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Object:Ahas mass mA=7kgand initial momentumpA,i=17,-5,0kgm/s2, just before it strikes object B, which has mass mA=11kg. Object Bhas initial momentumpB,i=4,6,0kgm/s2. After the collision, object Ais observed to have 铿乶al momentum pA,f=13,3,0kgm/s2. In the following questions, 鈥渋nitial鈥 refers to values before the collisions, and 鈥滐瑏nal鈥 refers to values after the collision. Consider a system consisting of both objects AandB. Calculate the following quantities: (a) The total initial momentum of this system. (b) The 铿乶al momentum of object B. (c) The initial kinetic energy of object A. (d) The initial kinetic energy of object B. (e) The 铿乶al kinetic energy of object A. (f) The 铿乶al kinetic energy of object B. (g) The total initial kinetic energy of the system. (h) The total 铿乶al kinetic energy of the system. (i) The increase of internal energy of the two objects. (j) What assumption did you make about Q (energy 铿俹w from surroundings into the system due to a temperature difference)?

Short Answer

Expert verified

(a) 21,1,0kgm/s

(b) 8,-2,0kgm/s

(c) 20.64,1.78,0m/s

(d) 0.727,1.636,0m/s

(e)12.07,0.64,0m/s

(f) 2.909,0.181,0m/s

(g) 21.367,3.416,0m/s

(h) 14.979,0.821,0m/s

(i) 8.57,1.14,0m/s and -2.182,1.455,0m/s

(j) 0

Step by step solution

01

Identification of the given data

The given data is listed below as,

  • The mass of the object AmA=7kg .
  • The initial momentum of object A is, pA,i=17,-5,0kg.m/s .
  • The mass of object B is, mB=11kg .
  • The initial momentum of object B is, pB,i=4,6,0kg.m/s.

After the collision, the final momentum of object A is, pA,f=13,3,0kg.m/s.

02

Significance of the law of conservation of momentum, the first law of thermodynamics, and work-energy theorem for the objects

This law of conservation of momentum states that the total momentum of an object before and after collision with another object becomes equal.

The first law of thermodynamics states that the change in the internal energy of a system is equal to the difference between the heat added and the work done by the system.

The work-energy theorem states that the net change in the work is equal to the change in the kinetic energy.

The law of conservation of momentum gives the initial and the final momentum of objects A, B, and the system. The first law of thermodynamics and the work-energy theorem gives the increase in the internal energy of the system along with its kinetic energies of them

03

Determination of the initial momentum

.-p{"x":[[4,46],[32,47],[31,46],[17,17,17,24,30,31,24,17],[-38.93764355224437,-38.93764355224437,-38.35321233769165,-36.015487479480775,-23.158000759320984,-6.2094955372921685,-0.9496146063177077,4.894697539209471,7.81685361197306,11.323440899289366,11.907872113842085,13.07673454294752,13.07673454294752],[-99.1340586511743],[-98.54962743662159,-98.54962743662159,-99.1340586511743,-99.1340586511743,-97.96519622206887,-96.79633379296344,-92.12088407654169,-86.27657193101452,-83.93884707280364,-79.84782857093461,-75.7568100690656,-72.25022278174929,-71.08136035264386,-68.74363549443298,-67.57477306532755,-64.65261699256395,-63.48375456345852,-62.899323348905796],[-70.49692913809113,-62.899323348905796,-61.730460919800365,-54.132855130615035,-52.963992701509596,-51.79513027240416,-48.28854298508785,-47.704111770535135,-47.704111770535135,-48.28854298508785,-48.87297419964057,-50.041836628746005,-50.62626784329873,-51.21069905785144,-51.79513027240416,-52.37956148695688,-53.54842391606231,-54.71728634516775,-55.88614877427319,-57.63944241793134,-58.22387363248406,-58.22387363248406,-58.80830484703677,-59.392736061589495,-59.97716727614221,-60.56159849069493,-60.56159849069493,-61.730460919800365,-62.31489213435308,-62.899323348905796,-63.48375456345852,-64.06818577801124,-64.65261699256395,-65.23704820711667],[-85.6921407164618,-86.27657193101452,-86.27657193101452,-79.2633973563819,-76.92567249817102,-74.58794763996016,-73.41908521085472,-72.25022278174929,-72.25022278174929,-73.41908521085472,-74.00351642540744,-74.00351642540744],[-85.6921407164618,-85.6921407164618,-85.6921407164618,-83.93884707280364,-82.18555342914549,-79.84782857093461,-77.51010371272375,-75.7568100690656,-74.00351642540744,-72.25022278174929,-71.08136035264386,-71.08136035264386,-70.49692913809113,-69.91249792353841,-69.91249792353841,-69.91249792353841,-69.91249792353841,-69.91249792353841,-69.91249792353841,-69.91249792353841,-71.08136035264386,-71.08136035264386,-72.25022278174929,-74.00351642540744,-75.7568100690656,-76.34124128361832,-76.92567249817102,-77.51010371272375,-78.09453492727647,-79.2633973563819,-79.2633973563819,-79.84782857093461],[-66.4059106362221,-66.4059106362221,-65.8214794216694,-65.8214794216694,-64.65261699256395,-64.65261699256395,-64.65261699256395,-64.06818577801124],[-65.23704820711667],[-59.392736061589495,-58.80830484703677,-59.392736061589495,-59.97716727614221,-59.97716727614221,-60.56159849069493,-60.56159849069493,-59.97716727614221,-59.392736061589495,-59.392736061589495,-58.80830484703677],[-57.05501120337862,-57.05501120337862,-56.470579988825904,-53.54842391606231,-51.79513027240416,-51.79513027240416],[-54.132855130615035,-54.132855130615035],[-51.21069905785144],[-39.52207476679708,-40.106505981349805,-40.69093719590252,-41.275368410455236,-41.275368410455236,-41.85979962500796],[-44.781955697771544,-44.781955697771544,-44.781955697771544,-44.781955697771544],[-34.846625050375344,-29.002312904848164,-28.417881690295445]],"y":[[23,22],[9,22],[37,23],[99,47,47,48,54,65,71,71],[54.592528497615675,54.00809728306295,54.00809728306295,53.42366606851024,51.08594121029937,49.91707878119393,49.91707878119393,49.332647566641214,49.332647566641214,49.332647566641214,49.332647566641214,49.332647566641214,48.74821635208849],[55.17695971216839],[15.435637122583577,16.020068337136294,16.020068337136294,17.18893076624173,17.18893076624173,17.18893076624173,17.18893076624173,17.18893076624173,17.18893076624173,17.773361980794448,17.773361980794448,17.773361980794448,17.773361980794448,17.773361980794448,17.773361980794448,17.773361980794448,17.773361980794448,17.773361980794448],[4.331444046081938,7.838031333398245,7.838031333398245,11.344618620714552,11.92904983526727,11.92904983526727,13.097912264372706,13.097912264372706,13.682343478925423,13.682343478925423,14.26677469347814,15.435637122583577,16.020068337136294,16.020068337136294,17.18893076624173,17.773361980794448,18.942224409899882,20.11108683900532,20.11108683900532,21.279949268110755,21.279949268110755,21.864380482663474,21.864380482663474,23.03324291176891,23.03324291176891,23.03324291176891,23.617674126321628,23.617674126321628,23.617674126321628,24.202105340874343,24.202105340874343,24.786536555427062,24.786536555427062,24.786536555427062],[30.046417486401523,29.461986271848804,28.87755505729609,49.91707878119393,55.761390926721106,61.02127185769557,62.77456550135372,63.94342793045916,64.52785914501187,64.52785914501187,63.94342793045916,62.77456550135372],[32.968573559165115,32.38414234461239,31.799711130059677,30.046417486401523,28.87755505729609,26.539830199085216,25.37096776997978,24.786536555427062,24.786536555427062,24.786536555427062,24.786536555427062,25.37096776997978,25.37096776997978,25.37096776997978,25.955398984532497,26.539830199085216,27.124261413637935,27.70869262819065,29.461986271848804,30.046417486401523,31.799711130059677,32.38414234461239,34.72186720282327,35.8907296319287,38.81288570469229,39.39731691924501,40.566179348350445,4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The expression for the total initial momentum of the system is expressed as,

