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24 March, 02:36

A comet is traveling through space with a speed of 3.40 ✕ 104 m/s when it collides with an asteroid that was at rest. The comet and the asteroid stick together during the collision process. The mass of the comet is 1.05 ✕ 1014 kg, and the mass of the asteroid is 7.05 ✕ 1020 kg.

a. What is the speed of the center of mass of the asteroid-comet system before the collision?

b. What is the speed of the system's center of mass after the collision?

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  1. 24 March, 05:57
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    a) vcm = 5.06*10⁻³ m/s

    b) vcm = 5.06*10⁻³ m/s

    Explanation:

    v₁ = 3.40*10⁴ m/s

    v₂ = 0 m/s

    m₁ = 1.05*10¹⁴ Kg

    m₂ = 7.05*10²⁰ Kg

    vcm initial = ?

    vcm final = ?

    a) Before the collision

    vcm = (m₁*v₁ + m₂*v₂) / (m₁ + m₂)

    vcm = (1.05*10¹⁴ Kg*3.40*10⁴ m/s + 7.05*10²⁰ Kg*0 m/s) / (1.05*10¹⁴ Kg + 7.05*10²⁰ Kg)

    vcm = 5.06*10⁻³ m/s

    a) After the collision

    m₁*v₁ + m₂*v₂ = (m₁ + m₂) * vcm

    ⇒ vcm = (m₁*v₁ + m₂*v₂) / (m₁ + m₂)

    vcm = (1.05*10¹⁴ Kg*3.40*10⁴ m/s + 7.05*10²⁰ Kg*0 m/s) / (1.05*10¹⁴ Kg + 7.05*10²⁰ Kg)

    vcm = 5.06*10⁻³ m/s

    The speed of the system's center of mass is the same value.
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