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A 12 -in.-radius cylinder of weight 16 lb rests o…

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Problem 106 Easy Difficulty

A 12 -in.-radius cylinder of weight 16 lb rests on a $6-1 \mathrm{b}$ carriage. The system is at rest when a force $\mathbf{P}$ of magnitude 4 lb is applied. Knowing that the cylinder rolls without sliding on the carriage and neglecting the mass of the wheels of the carriage, determine
(a) the acceleration of the carriage, ( $b$ ) the acceleration of point $A$,
$(c)$ the distance the cylinder has rolled with respect to the carriage after 0.5 s.

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Video Transcript

We have two different bodies here, so people started them separating. First we draw the F feeling for these lender alone. The cylinder will be called a light in the book and the carriage mean, as you can see from the pretty taking the summer off moments around the center of must that years must moment off inertia so it can be done as Sigma MGI is a quote you I have but Sigma mg Zago do f uh is a gradual one. How m e r Square? I thought. So. We can write. I'll fight is well Jew do Meal G of one are also taking Newton's second law around the X axis. Begin right Sigma epics is a quality job. I m a you a eggs. Therefore, it is a quarter Jew Me allergy. I changed the name off a salvation from X to a. Since they're on, Lee is as elevation in the X direction for the center of months. So in Busan need to obey the noted. It's easier to understand now. If you have sold enough off this problems, you should feel that we need a relationship to relate the angular acceleration off the Celinda really a simulation offered center off months now if instead, off the carriage people have solid, having grown that isn't affected by the force of friction. The Selinger off place we could drive back for the no slogan so accordingly okay, so accordingly I can write the equation as yeah. Is it? Well, Jew are far. However, the that is not the case here. So let's think off how we can make that case. If we can make the carriage, not move with respect to these Linda, then begin use the overall equation. If that's all this is really easy to do since for the related acceleration. If they subtract the reservation off the carriage from the acceleration off the slender, then to the slender the carriage appears to not be as a rating at all in magd. Um, this is translated to I was, uh It's a question too, Bobby. Minus of are in. Sorry, I r is a Jew. A B minus 80. Now next, wrong the FBT and then study the carriage with the name the B. You can see it in the diagram taking Newton's second law in the hall is under direction. Begin marriage Sigma FX is a go through MB A me eggs Therefore a B is a cordial being minus meu m a g a born and be no here. If you are wondering why I have only I didn't the mass off the carriage in the whole system, not that absolutely toe. It is because they are different systems and they only interact by the force of friction and the action force. Between them we have 40 questions and for a nonce, all we have to do now is solve this system. So again, right, Alfa, are is a Jew a B minus a But I find it's acquittal Tomb Yuji upon our into our is equal Jew baby minus a A change by putting is, uh, a creation here that means which we are having m u g minus being minus mu m a g a bone and be It's a Quito to Amud. Your other begins alone. Solving this in the form of Mu I can write new is a true summer deviously we're putting the values here so musical toe be that means four upon g the history do going to into three times MB the six point 32.2. Plus I m a. There is 16 of one. 30 Job behind you and solution off. This will give the answer 0.1176 Now, using this, we can find the values off the association off the cabbage. So that is nothing but a B is a gradual mut. But, um, you is little point The bourbon 76 into G is 32 point. Do be choosy on so three bind 79 feet per second square and the acceleration off the Solingen is can be calculated else. It is a question be that is four minus mu with 0.11 76 into em. They're the 16 upon 32.2 Indu jee There is 32.2 a phone i m e that is 16 upon for digital windrem which used the on so 11.4 beach per second squared next to find their distance, the Solingen has rolled in fitness back to carriage. We need to find the observation off the surrender with respect to the carriage which we before found out that waas I For me a is a question. How far are is a good toe for B minus, I'll find or a B minus A. That means Evie is 11.4 minus e is 3.79 which is equivalent to seven point 61 beautiful second square. The translation motion in a straight line which constant as elevation is given by X is a gun room X zero Bless Busy Georgie Bless are for me A I'm stay square off random. Since the system starts from rest than x zero will be Zito. V zero is also zero anti physical do point Fine. So they explored the value here. So we really gauge exes. According true, zero point nine by 1 ft Because the hell exitos Edo the zero vido and G is it gonna do flanked by Okay, so finally we have this eggs.

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