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$\bullet$ Two identical masses are released from rest in a smoothhemispherical bowl of radius $R$ , from the positions shown inFig. 8.46 . You can ignore friction between the masses and thesurface of the bowl. If they stick together when they collide,how high above the bottom of the bowl will the masses goafter colliding?

$h=\frac{R}{4}$

04:35

Guilherme B.

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

University of Washington

Simon Fraser University

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in this question, we will make certain assumptions, one of which is all muscle that point sized. So the block on the point personally off Marston is a point size months as well. Is the block on position be on the bottom of the hemispherical ball is a point must. Then there isn't no nose off an initiative to fiction. As we all know, that friction is absent for this hemispherical surface. This is a smooth surface, so there will be no losses. You dio these forces like friction and viscous forces. Then motion along the surface of the ball in circular motion. This motion along the surface is a circular motion block off. Marston traces almost a circle. Then when we are in a position to write the energy in the recent principle for the block off Marston from point A to when we when this block tremors down the mid spherical surface down this part towards more Brock at Position B, it loses certain amount of potential and it the gravitational potential energy stored in it to do its hide from the ground which is equal to the radius off the hemispherical surface. So it loses this much potential energy and in return ganged certain amount off kind of beginners. That kind of energy is equal to laws and the potential, and that's the blood starts from rest. So los ing what insulin is equal to gain in vanity energy Now enjoy. Rotation begins, right? Kind of the energy years, Half island or legal in square. What does Ivan Ivan is? The moment off Inertia, Matson. Omega one is its angular velocity and position be so for a single point sized mass weaken, right? I yes, m r school Masked men deployed Valuev's distance from access or tradition, which is our so half m r squared market pair by Omega Manezh Square is equal to loss in potential energy is energy The weight of the block multiplied by the Heidi closes So lost height equal to the alias which is our so energy No, At this point we can write half Amar square No middle in squared equal doing JIA, you can cancel old systems. I'm Jensen and William. This are square. Is army deployed? They are beginning. Cancel one by this are on the opposite side off equality simplifying. We will get that or may govern square is equal to do Jebalya now a point B. We certainly cannot conserve energy because there's a collision occurring between the first month and the second month. So there will be forces off unknown nature and cannot conserve energy here, but rather weaken. Always concerned angular momentum because there isn't no external thought present for this. Some Miley system of mass is so we can say that I even though Michelman, the angular woman, don't first months, is equipped. So I do a big toe. The angular Momenta moda combined. The system of mass is up in a collision. His is folk. So Ivan can. Britain is for single mass. M r squared my depression omega one than I do because there are two point sized masses at a distance r from the access off traditions weaken right to m r squared is my depriving Omega Tau. By doing further cap mission, we will get there. This artist square can be answered by this are square in this mosque and also can cancer right this month. Then you begin. That will mean a one by two is equal to a meager two square. Both sides were Gannett Omega one square directed. 40 Quito Megan Boost but way have already calculated Omega one square here. This is Tuesday by so substitute this value over here. FUJI Divided by R in this four year Is it going toe omega? Who square now after the motion from being to see a burner position, Be the motion from B to position. See both the masses. They stick together and combine on their held A combined the angular last, the Omega Do and the travel the Proficiency Religious at Bay Word Eagle Height edge from Rome So what? Chicken Dre. What a question We can write for this motion. Same principle, and Jessica in the recent principal Begin apply over here for the position. Be to see if you can write them. There are on the combined mass off toward the blocks is too well so 12 might be played by Jim and England Betis's 14. She'll energy at height it to L. D. Multiplied by height. Is it Plato lasting kinetic energy at point B? Both the masses has some kinetic and receive, and they claimed up to hide H. This kinetic energy is converted to potential energy so it can militant two MGs equal to half. I told me to square Now I do the moment of initial Buddha. My system mind obviously already know, um are square and the angular velocity now angular, Rusty, omega to square. The only calculated to be to see pay for up To substitute these values here to, well, r squared multiplied breakthroughs You buy for a and just have She can cancel this to buy this too. Yes. No, this m can We can sit by this. Um And this truly scan said And this too can we cancelled by one more to president On the opposite side of this equality This this one you can cancel out. Finally, we will get a simplified expression for high, which is I'd reached way born The blocks is are by for So this is the final answer

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