Dynamics: Moving wedge with mass on it

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SUMMARY

The discussion centers on a physics problem involving a small block of mass "m" on a frictionless triangular wedge of mass "M". The required force "F" to keep "m" stationary on the wedge is determined to be F = (m+M)g*tan(THETA), where "g" is the acceleration due to gravity and "THETA" is the angle of the wedge. The solution involves understanding the concept of pseudo forces and the acceleration of the combined wedge and mass system. The participant "k" successfully solved the problem, clarifying the relationship between the applied force and gravitational forces acting on the block.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the concept of pseudo forces
  • Knowledge of trigonometric functions, specifically tangent
  • Basic principles of mechanics involving inclined planes
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  • Study the application of pseudo forces in non-inertial reference frames
  • Explore the dynamics of systems involving inclined planes and frictionless surfaces
  • Learn about the derivation and application of forces in static equilibrium
  • Investigate advanced problems involving multiple masses and angles in mechanics
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Students studying physics, particularly those focusing on mechanics, educators teaching dynamics, and anyone interested in solving problems involving forces on inclined planes.

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Homework Statement


Small block of mass "m" rests on sloping side of triangular block of mass "M" which itself rests on table. Assuming all surfaces are frictionless, determine force "F" that must be applied to "M" so that "m" remains fixed. Wedge incline is "THETA"

Homework Equations


The Attempt at a Solution


attached is picture. I don't know where to start, so no attempted solution. The answer is:
F = (m+M)g*tan(THETA). i don't see why the mass on the wedge would move up the ramp if a force is applied to the left of the wedge.

where g is acceleration due to gravity
 

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Because of the pseudo force. If a pseudo force F is applied to the wedge, then the acceleration of the wedge+mass system is F/(M+m) and the force on m is mF/(M+m). The projection of that force along the surface of the wedge is equal to the gravitational force acting along the surface of the wedge.
 
k solved it thanks
 

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