What is the new speed v’ away from the wall when rolling motion is re-established?

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  1. A wheel (mass M, radius R) rolls with speed v and angular velocity w (v=ωR) and collides elastically with a wall. Immediately after the collision it has v away from the wall, but the same ω as before – so it’s skidding, not rolling. Friction at the floor will eventually re-establish rolling motion, by doing negative work on the system and applying a torque that will change ω. What is the new speed v’ away from the wall when rolling motion is re-established?

    Answer by RickB
    That's an interesting question! First, let's set up direction conventions. Let's say: * The wall is on the left, so the wheel bounces off to the right. Let's call "rightward" the positive linear direction. * Let's call "clockwise" the positive angular direction. (That means the wheel's rotation is negative immediately after the bounce.) During skidding, the force of friction is more or less constant (given by: (normal force)×(coef. of sliding friction)), so we can say that "Ff" is the (constant) force of friction during the skidding phase. The force Ff produces a torque on the wheel, in the amount of: τ = (Ff)R. (This is a positive torque, since Ff points to the left and therefore tends to drive the wheel clockwise.) We know that the angular acceleration is given by: α = τ/I = (Ff)R/I where "I" is the wheel's moment of inertia. I'm not sure what kind of wheel this is, but its moment of inertial can be represented as: I = βmR², for some "β" that depends on how the wheel's mass is distributed. (It's some constant between 0 and 1.) So we can write: α = (Ff)/(βmR) At the same time, the ball's linear acceleration is: a = -Ff/m (Here we use negative Ff, since the force points toward the left) With these two values, we can write the ball's angular and linear velocities as a function of time: ω(t) = ω0 + αt = ω0 + (Ff)t/(βmR) (where ω0 is the ball's angular velocity right after collision) and: v(t) = v0 + at = v0 + (−Ff/m)t (where v0 is the ball's linear velocity right after collision) We are also given that ω0 = −v0/R, so we can rewrite the ω(t) equation as: ω(t) = −v0/R + (Ff)t/(βmR) Now, at some time t′, rolling is re-established. That means: v(t′) = ω(t′)R or: v0 + (-Ff/m)t′ = −v0 + (Ff)t′/(βm) From which: t′ = 2(v0)mβ/[Ff(1+β)] Now plug that value back into the "v(t)" equation: v′ = v(t′) = v0 + (-Ff/m)2(v0)mβ/[Ff(1+β)] = v0 - 2(v0)β/(1+β) = v0(1 - 2β/(1+β)) = v0(1-β)/(1+β) So for example, if you assume that the wheel has a uniform density, then β=½, in which case v′ = v0/3.

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    Answer by Benjamin
    The fit of most of the crew necks (2001, BB401, TR401, 6401) is closer to the regular v neck (2456) Go with XS in unisex styles and a S in womens.

  3. What current would flow in an ordinary 110 V household circuit, if a 1210 W hair drier and a 700 W microwave oven were operating simultaneously on this line? Answer - 17.36 A How much current would the hair drier and microwave from the previous question draw, if they were connected to the 110 V line in series?

    Answer by Kim
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DIRECTVI did not realize that when I went from my local cable company that I would be getting those great music channels on my new satellite programming. I was so excited because I was actually getting the satellite radio that a lot of people pay a lot of money for. However, this was included in the large package that I was paying a lot of money for. I was happy to see that one of my favorite radio talk show hosts was even included in my http://directsavingstv.com/ package and I could not believe that they would be able to include him in the package that I was getting. Instead of listening to the local news every morning after the kids went to school, I would put on his channel and listen to him as I read or did a lot of the housework, I was so happy and it seemed to make me in a better place each day.

My husband was happy when he came home from work and he saw that we also had the seasons channel. The seasons channel plays a lot of holiday music that is appropriate with the season of the year. We love Christmas music and they started to play the music in late October, which was just great with us. We started to sing carols on Halloween and it continued for the next few months. We noticed that when we ate dinner as a family at the dinner table that we were all enjoying whatever channel was on at the time. The little kids also enjoyed the kids station that had kids singing popular songs that were appropriate for their age, it was such a great deal for us and we are enjoying every minute of it, no matter what the cost is.

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Most effective Nine Ideas – The Most Important Home Mortgage Information And Tips

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To make your application for a mortgage fast and easy, make electronic copies of your last two pay checks, two recent bank statements, W2s, and tax information. Lenders will ask for all of this information to go with the application and having them on hand in electronic format makes it easy to supply this information. When you decide to apply for a mortgage, make sure you shop around. Before deciding on the best option for you, get estimates from three different mortgage brokers and banks. Although, interest rates are important, there are other things you should consider also such as closing costs, points and types of loans. Pay at least 20% as a down payment to your home. This will keep you from having to pay PMI (provate mortgage insurance) to your lender. If you pay less than 20%, you very well may be stuck with this additional payment along with your mortgage. It can add hundreds of dollars to your monthly bill. Read the fine print of your mortgage contract before signing. Many times home buyers find out too late that their fixed rate loan has a balloon payment tied to the end of the loan Check This Link

