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. 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 2.00 m/s. What is the velocity of the block of mass m? Find the system's initial potential energy, take m = 0.350 kg. Is the initial energy in the spring or the cord? Explain. Is the momentum of the system conserved in the bursting process? Explain.

Explanation / Answer

(a)
Using Momentum Conservation,
Initial Momentum = Final Momentum
0 = - m*v + 3m * 2.0 m/s
v = 6.0 m/s

(b)
m = 0.35 Kg
Using Energy Conservation,
Initial Potential Energy = Final Kinetic Energy
P.Ein = 1/2*m*v^2 + 1/2*3m*2.0^2
P.Ein = 1/2*0.35*6.0^2 + 1/2*3*0.35*2.0^2 J
P.Ein = 8.4 J

(c)
As spring gets compressed, The initial energy is in the spring.
(d)
Momentum of a system is constant if there are no external forces acting on the system. So Yes the momentum fo the system remains conserved in the bursting process and that's what we are using to solve the question !!

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