2. Two blocks of masses m and 2m are placed on a frictionless, horizontal surfac

Question

2. Two blocks of masses m and 2m are placed on a frictionless, horizontal surface. A light spring is attached to the more massive block, and the blocks are pushed together with the spring between them as shown above. A cord initially holding the blocks together is burned; after that happens the block of mass 2m moves to the right with a speed of 6.05 m/s. a. What is the velocity of the block of mass m?  m/s b. Find the system's original elastic potential energy, taking m = 0.40 kg.  J c. Is the original energy in the spring or in the cord?  (1 = Spring, 2 = Cord) Before ? m/s ? m After

Explanation / Answer

SOLUTION:

(a) Mass of the first block, M

Mass of the second block, 2M

final speed of the second block, V2f = 6.05 m/s

Before the cord burns, both masses are in rest oposition,

Hence, initial speed of thenm is 0,

They are V1i, V2i = 0 m/s

Hence, by conservation of momentum,

    M V1i + 2M V2i = M V1f + M V2f

     M(0) + 2M (0) = MV1f + 2M (6.05 m/s)

                        V1f = -12.1 m/s    (left)

(b) Kinetic energy of the system,

   K.E = 0.5 x M x V1f2 + 0.5 x 2M x V2f2

         = 0.5 x (0.40 kg)(12.1 m/s)2+ 0.5 x (0.8)(6.05 m/s)2    (given, M = 0.40 kg)

         = 29.28 J + 14.64 J

        = 43.92 J

According to conservation of energy,

The loss of kinetic energy is used to gain in original elastic potential energy

Hence, original elastic potential energy = 43.92 J

(c) Since, the potential energy is stored in the spring,

Therefore, the original energy is in the Spring

Please rate my answer, good luck...

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