A(n) 7.9-kg object is sliding across the ice at 2.34 m/s in the positive x direc

Question

A(n) 7.9-kg object is sliding across the ice at 2.34 m/s in the positive x direction. An internal explosion occurs, splitting the object into two equal chunks and adding 19 J of kinetic energy to system. The explosive separation takes place over a 0.16-s time interval. Assume that the one of the chunks after explosion moves in the positive xdirection. The x component of the average acceleration of this chunk during the explosion is afrontx, the x component fo the average acceleration of the other chunk during the explosion is arearx.

What are the x components of the average accelerations of the two chunks during the explosion? afrontx, arearx

Explanation / Answer

m = 7.9 kg, v = 2.34 m/s, E = 19 J , t = 0.16 s

initial KE = (1/2)mv^2

KEi = 0.5*7.9*2.34^2 = 21.63 J

final KE = 21.63 +19 = 40.63 J

40.63 = 0.5*(7.9/2)*((2.34+v)^2+(2.34 - v)^2)

20.57 = 10.95 +2*v^2

v = 2.19 m/s

average acceleration a = v/t

a = 2.19/0.16

a = 13.7 m/s^2

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