NOTE: Points are noted on each problem Physics 218 Honors Final Exam; Secs. 201,202,203; Fall-li - vi) 1.. 2 / b Fr ; _...2_ YY R (ZL 3K C 3c2z Zb 1 1 lz_ z 1- a-30 j..) hs gravitational force exerted on each mass m due to the other two identical masses in addition to the large mass M) a) Compute the net centripetal force on one of the stars of mass m. (HINT: do not forget the b) Compute the period of the three stars in terms of G, M, m, and R circular orbit of radius R about a central star of mass M. The stars orbit in the same sense and are positioned one-third of a revolution apart from one another. 1.( 12 pts) A certain quaternary star system consists of three stars each of mass m, moving in the same Section. No: Name:
;::M s1- L f. Po = 1.25 kg/rn ; J2s;F-r/ 3 8,000 m? (Take PHC 0.180 kg/m 3.) Assume the balloon maintains a constant volume and the density of air 2.(10 pts) How many cubic meters of helium, are required to lift a balloon with a 400 kg payload to a height of 8 I 3 is the density of air at sea level C - 1k),. + 44 decreases with the altitude according to the expression Pair = Po e8 000 ) p, where z is in meters and _0J9t h Vg
a) the tangent to the cable makes an angle 0 with the horizontal. Express your answers in terms of W and 0. b) Find the tension in the chain at its midpoint. Draw a free body diagram for the half-cable 7- to a) Find the magnitude of the force that each peg exerts on the cable. Draw a free body diagram for the cable 3.(lO pts) A flexible cable of weight W hangs between the two pegs located at the same height. At each peg,
and 1. hi ; le (i Ci) iz1;? -TT 1 - TCT-i a: çi-r / 1J4e- A79J Y 0/d / a -r through its center is I. The spool is placed on a rough horizontal surface so that it rolls without slipping when a force T acting to the right is applied to the free end of the thread. below. The mass of the spool, including the thread, is m,and its moment of inertia about an axis 4.(12 pts) A spool of thread consists of a cylinder of radius R1 with end caps of radius R2 as shown a) Find the direction of the friction force. Explain. b) Find the magnitude of the friction force exerted by the surface on the spool in terms of T, R1, R2, m, +he- v y t S jr7c-
b) Is the collision elastic, inelastic, or perfectly inelastic? Justify your answer a) Find the final velocity of the 1.50 kg sphere velocity of the 0.500 kg sphere after the collision is given by ( 1.001+3.003 8.00k) mis.. I ki;e i fter z -1--- c I(,LS3 2 L )c be-to, L. b1& z 4 6i-/.S?? h,ze_e_ C J, - ic = (_ r A h 2f1 1% 9)g -3j * -if 7-1: ml / 0 D s another sphere of mass 1.5 kg that is moving with a velocity of ( 1.001 + 2.003 3.00 k) rn/s. The 5.( 10 pts) A 0.500-kg sphere moving with a velocity given by (2.001 3.003+1.00 k) mis strikes
1.00 kg block as shown below. The block, initially at rest on a frictionless horizontal surface, is b) Find the mechanical energy converted into internal energy in the collision. connected to a spring with force constant 900 N/rn. The block moves 5.00 cm to the right after impact before stopping. a) Find the speed at which the bullet emerges from the block 6. (12 pts) A 5.00 g bullet moving with an initial speed of 400 mis is fired into and passes through a EJ7 ; ),Izcj-i t212-j i 2 ;P6K 12,z.. h) Erry 2- S1O 3 (JoO*.A) POb4(f) 3 V I 19 d -3, I1Ivp-i, 1,4- M8Joc1e, 04 II lo C-4- i.c Ccv /4 7tet b41i--/ pi.s e ro y ).;, ei y - 0) 4OO yntt2,r 0YLL?2-1ird n- C - L7 y 0 i C >
a) With what speed does the ball leave the barrel of the cannon b) At what point along the barrel does the ball have maximum speed? c) What is this maximum speed? the ball. c. VSiiyC2) -I 0 -t fdry be I -- Pri21 ;: p(e J t6t c_it 1-L 5) 1i / Th,c mojf c cct)t j52)) I s 232O ± S3cXJ 2 4c-?( t,e. 2:.j- II w,r-ene-rpy I,, -ca z 4-L pr 1 15.i 15.0 cm through the horizontal barrel of the cannon and the barrel exerts a constant force of 0.0320 N on compressed by 5.00 cm and has a force constant of 8.00 N/rn. When the cannon is fired, the ball moves 7. (12 pts) A toy cannon uses a spring to project a 5.30-g soft rubber ball. The spring is originally
Express your answer in terms of T, L, IlL, and b) Find the time interval required for a transverse pulse to travel the length of the string. a) Find an expression for ji(x) as a function of x over the range 0 x L. 32 5 r ci 5 c!? ;Qt/: i7l1l/ 8.(12 pts) A string on a musical instrument is held under tension T and extends from the point x 0 to j k)k4 ff 4$.,? _; L+-P /44;,? V. t 2Z z:_14 2_,Ao) z/-4, increases uniformly from jio at x =0 to IlL at x = L. the point x = L. The string is overwound with wire in such a way that its mass per unit length jl(x)
75 Tz4Loi a) What is the frequency of vibration b) What is the length of the thick wire? in such a way that two antinodes are present, with the node between them being precisely at the weld. VLI 1rW -r 12- V4 v2-_ rf r: - L%j L A, S;n t2p1,a_3,.t IO II(1 /L4.2 S3 diameter of one is twice that of the other. They are subjected to a tension of 4.60 N. The thin wire has a 9. (10 pts) Two wires are welded together end-to-end. The wires are made of the same material, but the length of 40.0 cm and a linear density of 2.00 g/m. The combination is fixed at both ends and vibrated