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27 September, 20:07

If a 1000-pound capsule weighs only 165 pounds on the moon, how much work is done in propelling this capsule out of the moon's gravitational field?

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  1. 27 September, 21:24
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    W = 1,307 10⁶ J

    Explanation:

    Work is the product of force by distance, in this case it is the force of gravitational attraction between the moon (M) and the capsule (m₁)

    F = G m₁ M / r²

    W = ∫ F. dr

    W = G m₁ M ∫ dr / r²

    we integrate

    W = G m₁ M (-1 / r)

    We evaluate between the limits, lower r = R_ Moon and r = ∞

    W = - G m₁ M (1 / ∞ - 1 / R_moon)

    W = G m1 M / r_moon

    Body weight is

    W = mg

    m = W / g

    The mass is constant, so we can find it with the initial data

    For the capsule

    m = 1000/32 = 165 / g_moon

    g_moom = 165 32/1000

    . g_moon = 5.28 ft / s²

    I think it is easier to follow the exercise in SI system

    W_capsule = 1000 pound (1 kg / 2.20 pounds)

    W_capsule = 454 N

    W = m_capsule g

    m_capsule = W / g

    m = 454 / 9.8

    m_capsule = 46,327 kg

    Let's calculate

    W = 6.67 10⁻¹¹ 46,327 7.36 10²² / 1.74 10⁶

    W = 1,307 10⁶ J
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