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A cylinder of mass 8.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of 17.0 m/s_ (a) Determine the transla...

Question

A cylinder of mass 8.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of 17.0 m/s_ (a) Determine the translational kinetic energy of its center of mass(b) Determine the rotational kinetic energy about its center of mass(c) Determine its total energy.

A cylinder of mass 8.0 kg rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of 17.0 m/s_ (a) Determine the translational kinetic energy of its center of mass (b) Determine the rotational kinetic energy about its center of mass (c) Determine its total energy.



Answers

A cylinder of mass $10.0 \mathrm{~kg}$ rolls without slipping on a horizontal surface. At a certain instant its center of mass has a speed of $10.0 \mathrm{~m} / \mathrm{s}$. Determine (a) the translational kinetic energy of its center of mass, (b) the rotational kinetic energy about its center of mass, and (c) its total energy.

Okay. Hm. The transitional kind of energy is given by half MV squared. It was half times masses. 10 kg time philosophy is 10 m per second square. It was 500. Jewell rotational kinetic energy is given by half. I Omega squared. It was half I e is half Aimar squared on omega squared equals C squared over r equals 1/4 M V Square, which is half of this. So there's 250 Jewell. So total kind of the energy is the sum off these two 7 50.

This is Linda Riss Translational kind of energy cylinder. Translation. All frantic energy. It's cumin. Why one or two times? Mask times the center off a mass speed squared. Substitute values one or two times. 10 times 10 square. The excuse. US translation can take energy off. 500 jewels You bought B the rotational time. Take energy. Rotational Kandic energies One or two. I went off inertia times Omega Square, where the moment of inertia offs a lender is One word to him are square where the relation between we and our amigos we use a cult or America there will substitute those values for Ryan Omega in both equation. So this kid becomes one of what to one of what two are square into we or our square. This gives us one or four em. We square. So such really value for a bus which is 10 times, then square. Excuse us. The rotation Organic energy off the lender off to 50 Jules. But see, the total frantic energy total will be equal to frantic energy. Rotational plus can tick energy consolation. So traditional regard is a 2 50 and translation We got 500. This total becomes ah 7 50 Jules

Problem 11.10. So we have a hollow sphere rolling without slipping up an incline 30 degrees its size and moment of inertia or given here. And it has a kinetic energy at some initial point of plenty tools. So first we want to answer how much of the kinetic energy is rotation? So a professional over the center of mass motion related kinetic energy? Let's care occasional So, um, for a hollow sphere, the moment of inertia is 2/3 m r squared, and it may be handy for us to know, but the mass must be 2.7 kilograms. So 1/2 Iomega squared based on this is 1/3 em are split and Omega squared. Now we know that he is Omega Times are so our kinetic energy from the center of mass motion here be written as 1/2 and be square. But the spirit is also R squared Omega squared because it's not slipping us. Just the exact same thing here is on top R squared Omega Square. So canceling out all the m r squared Omega squared, we're left with the ratio 0.4, so 40 per cent of its kinetic energy is rotational, so we know what? No, uh, what's the initial speed of the center of mass? So we know that the center of mass kinetic energy is 40% of 20 inches. Eight, eight. Jules, wait. This is the rotational kinetic energy you can use either one, but you need to get the right the right number for the right thing. So this is 1/2 and r squared. I'm sorry. Not one. If you find physics confusing, don't worry. Everyone does and are spread of Vegas. So we can solve this for Omega, and you get 20 radiance per second, so that be not is equal. You are. They could not, Which is three meters now for part C and D. We suppose that it's gone one meter up the incline. So first of all, it's just gonna be one meter times a sign of 30 degrees for half a year. Okay, so proceed. We want to know what it's total kinetic energy is. We know that it's total energy is going to be 20 jewels because that was the initial kinetic energy. And we're assuming it started, you know, zero height. So there's no potential energy to begin with. So then this has to be equal to the kinetic energy, the total kinetic energy, Uh, plus the H. And so the total kinetic energy is 6.9. Jules, once it goes a meter up the ramp and so repeating basically what we did before, we know that 40% of the kinetic energy is rotational. And then we just repeat this process here, but with 6.9 drools instead of 20. And so then we find the The speed is 1.8 years per second. Now and again, that's just based on. But we already know because this doesn't depend on the values of any of these things, just what the functional form is that they have. And then it's just repeating this calculation.

The mass of the surrender families, equal student location and the radius of the center are 0.3 m the length of the center of this one and height of the plane engines. 0175 m 58 The initial An idea of the seven days M g. H and the final energy of the splendor is that kind of technology or from the contribution of energy. He is a costume and th are we. The total kinetic energy mass is two kg into 9.81 meters was second square in 20.75 India's of the total Kinetic Nigerians 14 points 71 party troops How part b The moment of finance you have to surrender. I is m r squared by two and far north. Leigh Omega is he puts two were gone by this The easy question Omega the total candidate energy that escaping total records too. King observational. That's Katie translational or product. Can I take energy? They need to tell with the costume how the moment of financial m R square upon to and for me to square plus have mm and these Omega Square r K total then equals two body by folk and Mark's square My last square less one by two I am on my last square. By this, we can say that their translational kinetic can achieve is every two translational It was 22 times of k rotational and the total kinetic energy Hey, total is three times of in rotation. Therefore, and so there is no kinetic energy gate rotational because to one of on field Mm hmm. Our security prevention ellipticals to one of them. Prayer 14.715 Jews or 80 generationally 4.905 tubes. How part? C e translational the constant to into Katie Vocational Ordered any questions going to 4.905 jewels or killed translational No question. 9.81 shoots.


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