A(n) 8.1-kg object is sliding across the ice at 2.34 m/s in the positive x direc

Question

A(n) 8.1-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 11 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

using conservation of energy
Ke of the two chunks after explosion is K1 = 0.5*m*v^2 - 11 = (0.5*8.2*2.34^2) - 11 = 11.44 J

then two chunks have Ke = 2*(0.5*m*v^2) = 11.44

v= sqrt(11.44/4.05) = 1.68 m/s

then during collisions

F*dt = change in momentum = (8.2*(2.34-1.68)) = 5.412

then averge force F = 5.412/0.16 = 33.825

m*a = 33.825

averageaccelaration a = 33.825/8.1 = 4.2 m/s^2

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