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center o bass
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Homework Statement
A small block of mass m is sliding along the inclined slope of a wedge of mass M.
The block slides without friction on the wedge and the wedge slides without friction on the floor. The slope on the wedge has an inclination [tex]\alpha[/tex] with the floor.
Homework Equations
Newtons etc... gravity, normal force.
The Attempt at a Solution
I reason as follows: Gravity pulls the upper box down along the wedge with a force [tex]mg \sin \alpha[/tex]
but it also has a component normal to the wegde being [tex]mg \cos \alpha[/tex].
Now this has to equal the normal force from the wedge on the box, so [tex]N =mg cos \alpha[/tex], but this is in an action-reaction par with the weight of the box acting on the wedge so the wedge feels a force in the negative direction along the plane of the floor of
[tex] mg \sin \alpha \cos \alpha[/tex] indicating that it would get an acelleration of [tex]a_M = \frac{mg}{M} \sin \alpha \cos \alpha[/tex] while the little box would get an acceleration of [tex]a_m = g\cos\alpha[/tex].
This is what I would naivly do, but after some time i realize that the box on top is in an
accelerated frame so I can't blindly apply Newtons laws here and therefore the reasoning fails. How would I then go about analyzing this problem?