Physics Problem on Potential and Kinetic Energy...?
I think this is how you solve it w = integral of f dx You can find the integration limits based on how far the chain falls If only the 1.2m section of the chain moved, this would be easy. Since sections of the chain on the table move less than the sections dangling, write the amount a "small" section has moved vertically as a function of how far it is from the top, (the end of the table section). (ie, a section at 1m from the top only moves 1m, while the very top moves 0) - No work is done to it while its on the table since the force is perpendicular to the direction of motion. Because the force is constant, multiply the expression for distance moved by the weight density, and integrate. If you dont know calculus, you can plot the graph of the function and find the area under the curve between the start at the distance moved when the chain falls off.1. Why is a 3-PDA no more powerful than a 2-PDA?Two stacks can emulate a Turing machine tape. Motion along the tape is isomorphic to popping some symbol $x$ from one stack and pushing it onto the other stack. Writing to the tape is isomorphic to popping something from one stack and writing the new thing to that stack. Thus, anything a one tape Turing machine can do, a 2-PDA can do. Since a Turing machine can simulate a $k$-PDA for finite $k$, it can certainly simulate a 3-PDA. Therefore a 2-PDA is just as computationally powerful as a 3-PDA.2. Is the equation of motion true for a non-uniform motion?A motion is said to be non uniform if it has an acceleration . If whatever is the acceleration then in such kind of nonuniformity motion equations of motion are valid but if in non uniform motion acceleration is not changing then it differential equation will be valid3. Should you strength train with resistance bands or dumbbells?If you've paid even a little attention to the boom in at-home workouts during quarantine, you've likely seen resistance bands popping up everywhere. Resistance band exercises are popular for good reason: compared to other fitness equipment, they are inexpensive, easy to store and simple to use at home (or anywhere for that matter). But do resistance band workouts really work? Who should be using them? And what is the best way to work out with a resistance band? For answers, we turned to orthopedic clinical specialist and physical therapist Erika Mundinger. Currently traveling the country in an RV, she's been discovering the best resistance band workouts in her own small space. "Can you get toned, can you get strong, can you get a good workout with resistance bands and hit weight-loss goals? Absolutely," Mundinger said. First, what is the difference in strength training with resistance bands versus weights? "If I grab a 15-pound dumbbell, the resistance of that 15 pounds stays consistent throughout the entire contraction," that's known as an isotonic contraction, Mundinger explained. "And then there's isokinetic, which is what we get from the resistance bands, and that's where the resistance changes as I move. [When] I grab that resistance band to do a bicep curl towards me, that resistance is going to get harder on the top and easier as I bring my hand back down. The more we are going through the motion, the resistance actually changes. So it just strengthens the muscles a little bit differently." Various bands come in different levels of resistance. "Each brand is going to have their own pretty rainbow color scheme," Mundinger said, "and it's pretty standard that lighter colors are typically lighter resistance, and as it gets darker it gets harder." When you can consistently maintain your form through a full range of motion with a band, you can begin to work your way up to the next one, she said. All you need is a set of bands and something stable to fasten them to. Emphasis on stable: if you try to anchor them to a table leg, "unless it's like an oak table that seats 12 you are going to pull the table over," she said. Think a banister or post, or if you actually have a home gym, a squat rack. "If you do not have something to anchor them to, that means you are going to be anchoring them underneath your foot or your arm," Mundinger said. In that case, "the most versatile ones are the long tubes with the handles." "It's hard to know exactly how much resistance you are pulling with," Mundinger said, so people who really want to be scientific about the amount of weight they are lifting wo not be able to do that. They are also not as helpful for training power moves like Olympic lifts, she said. "And you are probably not going to get quite as ripped," she said. "Because the resistance is changing as I move, I can not take my body through a full range of motion." With a squat, for example, "I can not get my body to do a full deep squat with resistance bands unless they are really light," she added. "To get big and strong and ripped like we would with full-body motions that we can do with dumbbells, kettlebells and barbells, it's hard to do because you are going to be starting at the bottom with really light resistance and ending with really hard resistance, and it's just impossible to create that power motion." "Because it is isokinetic and it gets harder as you move through, we start to activate our stabilizer muscles a lot more," Mundinger said. "So the more I am pulling on that band, the more my core muscles have to engage, the more I am raising my arms up overhead, the more my stabilizer muscles around my shoulder blades have to engage. So in physical therapy we love resistance band isokinetic stuff because it really trains that core stability." They can also help you improve your other workouts, including those using dumbbells. After working with resistance bands, "when I go back to those big foundational moves like the bench press or the squat or the deadlift, I am stronger because I have those accessory muscles now engaging more," Mundinger said. "Even if you are not hitting the weight room, they are just great for overall functional strength that I need to have throughout my day." Physical therapists love resistance bands, Mundinger said. "They are a good exercise for people who have injuries to be able to still build some core strength and stability and not flare up injuries and inflammation." Isokinetic exercises allow you to perform a lot more repetitions with lighter resistance, which comes with a lower risk of injury compared to performing isotonic exercises, she said. They also make it easy to "modify and substitute and limit your range of motion as much as or as little as you need to," she added. For anyone who can not load their lumbar spine with barbell squats, you can still train body-weight squats with bands, Mundinger said, "and then you get the cardiovascular component of the squat without causing back pain." OK, but we all want to know: Can we burn fat specifically in the stomach area? "Are you going to burn belly fat because you are burning calories and getting a workout? Yes," Mundinger said. Can you isolate your belly to burn fat with resistance bands? Not exactly. "Normal exercise will help you be able to do that," Mundinger said. "You will burn belly fat because you are working out, period." Ready to give resistance bands a try? Here is a 15-minute resistance band routine that will work your entire body