2 carts of masses m1 and m2 collide head on on a low friction track. Before the

Question

2 carts of masses m1 and m2 collide head on on a low friction track. Before the collision, which is in elastic cart 1 is moving at 10m/s to the right and cart 2 is moving to the left at 2m/s. After the collision cart 1 is moving to the left at 5 m/s. A) what are the speed and direction of cart 2 after the collision? B) if m2 is 6kg, what is the value of m1 2 carts of masses m1 and m2 collide head on on a low friction track. Before the collision, which is in elastic cart 1 is moving at 10m/s to the right and cart 2 is moving to the left at 2m/s. After the collision cart 1 is moving to the left at 5 m/s. A) what are the speed and direction of cart 2 after the collision? B) if m2 is 6kg, what is the value of m1 A) what are the speed and direction of cart 2 after the collision? B) if m2 is 6kg, what is the value of m1

Explanation / Answer

Let the masses of the two carts 1 & 2 be m1 and m2 respectively

Initial velocity of the cart1 be u1 = 10 m/s to the right

Initial velocity of the cart2 be u2 = 2 m/s to the left

Final velocity of the cart1 be   v1 = 5 m//s to the left

Final velocity of the cart2 be v2

( 1 )Let us take velocity towards right as positive

As the collision is elastic , momentum and kinetic energy of the system are conserved

The relative velocity of the approach is given by

           u1 – u2 = v2 – v1 ………….. ( 1 )

          10 – ( - 2 ) = v2 – ( - 5 )

Here we have taken velocities towards left as negative

               v2 = 12 – 5 = 7 m/s

so the velocity of the cart2 is v2 = 7 m/s and the + ve sign indicates the motion of cart2 is towards right

( 2 )Let us apply law of conservation of momentum to find mass m1

Given that m2 = 6 kg

So m1 * u1 + m2 * u2 = m1 * v1 + m2 * v2

      10 m1 + ( – 2 * 6 ) = - 5 m1 + ( 6 * 7 )

                 10 m1 – 12 = - 5 m1 + 42

             10 m1 + 5 m1 = 42 +12

                        15 m1 = 54

                             m1 = 54 / 15 = 3.6 kg

so the mass of the cart1 m1 = 3.6 kg

we can verify it by simply substituting the values m1 , m2 , v1 and v2 either in law of conservation of momentum or energy

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