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Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of the vector diagrams that were discussed in an earlier unit. These diagrams will be used throughout our study of physics.

The above diagram is constructed as per the question.

Now,

Drawing a free body diagram of mass m

Here, N represents the Normal component, g represents the acceleration due to gravity.

Since the mass m

Now,

Drawing the free body diagram of the wedge,

So, clearly from the above and by balancing all the forces, we can write,

\[

Ny = (m_2 \times g) + (N\cos \theta ) \\

Ny = (m_2 \times g) + (m_1g\cos \theta \times \cos \theta ) \\

Ny = (m_2 \times g) + (m_1g{\cos ^2}\theta ) \\

\]

And, by balancing forces in X direction we can write,

$

Nx = N\sin \theta \\

Nx = m_1g\cos \theta \sin \theta \\

$

Now, since we know that weight balance only reads upward normal force, therefore it will only read Ny.

Thus,

$

Ny = m_2g + m_1g(1 - {\sin ^2}\theta ) \\

Ny = g(m_2 + m_1) - m_1g{\sin ^2}\theta \\

$