Two objects of different mass start from rest, are pulled bythe same magnitued n

Question

Two objects of different mass start from rest, are pulled bythe same magnitued net force, and are moved throught the samedistance. The work done on object A is 500 J. After theforce has pulled each object, object A moves twice as fast asobject B. Answer the following questions and show yourwork.       *How much work is done onobject B?       *What is the kineticenergy of object A after being pulled?       *What is the kineticenergy of object B after being pulled?       *What is the ratio of massof object A to the mass of object B? Two objects of different mass start from rest, are pulled bythe same magnitued net force, and are moved throught the samedistance. The work done on object A is 500 J. After theforce has pulled each object, object A moves twice as fast asobject B. Answer the following questions and show yourwork.       *How much work is done onobject B?       *What is the kineticenergy of object A after being pulled?       *What is the kineticenergy of object B after being pulled?       *What is the ratio of massof object A to the mass of object B?

Explanation / Answer

    Let     Mass of the first object = Ma     Mass of the second object = Mb     Work done on the first object , Wa = 500 J     Initial velocity of each , U = 0 m/s     Final velocity of first object = Va     Final velocity of the second object = Vb     Net force on each = F     Distance moved by each = S (a)     Work done = Force * distance     As, force and distance are same for both, thesame work is done in the case of 'B' as that of 'A'     Work done on 'B' = 500 J (b)     Work done = Final K.E - Initial K.E.     But, Initial K.E = 0 J ( because initialvelocity = 0 )     Work done = Final K.E     Hence, Final K.E of A = 500 J (c)     Work done = Final K.E - Initial K.E.     But, Initial K.E = 0 J ( because initialvelocity = 0 )     Work done = Final K.E     Hence, Final K.E of B = 500 J (d)     Kinetic energy = ( 1/2 ) M V 2     Final Kinetic energy of the first body =Final Kinetic energy of the second body                             ( 1/2 ) Ma Va 2 = ( 1/2 ) Mb Vb 2                                      But, Va = 2 Vb                                      Ma ( 2 Vb ) 2 = Mb Vb 2                                                   Ma * 4 Vb 2 = Mb * Vb 2                                                 Ma / Mb = 1 / 4

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