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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 frictionless.

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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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