Suppose the moon has a radius of R miles and a payload weighs P pounds at the surface of the moon (at a distance of R miles from the center

Question

Suppose the moon has a radius of R miles and a payload weighs P pounds at the surface of the moon (at a distance of R miles from the center of the moon). When the payload is x miles from the center of the moon (x ≥ R), the force required to overcome the gravitational attraction between the moon and the payload is given by the following relation: required force = f(x) = R2P x2 pounds For example, the amount of work done raising the payload from the surface of the moon (i.e., x = R) to an altitude of R miles above the surface of the moon (i.e., x = 2R) is work = b f(x) dx a = 2R R2P x2 dx R = RP 2 mile-pounds How much work would be needed to raise the payload from the surface of the moon (i.e., x = R) to the “end of the universe”? work = mile-pounds

in progress 0
Elliana 2 months 2021-10-08T22:24:33+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-08T22:25:40+00:00

    Answer:

    Step-by-step explanation:

    End of the universe i.e infinity(∞)

    So, the work needed to raise the payload from the surface of the moon(i.e x = R) to the end of the universe (i.e x = ∞) is given by:

    work=\int\limits^{x=\infty}_{x=R} {f(x)} \, dx \\\\=\int\limits^\infty_R {\frac{R^2P}{x^2}} \, dx \\\\=R^2P\int\limits^\infty_R {\frac{1}{x^2}} \, dx \\\\=R^2P[{-\frac{1}{x^2}}]\limits^\infty_R\\\\=R^2P[-0+\frac{1}{R}]\\\\=R^2P[\frac{1}{R}]\\\\=PR

    where R= radius of moon; P= weight of payload are constant

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )