A 12 kg body is moving through space in the positive direction of an x axis with a speed of 210 m/s.?

A 12 kg body is moving through space in the positive direction of an x axis with a speed of 210 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 4.3 kg, moves away from the point of explosion with a speed of 160 m/s in the positive y direction. A second part, with a mass of 3.5 kg, moves in the negative x direction with a speed of 480 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.

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  • 3 years ago
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    Conserve east-west momentum:

    12kg * 210m/s = 0 + 3.5kg * -480m/s + (12 - 4.3 - 3.5)kg * V * cosΘ

    where Θ is measured below the +x axis. So

    V*cosΘ = 4200kg·m/s / 4.2kg = 1000 m/s ◄ x-component (b)

    Conserve north-south momentum:

    0 = 4.3kg * 160m/s + 0 - 4.2kg * V * sinΘ

    V*sinΘ = 164 m/s ◄ y-component (b)

    Bonus: find the direction of travel and the velocity.

    Divide the two results:

    VsinΘ / VcosΘ = 164 / 1000

    tanΘ = 0.164

    Θ = 9.3º below +x axis

    Vcos9.3º = 1000m

    V = 1013 m/s

    or

    V = √(Vx² + Vy²)

    (c) initial KE = ½*12kg*(210m/s)² = 264 600 J

    final KE = ½8[4.3*160² + 3.5*480² + 4.2*1013²]J = 2 614 721.6 J

    so the energy released is the difference, 2.37e6 J = 2.36 MJ

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