Homework Help: Normal Force Problem

1. Nov 25, 2013

rajumahtora

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 :-

2. The attempt at a solution

Let normal force on A be N and on B be R.
My Diagram :-

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?

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2. Nov 25, 2013

Saitama

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.

3. Nov 25, 2013

rajumahtora

But how N is not equal to mgcosθ and is R = Nsinθ correct component

4. Nov 25, 2013

Saitama

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?

5. Nov 25, 2013

rajumahtora

But how N is not equal to mgcosθ?

6. Nov 25, 2013

ehild

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