Question

1. The spring shown in the diagram below is compressed 50cm and used to launch a 95kg physics student seated on a Skg sled. Friction on the track is a 0.15 on the shaded portions and negligible for the solid portions. The track's valley and hill consist of circular shaped segments of radius "R" What is the maximum height hmas from which the car can start so as not to fly off the track when going over the hill? (Give your answer as a multiple of "R".) (15pts) a. 80.000 N/m m-100 kg dina 10 m 25° 130° b. Now let R= 8m and h hmas which you found in part (a). This means the student and the sled will reach the end of the last portion of inclined track and fly off of the end. If the student and sled are caught by a hanging cart of mass 600kg, as shown below, how high in terms of the angle "e" will the cart containing the student and sled swing? (18pts) k= 80.000 N/m m100 kg 10 m 250 h 130

Answer 1

The solution of the problem is given below

Solution mass of car and student m= lookg 10m 25 coeff. of friction f = 0.15 - h. I'll let speed at pourte de o For car not to the off at pound c. the centepeted fire is just provided by weight ie ng a no VI SGR Apply conservetion of ME. at pont Bond poins c M.EB KEct kec z ingx2R & Imuz M.EB = singR (6=JgR)

( sme Applying work energy theorem from pont A to B - - Wonet = DUE. - We = DutDKE - pengco 25 x 4 = UB-UATKER - KEA = UBT KEB - UA-KEA — Ц Ч Св) 2.0 lo - ME - ЧА — Црн — І СА - grauitalial pt sprungle = ingr-mg (htlo) - 1 kkoo no = 50 cm 22 m ( compression in spring) - pex cot 25 x 10 = JR - (h+10) - 1 k no -0.15 x cot 25 °x10 > FR – Ch +10) – 5x90000 x h = 3/5 R - 10-10 + 32-16 hne R + 12-16 m (6) R=8m . . h= 5x8 +12-16232-16 m. WA ) 2 100x10 x D A B As pontc & Dare at same height.Consertli of mech. energy es alm applicable (as no friction force is involved) : ME c = MAMED u #keca UDTOKE uc=up = ingR,.. v=ve a JGR =√10x8 = 455 m/s

By conservation of momentin mv = m+ M) V MEbooky car & student mess of cart Vamp - mJgR M+M mUM V = 100 x 455 m/s 100+600 Applying consenizlion of energy I'm tm ) v = TM + h) gh hheight attened by cart + care student together finally 29 (g=10mila); h'= (405) hot a 2x lo Joo he lex. 80 - 49x20 h'a 0.081 m = 8 cm Angle of the string at final position with the verticel can be determined only if t length of string is given. e. Let leagth of strung be l then na e- leasa -no = In