Pinitial=PA,i+PB,iFor pA,i=17,-5,0kgm/sand pB,i=4,6,0kgm/s

Thus, the total initial momentum of the system is21,1,0kgm/s.

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Most popular questions from this chapter

In outer space a rock whose mass is 3kg and whose velocity was(3900,-2900,3000)m/sstruck a rock with mass 13kg and velocity(220,-260,300)m/s. After the collision, the 3kg rock鈥檚 velocity is(3500,-2300,3500)m/s. (a) What is the 铿乶al velocity of the 13kg rock? (b) What is the change in the internal energy of the rocks? (c) Which of the following statements about Q (transfer of energy into the system because of a temperature difference between system and surroundings) are correct? (1)Q0 because the duration of the collision was very short. (2)Q=Ethermal of the rocks. (3)Q0 because there are no signi铿乧ant objects in the surroundings. (4)Q=k of the rocks.

Object A has mass mA=7kgand initial momentumPAj=(17,-5,0)kg.m/s2, just before it strikes object B , which has mass mA=11kg. Object B has initial momentum pBj=(4,6,0)kh.m/s2. After the collision, object A is observed to have 铿乶al momentum PAf=(13,3,0)kg.m/s2. In the following questions, 鈥渋nitial鈥 refers to values before the collisions, and 鈥滐瑏nal鈥 refers to values after the collision. Consider a system consisting of both objects and . Calculate the following quantities: (a) The total initial momentum of this system. (b) The 铿乶al momentum of object B. (c) The initial kinetic energy of object A. (d) The initial kinetic energy of object B. (e) The 铿乶al kinetic energy of object A. (f) The 铿乶al kinetic energy of object B. (g) The total initial kinetic energy of the system. (h) The total 铿乶al kinetic energy of the system. (i) The increase of internal energy of the two objects. (j) What assumption did you make about Q (energy 铿俹w from surroundings into the system due to a temperature difference)?

Under what conditions is the momentum of a system constant? Can the x component of momentum be constant even if they component is changing? In what circumstances? Give an example of such behavior.

Car 1 headed north and car 2 headed west collide. They stick together and leave skid marks on the pavement, which show that car 1 was deflected 30掳(so car 2 was deflected 60掳). What can you conclude about the cars before the collision?

Consider a head-on collision between two objects. Object 1, which has mass m1, is initially in motion, and collides head-on with object 2, which has massm2and is initially at rest. Which of the following statements about the collision are true?

(1)p1,initial=p1,final+p2,final.

(2)|p1,final|<|p1, initial|.

(3) Ifm2m1, then|p1|>|p2|.

(4) Ifm1m2, then the final speed of object 2 is less than the initial speed of object 1.

(5) Ifm2m1, then the final speed of object 1 is greater than the final speed of object 2.

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