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

Question

Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A massless spring is attached to one of them and the blocks are pushed together with the spring between them. A cord ties the two blocks together. The cord is burned and after the blocks have seperated the 3M mass moves to the right with a speed v. (a) What is the velocity of the block of mass M? (b) Find the system’s original elastic potential energy. (c) Is the original energy in the spring or the cord? Explain your answer.

answer: (a) v2 = -3v    (b) 6Mv2 (c) Spring.

Please provide the necassary work to arriving at these solutions. Thank you.

Explanation / Answer

Spring force in internal for the system. net external force is zero.
By conservation of momentum

3M*V + M*V1=0

a) V1= -3V
b ) Potential Energy = Kinetic energy = 1/2*M*(3V)2+ 1/2*3M*(V)2 = 6MV2
c) Energy was stored in spring as spring was compressed.

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