- #1

- 560

- 2

## 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?