# Force applied to a mass of an inclined plane with mass

There is a box of mass m on a wedge of mass M with angle θ (the triangle also has a angle of 90 degrees). I need to find the force applied on the little mass, this is what I got:
F=-mgsinθ+Mgsinθ
Where the first term refers to the force of gravity applied to the mass m and the second term refers to the normal force applied on m by M.
I think my mistake is the normal force because looking at the limits when M is really big, the mass m moves in the opposite direction that gravity pushes it.

Can someone help me set this force up?

P.S. the surface of the wedge is frictionless and the surface in which the wedge lies on is frictionless.

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your mistake is that the normal force acting on the box should be equal and opposite to the force acting on it that is perpendicular to the surface that it's resting on

look at a simple example: box sitting on the ground, no angles

there is the force of gravity acting on this box, which is -mg

the normal force therefore is equal and opposite to the force of gravity, which in this case is also perpendicular to the surface

so the normal force acting on this block is +mg

an important thing to remember is that if an object is not moving or has a constant velocity, then the sum of the forces acting on that object need to equal zero.

This also applies for each component of the force. What that means is that if the box is not accelerating in the x direction, then the forces in the x direction must add up to be zero. And the same thing in the case of the y direction.

So, if we look at your example, we see a block on a wedge. Sometimes it helps to think about things in terms of common sense: if you put a block on a wedge, what would happen to the block. Obviously it would slide down the wedge.

So let's say that the y direction is perpendicular to the surface of the wedge, and the x direction is parallel to the surface of the wedge. And by surface I mean the surface on which the block is sitting.

If we think about it this way, we can see that there will be no acceleration in the y direction, but there will be acceleration in the x direction. There's no acceleration in the y direction because... well it's not like the block is going to fly off the wedge or fly "into" the wedge, that would make no sense.

Therefore, the forces in the y direction need to add up to zero.

But the forces in the x direction should *not* add up to zero.