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Hi Dr. Stephen. This is a very practical physics question. This question is actually a fairly simple question but it's not easy to verbalize. I weigh 165 lbs and I use a weighted vest when I work out. Let's say I add 15% to my weight (i.e., wear a 25 lb weighted vest) and go running outside (no incline). Of course my body has to work harder when I add the 25 lbs. As far as how much harder my body is working with the extra weight, what would be the equivalent incline w/o the weight? In other words, would running on level ground with 25 extra pounds be the equivalent amount of work of running (of course at the same speed) up a 10% incline?

How do I calculate this? What if I go running w/ 30 extra pounds, what incline would that be the equivalent of without the weight (of course assuming I am running at the same speed with or w/o the weight)?

Thanks so much!
David

Answer
This is a question for a kinesiologist, of course.  There's not as simple an answer to this as you think, really, since the running strides are completely different.  I can give you the quickest estimate possible,  but it doesn't even flex the muscles in the same way.  I would tell you that the weight of the runner multiplied by the sine of the angle should basically equal the weight added, but in practical terms I know that won't work...you don't even tell me how fast you're running.  As far as fundamental forces go, however, you have to add enough vertical spring (weight*tan(angle) = added weight) to overcome the added components of the force of the weight...it's not really a very useful metric and has a lot wrong with it from the perspective of changing stride.

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Dr. Stephen O. Nelson

Expertise

I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

Experience

I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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