A(n) 8.2-kg object is sliding across the ice at 2.34 m/s in the positive x direc

Question

A(n) 8.2-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 x direction. 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?

Explanation / Answer

here,

initial KE = 0.5 mv^2 = 0.5 * 8.2 kg * (2.34m/s)^2 = 22.45 J

final KE = initial KE + 19 J = 41.45 J

41.45 J = 0.5 * 4.1 kg * [(2.34m/s + dv)^2 + (2.34m/s - dv)^2]

solving for dv

dv = 2.19 m/s

avg acceleration a = dv / dt = 2.19 m/s^2 / 0.16s = 13.7 m/s^2

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