Normal Force Problem: Find Contact Force b/w Sphere, Wedge A & Wall B

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Homework Help Overview

The problem involves determining the normal contact force between a sphere and a wedge, as well as between the wedge and a wall, under the condition that all surfaces are frictionless and the system is at rest. The discussion centers around the relationships between the forces acting on the sphere and the wedge, particularly focusing on the normal forces involved.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationships between the normal forces, questioning the validity of the original poster's equations relating to the normal force on the wedge and the wall. There is a focus on drawing free body diagrams (FBD) to clarify the forces acting on the sphere.

Discussion Status

The discussion is ongoing, with participants providing guidance on the need to consider components of forces and suggesting the drawing of separate free body diagrams. There is a clear exploration of the relationships between the forces, but no consensus has been reached regarding the correct expressions for the normal forces.

Contextual Notes

Participants are working under the assumption that all surfaces are frictionless, and there is an emphasis on the need to balance forces in both horizontal and vertical directions. The original poster's equations are being scrutinized for accuracy.

rajumahtora
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Homework Statement



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
 

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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.
 
Pranav-Arora said:
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.
But how N is not equal to mgcosθ and is R = Nsinθ correct component
 
rajumahtora said:
But how N is not equal to mgcosθ and is R = Nsinθ correct component

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?
 
Pranav-Arora said:
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.
But how N is not equal to mgcosθ?
 
rajumahtora said:
But how N is not equal to mgcosθ?

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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