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Math Help - Two Gravity related questions that I would like checked.

  1. #1
    Member MathBlaster47's Avatar
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    Two Gravity related questions that I would like checked.

    Greetings once more MHF!

    I have a couple of questions related to gravity that I think I have worked out fully but need to make sure of.

    On all questions g=10m/s^2

    Q1):
    What force does earths gravity exert on a 81-kg astronaut who is orbiting in a space station at a distance from the surface of the earth equal to 2 earth radii? Show your calculations. Your answer must be in Newtons.

    A1):
    2 radii from the earth surface is equal to 3 radii from the center of the earth.
    By the inverse square law the gravitational, the gravitational force at '3d' is (1/3)^2=1/9.
    Therefore, if the astronaut weighs 81kg, he weighs 81*10=810N at 'd'. So at '3d' he weighs 810*1/9=90N

    Q2):
    The astronaut from the last question was launched into space by a Saturn rocket.
    The upward acceleration of a Saturn rocket shortly after blast-off is 80 m/s^2. When the Saturn rocket is accelerating, what is the apparent weight of the astronaut, that is, what does the astronaut experience as the weight of his body?Show your calculations. Your answer must be in Newtons.

    A2):
    If g=10 m/s^2 then 80 m/s^2=8g. Thus, the total force acting on the astronaut is g+8g=9g and 9g=90m/s^2
    Therefore, his apparent weight is 90*81=7290N.

    Thank you!
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  2. #2
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    Only one remark ...:

    Quote Originally Posted by MathBlaster47 View Post
    ...
    A2):
    If g=10 m/s^2 then 80 m/s^2=8g. Thus, the total force acting on the astronaut is g+8g=9g and 9g=90m/s^2
    Therefore, his apparent weight is 90*81=7290N.

    Thank you!
    1. In the last equation the RHS contains a unit (N) the LHS has no unit, and between the 2 sides is an equal sign.

    2. In my opinion you should have mentioned that 1 \frac{kg \cdot m}{s^2} = 1 N

    3. Then the last equation becomes:

    90 \frac{m}{s^2} \cdot 81 kg =7290 \frac{kg \cdot m}{s^2} =7290 N

    ... but as I've said: This is only a remark.
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  3. #3
    Member MathBlaster47's Avatar
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    Quote Originally Posted by earboth View Post
    Only one remark ...:



    1. In the last equation the RHS contains a unit (N) the LHS has no unit, and between the 2 sides is an equal sign.

    2. In my opinion you should have mentioned that 1 \frac{kg \cdot m}{s^2} = 1 N

    3. Then the last equation becomes:

    90 \frac{m}{s^2} \cdot 81 kg =7290 \frac{kg \cdot m}{s^2} =7290 N

    ... but as I've said: This is only a remark.

    Ok! Thanks!
    I'll put that in then!
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