Results 1 to 5 of 5

Math Help - Static EQUILIBRIUM of a body

  1. #1
    Junior Member turbod15b's Avatar
    Joined
    Dec 2006
    Posts
    57

    Static EQUILIBRIUM of a body

    The beams of negligible mass with an overall length of 7m
    The beam is supported by a pivot point that is 3m from the left hand side
    and 4m from the right

    To the right on the pivot, FORCES of 10N and 25 N are applied at a distance of 1m and 4m respectively

    to the left of the pivot is an unknown force, F, which is applied 3m from the pivot

    the direction of action of each of these forces is as shown

    determine the value of the unknown FORCE F, needed to preserved EQUILIBRIUM

    is it M=F*d
    Moment = Nm
    Force = N
    distance = Meters

    how i work it out?
    cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Take moments about the frustum point.

    F(3) - 10(1)-4(25) = 0

    Solve for F
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member turbod15b's Avatar
    Joined
    Dec 2006
    Posts
    57
    can u explain in more detail plz sorry
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,057
    Thanks
    369
    Awards
    1
    Quote Originally Posted by turbod15b View Post
    The beams of negligible mass with an overall length of 7m
    The beam is supported by a pivot point that is 3m from the left hand side
    and 4m from the right

    To the right on the pivot, FORCES of 10N and 25 N are applied at a distance of 1m and 4m respectively

    to the left of the pivot is an unknown force, F, which is applied 3m from the pivot

    the direction of action of each of these forces is as shown

    determine the value of the unknown FORCE F, needed to preserved EQUILIBRIUM

    is it M=F*d
    Moment = Nm
    Force = N
    distance = Meters

    how i work it out?
    cheers
    I don't know if you in a Math or Physics course. I'll do it ala Physics.

    The object is in static equilibrium, meaning that it is neither moving nor rotating. Thus we know two pieces of information: the sum of all forces on the object is 0 N (Newton's 2nd Law) and the sum of all torques on the object about any axis is 0 Nm(rad) (from Newton's 2nd Law applied to rotations.)

    We have TWO unknown forces on the beam: F and the unknown upward force exerted by the pivot. All we need is the value of F, so let's use the rotational equilibrium to find it.

    The beam does not rotate about ANY axis, so we may choose whatever axis of rotation to calculate the torques as we please. The idea is to pick an axis that helps you out the most, and we can immediately see if we pick the axis where the pivot point is (what would be the physical axis of rotation if the beam were to rotate) then the torque due to the upward force from the pivot is 0 Nm(rad). (Since the "moment arm" of the position of the force to the axis is 0 m.) So the only unknown in calculating the sum of the torques about this axis is F.

    I will pick the standard that a counter clock-wise rotation is in the positive sense.

    Thus:
    Sum(torques) = (3 m)F - (1 m)(10 N) - (4 m)(25 N) = 0
    (All the forces are perpendicular to the beam, so we don't have any nasty angles to have to calculate. )


    3F - 10 - 100 = 0

    3F = 110

    F = 110/3 N = 36.67 N

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member turbod15b's Avatar
    Joined
    Dec 2006
    Posts
    57
    thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with these Static questions
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: April 27th 2011, 09:05 PM
  2. Replies: 6
    Last Post: November 28th 2010, 03:56 AM
  3. Static Equilibrium help
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: November 9th 2008, 02:50 AM
  4. 3D Equilibrium of a rigid body
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: November 3rd 2008, 09:31 PM
  5. static equilibrium of a body
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 25th 2007, 09:52 AM

Search Tags


/mathhelpforum @mathhelpforum