Two blocks of masses m and 3m are placed on a frictionless, horizontal surface.

Question

Two blocks of masses m and 3m 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 in the figure below. A cord initially holding the blocks together is burned; after that happens, the block of mass 3m moves to the right with a speed of 3m = 1.95 m/s. What is the velocity of the block of mass m? (Assume right is positive and left is negative.) m/s Find the system's original elastic potential energy, taking m = 0.310 kg. J Is the original energy in the spring or in the cord? in the spring in the cord Is the momentum of the system conserved in the bursting-apart process?

Explanation / Answer

(a) Mass of the first block, M Mass of the second block, 3M final speed of the second block, V2f =1.95 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, MV1i + 3MV2i = MV1f + MV2f M(0) + 3M (0) = MV1f + 3M (1.95 m/s) V1f= -5.85 m/s (left) _________________________________________________________ _________________________________________________________ (b) Kinetic energy of the system, K.E = 1/2 MV1f2 + 1/2 3M V2f2 =1/2 (0.31kg)(5.85 m/s)2+1/2(0.93)(1.955 m/s)2 (given, M = 0.310 kg) =5.0344875 J + 1.7681625 j =6.80265 J According to conservation of energy, The loos of kinetic energy is used to gain in original elastic potential energy Hence, original elastic potential energy = 6.80265 J _______________________________________________________________ _______________________________________________________________ (c) Since, the potential energy is stored in the spring, The original energy is in the Spring _______________________________________________________________ _______________________________________________________________ (e) In bursting-apart process, The conservation of momentum is Holds. answer: Yes _______________________________________________________________ _______________________________________________________________ (e) In bursting-apart process, The conservation of momentum is Holds. answer: Yes

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