Normal forces on inclined plane

AI Thread Summary
The discussion focuses on analyzing the forces acting on a 1.0 kg box on a 30-degree frictionless incline connected to a 3.0 kg box on a horizontal surface. The normal force for the inclined box is derived from its weight, while the tension in the connecting string does not affect the normal force of the box on the flat surface. It is emphasized that drawing free body diagrams (FBDs) for both boxes simplifies the analysis. The weight of the inclined box is not acting perpendicular to the incline, requiring resolution into x and y components. Understanding these forces is crucial for solving the problem accurately.
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A 1.0 kg box on a 30 degree frictionless incline is connected to a 3.0 kg box on a horizontal frictionless
surface. The pulley is frictionless and massless.

I got n=mg for m1 in the y direction, and in the x direction i got F+T=m1a. For m2 in the y direction i get N-m2gcos(theta)=0, and in the x direction i get m2gsin(theta)-T=m2a. Is this correct?
 

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Start with the box on an inclined plane, the gravity pulls down and the slope pushes perpendicularly to itself, then the normal force for the second box on the flat plane is mg the tension actually makes no difference to the normal force. If you are looking for all the forces then the tension is the horizontal component of the first normal force
 
You should have two FBD's for this problem. It makes things a lot easier IMO. Draw A fbw for both boxes as if they are on a flat surface. Draw one box with a tension force to the right (top box) and the other with a tension force to the left (bottom box). Here's the tricky part--the weight of the inclined box does not act normal to the surface of the plane (normal means 90 degrees btw or perpendicular). How many degrees is the weight of the box from the normal direction of the inclined box? Next, if I told you the weigh of the inclined box was the hypotenuse of a triangle would that help you resolve the weight vector into x-y vectors (hint hint).

good luck.
 
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