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The uniform rod $A B$ with a mass $m$ and a lengt…

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Problem 116 Easy Difficulty

A $4-$ lb bar is attached to a 10 -lb uniform cylinder by a square pin, $P,$ as shown. Knowing that $r=16$ in., $h=8$ in., $\theta=20^{\circ}, L=20$ in. and $\omega=2 \mathrm{rad} / \mathrm{s}$ at the instant shown, determine the reactions at $P$ at this instant assuming that the cylinder rolls without sliding down the incline.

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Video Transcript

Hello friends As surrender figure. There is a world off. Wait football and a plant continue. Inch is attached to the surrender off of it. £10 on radius, 16 inch value off edge is given eight inch on angle. Details. COMPUTER Lee If surrender is rotating and clocked by direction with angular velocity off to Radian per second, calculate the reaction at B. So this is the point. We admit we have to calculate the reaction. First, we will calculate moment off energy of the bar. And but after Endor, the mass of the bar is the divided by acceleration. Due to gravity. Date is given four points on excellence in due to gravity is 32.2, so this date becomes quite 1 to 4. There were two select, and it's the moment off. Energia, about center off months, is run by 12 top product top mass of the rod and the square off. It's lent, substituting the red. It's mass is 0.1 toe. Lend it 20 inch. We are using it in it, so divided by 12. So on solving it moment of inertia about the center off mask you will get 0.28 seven Double five Select in 2 50 square mask off the surrender. Great off surrender, divided by excellence and due to gravity, weight is given to deport. Sorry, it is given 10. 32.2. So it would be no. Quite three but 056 slips moment off. Energia off the cylinder about extent er off months, half walk. I'm seeing tow our script. Mosque is quite three, but 056 on radio are 16 upon Great, you will get fined 27 60 Fight Look! And 2 50 square. Now we have to discuss the dynamic ticks off the surrender on the road. Uh huh. Be plate in the X. People like acceleration is genuine ship on the normal center off months A little begic. This is instantaneous center seat. Thanks. Having acceleration issue normal and for But I see it acceleration. Angular acceleration is and for and clockwise direction the acceleration off center off months 80 at in the direction country degree down to the origin for ruling without selfie, that is, for purely a si will be zero and a C is defined that e g minus are alpha. That must be zero So a it's called toe Alfa. Acceleration off the the initial direction acceleration off G plus adding to welfare. So you may right, e g is our into fo acceleration off the point in normal direction zero black America square edge. Now let us hear the dynamics. We will draw free body diagram off the system. This is three point here. It will be normal reaction fiction the I'm seeing to the and being to the I ve in to help I see into Alfa must off road in tow. Technician mark off. Surrender in tow. Initial acceleration. No. Okay. Finding moment off couple and about three point taking drug buys to be positive. M C G in tow. Our sign up data and the G in tow are less edge. Sign off the top. It must be equal toe I see into welfare I see. And to a tendon ship And 25 that's I see into Alfa EMC and a into art ivy into Alfa and the and to 80 They in two parts less edge mhm From here you make a substitute. The value I see is I seem to help her Mhm initial is given are into well for what Ivy and the AP tin you ship are less edge. Alfa are left edge. Also, you can take common solving Europe equation for value off it will be Mars off. See splendor doing toe are march off but in tow, the and tow are less edge. Sign off, Tito divided by and I see Let's and seeing toe square ivy and being to our message substituting the all the parameters are given mass ob surrender is 10. Just a moment already. We have converted in two months so directly we can say to you miles off why 31056 that 8.2 and art 16 White but master of the Art Find 1 to 4 to two that it will find too. And R plus Edge R plus edge 16 plus 8.16 Signed up country divided by moment Obstinacy off the surrender. 5 to 7 60 Fight perhaps. MOSOP surrender 0.31056 and to Radio Sky Square, 16 12. Holy Square plus moment. Affinity off the bar 0.1 toe for two mark off the bar that I have substituted only moment. Officers off the bar is client Tzeitel 28755 must. Why one toe for Toto in tow. R plus edge, that is 16 plus eight eight diverted by 12. Holy square. Don't Mm. So on solving. That's why you will get five points. 3896 Radiant per second squared, then Initial acceleration off three point 24 by 12 and tow five point 3896 We stand point 7791 50 per second squared and it's a normal acceleration is eight by 12. And to quite square two point triple 67 good per second squared. Okay, using free body diagram off the bar. Now here we will draw on Lee the free body diagram off the bar. Wait. Um, being to G reaction along by axis along XX is I leave in tow, Alfa and we in tow candy, initial acceleration and the and normal. Actually, that can start solving it. Taking commission off All forces along XX is country right direction to be positive, you can write the extra the Puerto M B F B P course off 20 minus and the if he and sign off continue certain finger value Mass is full upon 32.2. Acceleration is 10 point 77 nights cause off country for about 32.2 normal acceleration. Off the road is booth like 666 Sign up computer on solving it. Reaction at the along XX is they will get 1.1450 now. Similarly, if we find the submission off forces along the vertical direction Yeah, Taking vertical Albert positive we will get. Be right. It's photo on being two d minus and the every Danish sign off convict and the acceleration normal course off country substituting mark is so it becomes weight that is full or upon 32.2. Acceleration is 10.779 signed off 20 fall upon 32.2 Acceleration normal two point triple 67 cause off country. So you will get reaction at three point in the by direction. This value is three points 2307 points. So we can say the SPX This is the right but its magnitude will be rooftop 1.14 50 square 3.2307 Holy square. So this magnitude you will get three while photo. They won't take part and it will be in that direction yet. This is Peter on Vita will be tell in words off 3.23 You don't save it upon 1.1 ft 50 on this would be quite toe 70.5 degrees. So this is the answer for this problem? I am underlining. They're start for it. Thanks for watching it.

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Vector Mechanics for Engineers: Statics and Dynamics

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Problem

The uniform rod $A B$ with a mass $m$ and a lengt…

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Vector Mechanics for Engineers: Statics and Dynamics

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Video Transcript

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Liev Birman

Marshall Styczinski

Jared Enns

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Liev Birman

Marshall Styczinski

Jared Enns

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek Vector Mechanics for Engineers: Statics and Dynamics

Elyse Gonzalez

Liev Birman

Marshall Styczinski

Jared Enns

Ferdinand P. Beer, E. Russell Johnston, Jr., David F. Mazurek

Vector Mechanics for Engineers: Statics and Dynamics