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 V3m = 1.70 m/s. Sm Befure After (a) What is the velocity of the block of mass m? (Assume right is positive and left is negative.) b) Find the system's original elastic potential energy, taking m 0.360 kg (c) Is the original energy in the spring or in the cord? m/s in the spring o in the cord lain answer to part (c This answer has not been graded yet. (e) Is the momentum of the system conserved in the bursting-apart process? o Yes o No Explain how that is there are large forces ac This answer has not been graded yet. how that is possible considering there is no motion beforehand and plenty of motion afterward?

Explanation / Answer

(A) spring force was internal force for two block system.

Applying momentum conservation,

0 = m v + 3 m (1.70)

v = - 5.1 m/s

(b) from energy conservation,

initial elastic PE = final KE

Pe = (0.360 x 5.1^2 / 2) + (3 x 0.360 x 1.70^2 / 2)

PE = 6.24 J  

(c) in spring.

(D) cord have to consider intexible, and sping was compressed so all PE was stored in spring.

(e) Yes. Bursting-apart also done by internal forces.

(f) forces are very large.

but they act in pair of same magnitude in opposite direction.

so net force will zero.

(g) there is plenty of motion after but they are in a way then net momentum (vector sum of all particles's momentum) will be zero.

thus afterwards center of mass is still at rest.

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