Results 1 to 3 of 3

Math Help - Find the angle.

  1. #1
    Junior Member
    Joined
    Nov 2007
    Posts
    41

    Find the angle.

    I didn't know where else to post this, but I need a lot of help.
    I'm stuck on this physics question:

    A highway curve in the horizontal plane is banked so that vehicles can proceed safely even if the road is slippery. Determine the proper banking angle for a car traveling at a constant velocity of 97km/h on a curve of radius 450.

    I don't even know where to start. Please and thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2008
    Posts
    3
    Hello,

    I car on a slope....

    The centripetal force, (mv^2)/r , acts horizontally away from the centre of the bank. The component weight of the car down the slope is mgsin(x).

    For the car to not slide up or down the track, this force mgsin(x), must be equally balance by another force which happens to be the component of the centripetal force up the track.

    So, mgsin(x) = (mv^2)*cos(x)/r

    Then the masses cancel and you can rearrange for the angle, x.

    The beauty of this is no matter if you are driving a (frictionless) tractor or riding a bicycle, as long as you are travelling at the critical velocity, you will not slip.
    Last edited by sandstorm; March 5th 2008 at 10:20 AM. Reason: Centrifugal is inwards, centripetal outwards - Thanks Topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,184
    Thanks
    403
    Awards
    1
    Quote Originally Posted by sandstorm View Post
    Hello,

    I car on a slope....

    The centrifugal force, (mv^2)/r , acts horizontally away from the centre of the bank. The component weight of the car down the slope is mgsin(x).

    For the car to not slide up or down the track, this force mgsin(x), must be equally balance by another force which happens to be the component of the centripetal force up the track.

    So, mgsin(x) = (mv^2)*cos(x)/r

    Then the masses cancel and you can rearrange for the angle, x.

    The beauty of this is no matter if you are driving a (frictionless) tractor or riding a bicycle, as long as you are travelling at the critical velocity, you will not slip.
    You would do better to remove all references to the "centrifugal" force here. So the centripetal force has a magnitude of mv^2/r in the direction of the center of the circle etc. etc.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 4th 2011, 12:36 PM
  2. Please help to find the angle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: August 28th 2010, 05:33 PM
  3. Replies: 3
    Last Post: April 16th 2009, 09:45 AM
  4. find the angle
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 28th 2007, 02:50 PM
  5. find the angle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 20th 2007, 07:07 PM

Search Tags


/mathhelpforum @mathhelpforum