Two carts of equal mass, m = 0.280 kg, are placed on a frictionless track that h

Question

Two carts of equal mass, m = 0.280 kg, are placed on a frictionless track that has a light spring of force constant k = 47.6 N/m attached to one end of it, as in the figure below.

Part One:
The red cart is given an initial velocity of v0 = 3.10 m/s to the right, and the blue cart is initially at rest. If the carts collide elastically, find the magnitude of the velocity of the red cart just after the first collision.

Part Two:
Find the magnitude of the velocity of the blue cart just after the first collision.

Part Three:
Find the maximum compression in the spring.

Explanation / Answer

==> mvo +0 = mv1+ mv2

==> vo – v1 = v2…………(1)

and   Conservation of energy

==> 1/2mvo2 +0 =1/2mv12+1/2mv22

==> Vo2 –v12 =v22

==> (Vo – v1)(vo +v1) = v22...........(2)

dividing eq (2) by eq (1), we get

==> Vo + v1 = v2....................(3)

From eq (1) and eq (3),

==> 2vo = 2v2

and v1 = 0, for the velocity of the red cart

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