Problem on block sliding on a wedge

AI Thread Summary
The discussion focuses on calculating the acceleration of a block of mass 'm' on a right triangular wedge of mass 'M' without friction. The normal force exerted by the block on the wedge is given by N=mg*cos(α), where α is the angle of the wedge. The horizontal force between the block and the wedge is F=N*sin(α)=mg*cos(α)*sin(α), leading to the wedge's acceleration a=F/M=(m/M)g*cos(α)*sin(α). The question arises about whether the block must remain stationary relative to a fixed coordinate system or just the wedge itself. Understanding this distinction is crucial for determining the applied force needed to keep the block from moving.
gauravkukreja
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Consider a block of mass 'm' kept on the hypotenuse of a right triangular wedge of mass 'M'. Calculate the accelaration of the wedge and the block.
Hence find the force that should be applied to 'M' so that 'm' does not move?
 
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is there no friction?
in this case the interaction force between the block and the wedge is the normal vincular reaction, that is equal to the normal compnent of the block weight that is:
N=mg\cos\alpha
where alpha is the lower angle of the wedge. So the horizontal force between the wedge and the block is
F=Nsen\alpha=mg\cos\alpha\, sen\alpha
Considering the wedge it receives a force equal to F so it moves with an acceleration equal to
a=\frac{F}{M}=\frac{m}{M}g\cos\alpha\, sen\alpha
 
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For the second question I don´t understand if m must not move respect a fix coordinate or respect to the wedge...
 
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