Question

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.

Answer 1

We have that the expression for the magnitude of the horizontal force F is

$F=(m_1+m_2)gtan\phi$

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

$N=\frac{n_2g}{cos\pji}$

Where

a signifies acceleration

$Nsin\phi=m_2a$

Therefore

Equating above equations

$a=\frac{Nsin\phi}{m^2}\\\\a=gtan\ph$i

Generally the equation for Force on wedge   is mathematically given as

$F=m_1a+Nsin\phi$

$F=(m_1+m_2)gtan\phi$

Therefore

The expression for the magnitude of the horizontal force F is

$F=(m_1+m_2)gtan\phi$

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