A wooden block is cut into two pieces, one with three timesthe mass of the other

Question

A wooden block is cut into two pieces, one with three timesthe mass of the other. A depression is made in both faces ofthe cut, so that a firecracker can be placed in it with the blockreassembled. The reassembled block is set on a rough-surfacetable, and the fuse is lit. When the firecracker explodes,the two blocks separate and slide apart. What is the ratio ofdistances each block travels? A wooden block is cut into two pieces, one with three timesthe mass of the other. A depression is made in both faces ofthe cut, so that a firecracker can be placed in it with the blockreassembled. The reassembled block is set on a rough-surfacetable, and the fuse is lit. When the firecracker explodes,the two blocks separate and slide apart. What is the ratio ofdistances each block travels?

Explanation / Answer

by newton's 3rd law, same magnitude force f is acting on each piecefor the same contact time t. since impulse imparted is the same, the momentum of the 2 pieces will bethe same. assuming mass m moves to the right (positive direction) and mass 3m moves to the left, momentum of m = p = mv momentum of 3m = -p = -(3m)(v/3) if m moves a distance d against friction mg and 3m moves adistance D against friction (3m)g, then mgd = initial KE of m = (1/2)mv^2 3mgD = initial KE of 3m = (1/2)(3m)(v/3)^2 = (1/6)mv^2 taking ratio 3D/d = (1/6)/(1/2) = 1/3 D/d = 1/9

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