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Thread: Fitzpatrick mechanics question

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    Fitzpatrick mechanics question

    9. A body is fired vertically from the surface of the moon with initial velocity v0.
    (i) Find the velocity of the body as a function of its distance r from the centre of the moon.
    (ii) Find the escape velocity. (Take the radius of the moon as R and gravitational acceleration on the moon as g/6.)

    ANSWER AT B.O.B:
    (i) v^2=v0^2+gR/3 (R/r - 1)
    (ii) sqrt (gR/3)

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    Re: Fitzpatrick mechanics question

    Hey.

    Just a couple of things. Firstly I think it's easiest to visualize (by drawing a diagram with the moon/centre/radiis etc) what's going on so you can intuitively work out stuff. Secondly you need to assume that the acceleration due to gravity at the Moon's surface is for both parts of the question. Thirdly you need to assume that the acceleration due to gravity at a point outside the Moon is inversely proportional to the square of the distance from the centre of the Moon i.e.




    Sorry don't know how to put space in the text, so here's a link to a picture of it mechanics q.png
    Last edited by BenHowe; 20 Feb 2017 at 7:28 PM.
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    Re: Fitzpatrick mechanics question

    Quote Originally Posted by BenHowe View Post
    Sorry don't know how to put space in the text, so here's a link to a picture of it mechanics q.png
    Use \text{}. eg: \text{This is a phrase} would produce:

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    Re: Fitzpatrick mechanics question

    Quote Originally Posted by envlam View Post
    Use \text{}. eg: \text{This is a phrase} would produce:
    . I was just going \hspace{0.5cm} but then my equation become too long or I fked something up and it became invalid -_-
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    Re: Fitzpatrick mechanics question

    Thank you for your help. I still have a few questions though. isn't the acceleration due to gravity g/6 at all points around the moon. Also, when you say at the surface of the earth, do you mean on the moon? and I don't quite understand what you did for part (ii)

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    Re: Fitzpatrick mechanics question

    Ok, well firstly the acceleration due to gravity is only on the surface of the moon. The easiest way to think about this is, consider the Earth. Is g constant? No. It varies with altitude,location etc. This is why I put in that statement about the acceleration, that allows you to determine the acceleration for the body at all positions not on the surface of the moon i.e. some distance. They just include that stuff so you can find the constant term. You also have to be careful that the acceleration is always negative because of how you have defined distance with respect to the centre of the Moon's mass or Moon.

    To answer your next point, when I said Earth I meant moon, that was a complete fk up

    Ok and for part (ii) I skipped a few steps because I was afraid my equation would be too long to pop it in one post. Anyways, all I did was get the equation I derived in (i) but without putting in the limits (think of the integral in (i) as indefinite not definite). Then this is where the logic comes into play. Escape velocity is the minimum velocity required for the body to JUST escape the gravitational force of the Moon and enter space. Hence you assign the condition , so you will be able to find the minimum velocity for the body to escape! Also technically you should specify direction i.e. away from the Moon's centre of mass etc. So the answer they've given is technically not correct it should be > not equal to it, because when it is equal it will orbit, but that's bordering into the realm of physics.

    Here, let me post a picture of my diagram and also of my working.

    mechanic q diagram attempt 2.JPG




    Hope this helps
    Last edited by BenHowe; 21 Feb 2017 at 12:17 PM.
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    Re: Fitzpatrick mechanics question

    Quote Originally Posted by BenHowe View Post
    Ok, well firstly the acceleration due to gravity is only on the surface of the moon. The easiest way to think about this is, consider the Earth. Is g constant? No. It varies with altitude,location etc. This is why I put in that statement about the acceleration, that allows you to determine the acceleration for the body at all positions not on the surface of the moon i.e. some distance. They just include that stuff so you can find the constant term. You also have to be careful that the acceleration is always negative because of how you have defined distance with respect to the centre of the Moon's mass or Moon.

    To answer your next point, when I said Earth I meant moon, that was a complete fk up

    Ok and for part (ii) I skipped a few steps because I was afraid my equation would be too long to pop it in one post. Anyways, all I did was get the equation I derived in (i) but without putting in the limits (think of the integral in (i) as indefinite not definite). Then this is where the logic comes into play. Escape velocity is the minimum velocity required for the body to JUST escape the gravitational force of the Moon and enter space. Hence you assign the condition , so you will be able to find the minimum velocity for the body to escape! Also technically you should specify direction i.e. away from the Moon's centre of mass etc. So the answer they've given is technically not correct it should be > not equal to it, because when it is equal it will orbit, but that's bordering into the realm of physics.

    Here, let me post a picture of my diagram and also of my working.

    mechanic q diagram attempt 2.JPG




    Hope this helps
    Thanks for your detailed response. I'm just confused about the last bit. why is it x>R? wouldn't this be just above the moon's surface, not escaping its gravitational field. I thought escape velocity was found by putting x approaches infinity.

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    Re: Fitzpatrick mechanics question

    no no. You're getting it confused with that physics formula I think where they derive Ep and use the defintion to account for the negative in the equation. For mx2 escape velocity is the velocity required for a body to leave the planet, dont go into gravitational field in e2.
    Last edited by BenHowe; 21 Feb 2017 at 4:59 PM.
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    Re: Fitzpatrick mechanics question

    Quote Originally Posted by BenHowe View Post
    no no. You're getting it confused with that physics formula I think where they derive Ep and use the defintion to account for the negative in the equation. For mx2 escape velocity is the velocity required for a body to leave the planet, dont go into gravitational field in e2.
    It's still the speed required to escape the gravitational field. Any (positive) launch speed would make it leave the surface of the planet of course (e.g. just imagine throwing a ball up).

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    Re: Fitzpatrick mechanics question

    *Facepalm
    Last edited by BenHowe; 21 Feb 2017 at 9:23 PM.
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