A 18 kg body is moving through space in the positive direction of an x axis with

Question

A 18 kg body is moving through space in the positive direction of an x axis with a speed of 110 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 7.9 kg, moves away from the point of explosion with a speed of 190 m/s in the positive y direction. A second part, with a mass of 2.4 kg, moves in the negative x direction with a speed of 490 m/s. What are the (a) x-component and (b) y-component of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force. (a) Number Units (b) Number Units (c) Number Units

Explanation / Answer

Here ,

let the speed of the third part is v m/s

as there is no external force working on the body ,

initial momentum = final momentum

18 * 110 i = v * (18- 7.9 - 2.4) + 7.9 * 190 * j - 2.4 * 490 i

solving for v

v = 409.9 i - 62.2 j m/s

a) the x -component of the velocity of third part is 409.9 m/s

b) y - component of the velocity of third part is -62.2 m/s

c)

speed of third part , v = sqrt(409.9^2 + 62.2^2)

v = 414.6 m/s

energy released = final kientic energy - initial kientic energy

energy released = 0.5 * (7.7 * 414.6^2 + 7.9 * 190^2 + 2.4 * 490^2 )- 0.5 * 18 * 110^2

energy released = 9.836 *10^5 J

the energy released during explosion is 9.836 *10^5 J

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