Two identical carts are riding on an air track. Cart 1 is given a quick push in

Question

Two identical carts are riding on an air track. Cart 1 is given a quick push in the positive x direction towards cart 2. When they hit, they stick to each other. The graphs below describe some of the variables associated with the motion as a function of time beginning just after the push is completed. For the experiment described and for each item in the list below, identify which graph is possible display of that variable as a function of time. If none apply, write N (for none). a. the momentum of cart 1 b. the total momentum of the two carts c. the kinetic energy of cart 1 d. the force on cart 1 e. the force on cart 2

Explanation / Answer

Part a.

both B and H are correct graph for momentum of cart1.

as before collision cart1 is moving towards +x direction, hence velocity is positive,so momentum of cart1 =m1v is positive.

and after collision cart1+cart2 combination will move in +x direction due to consevation of momentum. but with smaller velocity V.

so final momentum of m1 is m1V is less than m1v . as graph is not upto the scale so both B and H graph are correct.

Part b

graph C is correct option.

as there is no net force acting on the system (cart1+cart2). so net momentum of system is conserved throghout the motion. so total momentum has a fix value. as initialy cart1 has +momentum as explained in part a . and cart2 is initialy at rest , so has zero initial momentum. so total momentum is positive in direction of +x axis.

hence graph C is correct.

Part c

correct option is B and H.

as kinetic energy is =1/2 mv^2

as final speed of cart1 after collision is less than speed before collision .

so kinetic energy is less after collision than kinetic enrgy before collison.

also as kinetic energy cann't be negative, as both m and v2 cann't be negative.

hence correct option is B and H.

Part d

correct option is G.

as initially there is no force on cart1,

during collision a retarding force will act on cart1 which tries to slow down cart1. magnitude of force increase as it come closer to cart2 . than after a limit when cart2 starts to move magnitude of force will decrease .

and when they separate each other force on cart1 will again zero.

so correct option is G.

Part e

correct option is H.

as initially there is no force on cart1,

during collision a accelerating force will act on cart2 which tries to speed up cart2. magnitude of force increase as cart1 comes closer to cart2 . than after a limit when cart2 starts to move magnitude of force will decrease .

and when they separate each other force on cart1 will again zero.

graph will be similar to G but curved portion will be above the time axis. force on cart2 is positive.

Hence all given graph are incorret , so option H is correct option.

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