Forces on a Ramp: Understanding Fcosθ - mgsinθ = ma

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The discussion focuses on understanding the equation Fcosθ - mgsinθ = ma in the context of forces acting on an object on a ramp. The equation represents the x components of the forces acting along the ramp, with F being the applied force and mg being the gravitational force. Clarification is provided that the positive x direction is defined as up the ramp, which is essential for correctly applying the coordinate system. Drawing a free body diagram is recommended to visualize the forces and their components more clearly. Understanding these components is crucial for solving physics problems related to motion on inclined planes.
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Here is the link to the problem http://imgur.com/9Vnc5Er

Alright, so I already know how to solve this problem, I am just struggling with the why. This is for my physics test, and he posts the answers to these in class assignments so we can review them.

Looking at step 2, we are supposed to use the equation Fcosθ - mgsinθ = ma(in the x direction). Why is this? Is this because those are the x components of the forces? I don't understand where he is getting those from. If you could shed some light on it that would be awesome. Thanks
 
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The x-direction used is clearly along the ramp with positive direction going up along the ramp, I hope you are not confused about how the x-y coordinate system is defined in the given solution. You might want to draw a free body diagram to clear things up. When you take component of forces along the ramp, that is what you'll arrive at.
 

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