Transcription of Problem Set V- Assign October 2, 2006 Due …
1 Problem Set V- Assign October 2, 2006 Due October 2006 Physics 200aR. ShankarMany problems ask for answers in terms of symbols and not numbers. You may need toinvoke things likegin the answer even if I did not explicitly define Consider massesm1,m2,m3atx1,x2,x3. FindX, the CM coordinate by findingX12,the CM of mass of 1 and 2, and combining it withm3. Show this is gives the sameresult asX= 3i=1mixi 3i=1mi2. Consider a square of mass 4 kg, side 2m, negligible thickness, with its sides orientedalong the usual axes with its center at (0,0). (i) Determine its CM using symmetryarguments. (ii) Imagine that the 1m 1m part of it in the fourth quadrant ischopped off. Where is the new CM? Do this using the extension of result in previousproblem. Repeat using the following trick: view the chopped off shape as the fullsquare plus a 1m 1m square ofnegativemass 1kg in the fourth quadrant. (iii)A disk of radiusRcentered at the origin has a circular hole of radiusR/2 centeredat (x= R/2,y= 0). Where is its CM?
2 3. Ideal Zorro (massM, no height) swings down on a vine of lengthLfrom a heightHand grabs a kid of massm(zero height, standing on the ground) and togetherthey barely reach safety at a heighth. RelateHto the other parameters. GiveHin meters ifL= 40m,M= 100kg,h= 6m,m= Two identical stars of massMorbit around their CM. Show thatT2=2 2R3 GMwhereRis the distance between planets. (Draw a figure and keep track of thegravitational force on either star as well as its centripetal acceleration.) (ii) Repeatfor two unequal massesmandMand showT2=4 2R3G(M+m)whereRis the separation between Consider a massless boat of lengthLon frictionless water. At the left end is apersonP1of massm1holding a writhing snake of massm3(Treat snake as rigidpoint particle. TreatP1who is clearly rigid at this point as a point.) At the rightend is a personP2of massm2. Att= 0,P1throws the snake towardsP2at a speedv. (i) What isV, the magnitude of the velocity of the boat and passengers relativeto water when snake is airborne?
3 (ii) How long does snake take to reachP2? (iii)During this time how much has the boat moved to the left? (iv) Locate the CM atthe end of all this snake throwing and show it is same as at 1: The balls are identical and frictionless and the collision is symmetric, , center of projectile is in linewith point of contact of other Find the CM of a cone of radiusRand heighth. (Think in terms of slices ofthicknessdyat heighty. )7. A person of massM= ice disdainfully throws my quantum text bookweighingm= 12m/s. The book is thrown from zero height and thetotal distance between the book and the offender is the book lands. Atwhat angle was this excellent book thrown? How fast is the offender moving?8. Block A of massmis moving at velocity +vtowards mass B of mass 2mwhich is atrest. To its right and at rest is mass C of massm. Find the ultimate velocities of allthree masses assuming all collisions are Two identical frictionless billiard balls are symmetrically hit by a third identical ballwith velocityiv0as in Figure (1).
4 Find all subsequent velocities following this elasticcollision. (Draw a picture at the moment of collision. What does no friction sayabout direction of forces?)
