9:: H h tpt Physics 218 Honors Final Exam; Secs. 201,202,203; Fall-lO. 2d&O 4_ i1. Name: Section. No: NOTE: Points are noted on each problem

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1 Physics 218 Honors Final Exam; Secs. 201,202,203; FalllO Name: Section. No: NOTE: Points are noted on each problem 1.(1O pts) The upper surface of water in a standpipe is a height H above the level ground a) At what depth h from the upper surface should a small hole be put to make the emerging horizontal water stream strike the ground at the maximum distance from the base of the standpipe? b) What is this maximum distance? Express your answers in terms of H.. N 9:: H h tpt 10 2 L ca 0 a 2d&O 4_ i1

2 2.(1O pts) A convex object floating on mercury has ¼ of its volume submerged. cover the object (specific gravity of mercury is 13.6 and the density of water is p = a) What fraction of its volume will remain immersed in mercury? b) Does the answer depend on the shape the body of f enough water is added to 3) 1000kg/rn ::::.::.:::::::::H.:.::::::::::::::::;::::::::::::::::::: f s, )e# 4: çk/2,t, q /Le ifr /f rch 1J42 Je5 1? fly 1e i2 C 0 f /,. /e. :. 1:;,.:: :y fd1jj..f 2c,Ufr f4ll gf 4D (.: 2+ f 1.c) tf P L)ps JeJ cl 1(

3 of masses M and m, of mass. (see Fig. below). By applying Newton s of mass impose on ri and r2 in terms of M and m. 3.(12 pts) Two stars separated by a distance d, revolve in circular orbits about their center law to each star, a) What condition does the center b) Find the period T of each star in terms of M, m, G, and d. 2nd 7. / v\ / CM1 \,i 2 / J \ 1 5t.ar l ci frt tc) ri d (c,i* ) ci # J 1/ fr CM+) T=ir

4 4.(12 pts) A yoyo is made from two uniform disks of radius R and combined mass M (disk MR 2/2). The short shaft connecting the disks has a small radius r and negligible mass. A string of length L+R is wrapped around the shaft several times by an expert yoyo operator, who releases it with zero speed. Assume the string is vertical at all times. NOTE: express all answers in terms of M, r, R, L, and g a) What is the tension in the string during the descent of the yoyo? b) What is the acceleration of the CM of the yoyo? c) How long does it take the yoyo to reach its maximum vertical distance before turning around and climbing back up the string? 7fL. 9Th h f Cc Ti ivlj. (9).4J e 4 h stpvt( d 14fz1/S 7 %>/. \Jb, L k4

5 5.(l0 pts) When a massive aluminum sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves on the wire is Hz. The sculpture (but not the wire) is then completely submerged in water. What is the new fundamental frequency? NOTE: The density of aluminum is 2.7 x i03 Kg/rn 3. ti, 1 falv ft

6 6. (12 pts) Energy is released by the Crab Nebula at a rate of 5 x times the rate which the sun radiates energy. The Crab Nebula obtains its energy from the rotational kinetic energy of a rapidly spinning neutron star at its center. This object rotates once every s and this period is increasing by 4.22 x s for each second of time that elapses. a) f the rate at which energy is lost by the neutron star is equal to the rate at which energy is released by the nebula, fmd the moment of inertia of the neutron star. b) We think this neutron star has a mass about 1.4 times the mass of the sun. Modeling the neutron star as a solid unifçrm sphere ( calculate its radius in kilometers. NOTE: mass of sun =1.99 x 1030 kg c) Assume the neutron star is uniform and calculate its density 215), 2MR i W., about i05 ) tc) 271 cx i1 ( ( ( ;:z 2: ii] ) cl& z 1q.22..?c,c 13.sL...3 /11 3xltX /??X/D C) e frlzss

7 7. (12 pts) A fireworks rocket is fired vertically upward. At its maximum height of 80.0 m, it explodes and breaks into two pieces, one with mass 1.40 kg and the other with mass 0.28 kg. n the explosion, 860 J of chemical energy is converted into kinetic energy of the two fragments. a) What is the speed of each fragment just after the explosion? b) t is observed that that the two fragments hit the ground at the same time. What is the distance between the points on the ground where they land? Assume the ground is level and air friction is ignored. 10 C r 2) nhi\j 1 VL 2 1LJ. /4ft:.oiC1± 1 2X t,i?,j V2O,2 71S/ Va:: t b3 Y b) 51kac! +1t 7 4ts //y. y,z, y 2 / S2 z e fc m f) 2. 2 they 2ve. YLt434 V z)c,l,j(

8 8.(10 pts) n a shipping company, an open cart of mass 50.0 kg is rolling to the left at a speed of 5.00 mis (see Fig. below). You can ignore friction between the cart and the floor. A 15.0 kg package slides down a chute that is inclined at 37 from the horizontal and leaves the end of the chute with a speed of 3.00 mis. The package lands in the cart and they roll off together. the lower end the chute is a vertical distance of 4.00 m above the bottom of the cart, what are a) the speed b) the final speed of the cart? of the package just before it lands in the cart? f of b % 3M/1 3 4.(.i(J ll A:: V. Morn. &,1S 2) c.,7l M E. ii( i: h :1p V :: pvp r(p1pw 21 1 /e

9 t77 27 At 9. (12 pts) A small block with mass m is placed inside an inverted cone that is rotating about a vertical axis such that the time for one revolution of the cone is T (this the period). The walls of the cone make an angle 13 with the vertical. The coefficient of static friction between the block and the cone is j.t f the block is to remain at a constant height h above the apex of the cone, what are the minimum and maximum values oft? 5. T1 s 1 1o / M 7 i.j 2 hi4/ ç3ii2j A/ A/ A/21 W7 s) 1 f (;3 *J5 4a4