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    So if we were given r and v and had to find the the angle needed on a smooth bank for a car to counteract the tendency of the car to slip up the slope. I've formed 2 different equations, the second one works but the first doesn't.

    I don't understand why?

    Ncos(#) = mg resolving one way and the other mg=cos(#). Why does mg≠cos(#)?
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    (Original post by BDunlop)
    So if we were given r and v and had to find the the angle needed on a smooth bank for a car to counteract the tendency of the car to slip up the slope. I've formed 2 different equations, the second one works but the first doesn't.

    I don't understand why?

    Ncos(#) = mg resolving one way and the other mg=cos(#). Why does mg≠cos(#)?
    Name:  image-57b150ff-1993-47ec-bd10-b3add3bf93f2540201618-compressed.jpg.jpeg
Views: 18
Size:  35.0 KB

    You are mixing two “different” coordinates systems. The component of forces along the normal force direction is not Nmg cosθ = 0.

    When you are writing the following Netwon 2nd law equations,

    N cosθmg = 0

    N sinθ = mac

    you are using the coordinate system shown in blue.

    If you are writing the following Newton’s 2nd law equations,

    Nmg cosθ = mac sinθ

    mg sinθ = mac cosθ

    you are using the coordinate system shown in red.

    ac is the centripetal acceleration.

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    (Original post by Eimmanuel)
    You are mixing two “different” coordinates systems. The component of forces along the normal force direction is not Nmg cosθ = 0.

    When you are writing the following Netwon 2nd law equations,

    N cosθmg = 0

    N sinθ = mac

    you are using the coordinate system shown in blue.

    If you are writing the following Newton’s 2nd law equations,

    Nmg cosθ = mac sinθ

    mg sinθ = mac cosθ

    you are using the coordinate system shown in red.

    ac is the centripetal acceleration.

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Size:  70.9 KB
    Okay, thank you very much. One thing, where you say N-mgcos(theta) =ma sin(theta), should this not be N+ma sin(theta) =mg cos(theta) because ma and N are both acting in the same direction?

    Cheers
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    (Original post by BDunlop)
    Okay, thank you very much. One thing, where you say N-mgcos(theta) =ma sin(theta), should this not be N+ma sin(theta) =mg cos(theta) because ma and N are both acting in the same direction?

    Cheers
    No. You may want to revise how to do vector addition to give resultant vector.
    mac sinθ is the resultant force.
 
 
 
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