We have that the expression for the magnitude of the horizontal force F is
[tex]F=(m_1+m_2)gtan\phi[/tex]
From the question we are told
find an expression for the magnitude of the horizontal force f in the figure for which m1 does not slip either up or down along the wedge. all surfaces are friction-less.
Generally the equation for Normal force is mathematically given as
[tex]N=\frac{n_2g}{cos\pji}[/tex]
Where
a signifies acceleration
[tex]Nsin\phi=m_2a[/tex]
Therefore
Equating above equations
[tex]a=\frac{Nsin\phi}{m^2}\\\\a=gtan\ph[/tex]i
Generally the equation for Force on wedge is mathematically given as
[tex]F=m_1a+Nsin\phi[/tex]
[tex]F=(m_1+m_2)gtan\phi[/tex]
Therefore
The expression for the magnitude of the horizontal force F is
[tex]F=(m_1+m_2)gtan\phi[/tex]
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