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 tiny depression is made in both faces ofthe cut, so that a firecraker can be placed in it with the blockreassembled. The reassembled block is set on a rough-surfaced tableand the fuse is lit.when the firecracker explodes, the two blocksseparate and slide apart. the small pieces slides a distance "d",the big pieces slides a distance "D". what is the ratio of d/D ofdistance each block travles? (ignore firctional forces form the table during theexplosion) A wooden block is cut into two pieces, one with three timesthe mass of the other. A tiny depression is made in both faces ofthe cut, so that a firecraker can be placed in it with the blockreassembled. The reassembled block is set on a rough-surfaced tableand the fuse is lit.when the firecracker explodes, the two blocksseparate and slide apart. the small pieces slides a distance "d",the big pieces slides a distance "D". what is the ratio of d/D ofdistance each block travles? (ignore firctional forces form the table during theexplosion)

Explanation / Answer

The first response is incorrect. . By conservation of momentum... .     momentum of small piece = momentum of large piece .              m v         =   M V                  where I have used  v and V for thespeeds of the blocks .    divide both sides byMV...         mv / MV =   1        or         m v / (3m) V =    1 .    so...              v / V = 3 . Now... they are both stopped by friction after traveling adistance d   and   D   respectively. . The work done by friction on each must equal the kineticenergy of each block. So for the small block... .     (1/2) m v2  =   m gd         and the largeblock      (1/2) M V2 = M g D . We can simplify each of these .         v2 = 2 gd          and          V2 = 2 g D . Now... take the ratio of these two equations: .             v2 / V2   = 2 d g/ 2 g D . Simplify:         ( v/ V)2 = d / D . But we already know the ratio of the speed is 3  (from above)... . So...       d / D = 32              d / D = 9

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