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Normal Force Problem

  1. Nov 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Find Normal Contact force between the sphere and wedge A and wall B.
    All surfaces are frictionless and in rest.
    Diagram :-
    attachment.php?attachmentid=64277&stc=1&d=1385374828.jpg

    2. The attempt at a solution

    Let normal force on A be N and on B be R.
    My Diagram :-
    attachment.php?attachmentid=64278&stc=1&d=1385374984.jpg

    By The Diagram,
    N = mgcosθ ....eq(1)
    R = Nsinθ ...eq(2)
    = mgcosθsinθ

    But the answer if :- N = (mg)/cosθ
    it is not matching with eq(1).
    How is this possible?
    Please help me out and explain why it is wrong
     

    Attached Files:

  2. jcsd
  3. Nov 25, 2013 #2
    N is not equal to mgcosθ. There is a component of R along N. Draw a separate FBD for the sphere showing the three forces.
     
  4. Nov 25, 2013 #3
    But how N is not equal to mgcosθ and is R = Nsinθ correct component
     
  5. Nov 25, 2013 #4
    R=Nsinθ is correct. As I said before, there is a component of R along N so you will have to take that into account while balancing the forces in the direction normal to wedge. Do you see now?
     
  6. Nov 25, 2013 #5
    But how N is not equal to mgcosθ?
     
  7. Nov 25, 2013 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    R also has a component parallel to N.


    Resolve N into horizontal and vertical components. The sum of all forces is zero, and that is valid to the horizontal and vertical components, separately.

    ehild
     
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