top Tags * mathcad * group discussion * group document * programming * mathcad_prime_2.0 * matrix * error * engineering * Electric_circuit * prime * plot * prime_2 * solve * excel * mathcad_15 * units * ptc_mathcad * function * puzzle * civil_engineering * help * mathcad_prime * mathcad 15 * physics * mathcad_blog * ptcuser_portal * symbolic * vector * odesolve * building_structural_des… View all About PTC.com Products & Solutions Contact Resources My PTC - Support PTC University Help Center - Product Guides Product Documentation Success Paths - Planning & Implementation Guides Other PTC Communities On Shape Reality Lab Vuforia Engine PTC user Terms of Service Legal Policies facebook twitter linkedin youtube Top Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type. 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