A(n) 8.0-kg object is sliding across the ice at 2.34 m/s in the positive x direc

Question

A(n) 8.0-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 15 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

let the final speed of front particle is explosion is v1

final speed of rear particle is v2

Using conservation of momentum

4 * v1 + 4 * v2 = 8 * 2.34 ---(1)

using conservation of energy

0.5 * 4 * v1^2 + 0.5 * 4 * v2^2 = 0.5 * 8 * 2.34^2 + 15 ---(2)

solving 1 and 2

v1 = 4.27 m/s

v2 = 0.403 m/s

NOw , for average accelerations

afrontx = (4.27 - 2.34)/.16

afrontx = 12.1 m/s^2

for the rear particles

arearx = (0.403 - 2.34)/.16

arearx = -12.11 m/s^2

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