Two carts of unequal mass (massA>massB) move on parallel firctionless horizontal

Question

Two carts of unequal mass (massA>massB) move on parallel firctionless horizontal tracks. both carts start from rest and have the same constant force exerted on them.until they reach the finish line. The force begins to exert on car A first. the force acting on cart B only as cart A passes it. Both carts reach the finish line at the same time. At the finish, cart B is moving faster than cart A.

1)At an instant when both carts have the force exerted on them, is accelerating of cart A greater than, less than, or equal to the acceleration of B? explain.

2)Is the magnitude of the final momentum of cart A greater, less than, or equal to the magnitude of the final momentum of cart B? Explain

3)Is the final kinetic energy of cart A greater than, less than, or equal to the final kinetic energy of B?

Explanation / Answer

1 .

ma > mb ;

aa = F / ma

ab = F / mb ,

now since ma > mb , so F / ma < F / mb

or aa < ab ;

so acceleration of a is less than accelertaion of b ;

2 .

change in mometum = F.t ;

so although F is same for both the bodies A and B , but times are different ,

since A has more acceleration , it will take less time ,

t a < t b ,

or F. ta < F . tb ;

or change in mometum A < change in mometum of B

final momentum A < fianl momentum B

3 .

since force is constant , and distance is same for both ,

so

F.d = K ;

according to Work energy theorem .

so both end up with the same kinetic energy ,

KE A = KE B

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