It Is Actually True That You Are What You Eat

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Consuming ground turkey in place of ground beef is an excellent, healthy choice. However, the main reason more people do not do this is because of how dry ground turkey can be. Enhance the flavor and moisture of your ground turkey so you do not have to eat dry meat. This way you will be consuming less fat through your meat but still getting a great taste. Eat meat if you're trying to grow muscle. A study has shown that eating 4 to 8 ounces of meat a day can contribute more muscle mass to weightlifters, and while another group got stronger, the meat eating group had more muscle to show for it. So enjoy all types of meat and be stronger.Naturally, you want to make good choices when it comes to nutrition. However, it is not always easy to know what to believe and what to reject. This article gathers together several nutrition tips that are reliable and effective. Read on to see what they are, and then try them out for yourself.Limit your consumption of red meat to once a week or less. A great treat, red meat is not as healthy for you as other forms of protein. Try replacing some of your meals with Check This Link

What I truly feel – Complete Your Home Improvement Project With These Tips

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Display your jewelry on a coat rack mounted on the wall. It is important to keep your valuable jewelry out of sight and only hang jewelry on the rack that is not of the highest value. Hanging your jewelry on a wall can make a pretty decorative statement, as well as keeping the jewelry tangle-free. Display the items that you wear frequently, so they'll be at your fingertips when you're getting dressed. You can create an appealing and unique bookcase by using wallpaper. Choose a design that's unique and interesting. Put the wall paper on the back side of the bookshelf, when you put the books on it will show from behind them. Adding a little bit of edginess to you bookshelf will create a more modern look for not only the bookshelf, but the room that it is in.Serious drainage problems can surface during rainy periods if gutters are clogged. Clogged gutters can lead to leaks in your roof and damage to your basement due to seepage. You should take time, and clean your gutters before you have to deal with the mess. If there is a lot of space in the attic, you should install a dormer window to make Check This Link

Everyone may want to realize – Tips To Buying A New Car Or Truck

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Before you commit to purchasing a used car, have a mechanic check it out. Doing so lets you discover any mechanical problems the car may have. If a car has been in a wreck and the salesperson did not mention it, you should go to a different dealership. If there is a mechanical issue with the vehicle, ask for a lower price. Don't go to a car dealer with a shady looking lot. Some dealers sell cars that are no longer road-worthy. If the dealership looks suspicious, just head to the next one.While there are those that enjoy car shopping, others try to avoid it at all costs. By learning how to shop for a car, you can begin to enjoy your car shopping experience. Use these tips to find the right car and negotiate the price you want without letting the car shopping process cause you too much stress. When you're looking for a vehicle, think about how the fuel economy can affect you. For instance, you may want a large vehicle so you can tow your camper during the summer months. However, you have to consider whether you'll use that towing capacity and if you'll often use the extra horsepower of a V-8. Check This Link

Worried About Anxiety? How To Stop The Spiral Of Fear

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If necessary, see a therapist. Sometimes anxiety overwhelms people because there is no one for them to talk with about what is bothering them. Getting help from a therapist can ensure you rid yourself of anxiety. When anxiety threatens to consume you, surround yourself with distractions. Hang around other people as much as you can, and do an activity that you enjoy. This will help you stop thinking about things that are likely to make your condition worse than it already is, and allow you to start relaxing. Music can really help with anxiety. If you feel an attack coming on, pop on a CD. Get into the music. Before long you will experience a reduction in your anxiety and an improvement in your mind set. Having something to keep your mind occupied can really alleviate the anxiety you are feeling. Talk to somebody regarding your feelings, such as a doctor or a family member. When you keep all of you thoughts and feelings bottled up, they can come back worse. Releasing them can decreases anxiety and make you feel better. If you suffer from anxiety, you may want to consider seeing a therapist, particularly Check This Link

Popular 3 Pointers – What You Should Learn About Acupuncture Before Getting Started

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You may want to keep a record of your sessions when you're receiving acupuncture treatments. Record your feelings as well as any changes you feel after each treatment. At the start of each appointment, share your journal with your therapist. That way, they can make any necessary modifications to your plan.Now that you have read this article, you know that acupuncture can be beneficial to you. Before you read this article, you probably had little knowledge on the subject. With the knowledge you have gained, you are ready to incorporate its healing powers into your own life. Needles are integral to the practice of acupuncture. This is how it is: acupuncture requires needles. They are an integral part of this treatment. Try to accustom yourself to this idea before your appointment to avoid unnecessary stress. Don't be surprised by painful looking red splotches, bumps, or bruises following an acupuncture treatment. Those splotches aren't normally as painful as they look, and they are totally normal. The same with the dots and the bruises. They are all something that you should expect. These marks Check This Link

Ways To Cut Spending In Half By Using Coupons

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Using coupons can be an excellent source of savings to help someone who really needs some help. Through a small community effort, clipping coupons and using them to buy basic necessities can have a great impact on those who are less fortunate. These efforts can really help you do something great while saving through coupons.Always have the very best coupon from those available. A lot of time you will find a lot of different kinds of coupons for the same thing. There might be a coupon for a 10 percent discount, but also a 50 percent coupon. Think about which ones benefit you financially, but you may want to keep them both for two different occasions. You can save lots of money on certain items by shopping at dollar stores. Often, you can find brands that match your coupons. Many overstocked products are sometimes sent to low-end retailers to offset costs. You can be the one who really saves big by taking advantage of the low price.The obvious place to begin looking for coupons is in your Sunday paper. This is when most major papers have a big insert with coupons inside. Save these to help you Check This Link