Spring Launcher PLEASE HELP WITH PARTS D and E! Part C is not relevant to those

Question

Spring Launcher

PLEASE HELP WITH PARTS D and E! Part C is not relevant to those parts. Thank you for the help!

Spring Launcher cher. For examples Rube Goldberg machines see the beautiful d oort e M h b M As a parto a pr ect to construct a Rube Goldben machine, a student wishes to construct a sprin rlease of the spring with a faling ball oaded cube la sters y l y h ne ur studen p a s o gger he The small cu e l be aunched has a mass of 149.0 n. The a aia lenng is a very s6M but I ghi pri hal has a spr ng constant 443 / the spring s so ight that it may be con dered masslee T e s r ng will be mo urled he bat om a wooden ramp which ria es an an e u 4.0 e rees wilh the·har uttal the ength a he sprrng parale lo he ramp with ihe lawer end lte spnrg 1xed in place. For srnulK y, assurne ihal te or of the wooden ramp which is underneath he spring is hight o shed and very sick uume a urne no tric on on the cube by the amp at en the cube is movin on this portion of he ramp. For e est the coden amp. e coe en 8 of friction between the am surface and the cube surte e are 590 or ste friction and 0.4 10 or inetic friction. Measure on the equilbrium position of the free end of the mounted spring, the distance to the top of the ramp is 31.0 (this is measured along the ramp The plan is to compress the spring and maintain the compression with a simple trgger, which will be released by a falling bail. The cube wil be at rest on the free end of the compressad spring, When the tigger is released, the spring will expand, shooting tha cube up the ramp. The dasirad spead for the aube whan it machas the top of the ramp (whare the auba wil leave tha ramp as a projsctle to continua the Rube Goldberg sequence) s77.0 ms.Your utimatn task will he to calculatn the nacassary amount of compressian for the spring The Spring is Compressed by 7.7D Cm Safora attempting the ltimate task, answerthe following quastions (Parts A-B) for the case in which the spring is compressed by 7.70 cm and then eleased, shootirg the cube up tha ramp and into the air. Part A Find the work done an the cube by the spring during the tima that the cube is in contact with the spring Hints 1.31 J Submit MyArwww Give Up Correct Part B Whal is the speed of the cube at he he instant just before lhe sliding cube leeves the rarmp? Give your answer in cVs. HINT: use the Work-Kinelic-Erergy Thecrer. Hints 317 cm's Submit My Answers Give Up Correct Wre your exrsions ir Goad wark. Naw you wil be asked to compute the launch speed for arather possible compression distance. Wher you da, pay particular attertion to the furctions that yau use for coculating the work done by each of the forces acting on the cub terrms of an r coordinale system aligrned wilh the molion of the cube, w0 a the equlibrium position of the spring, and wih the pesiive z direclicn represening conpression o Ihe spring.

Explanation / Answer

d] By energy equation,

0.5 kx^2 = umg cos theta d + mg sin theta d + 0.5 mv^2

0.5*443 x^2 = 0.41*0.149*9.8* cos 54 degree *0.31 + 0.149*9.8* sin 54 degree *0.31 + 0.5*0.149*0.77^2

221.5 x^2 = 0.5195

221.5 x^2 - 0.5195 = 0

here A = 221.5, B = 0, C= -0.5195

partE] x^2 = 0.5195/221.5

x = 0.0484, -0.0484 m

after converting to cm

ordered pair = 4.84, -4.84 ANSWER

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