Let's say we have an object lying on a slope, the weight of the object can be divided into two components one horizontal and one vertical. My question is does the weight act only in these two directions or does it spread evenly between the the both components?
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$\begingroup$ The horizontal weight is zero. $\endgroup$– jinaweeDec 18, 2013 at 21:35
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2$\begingroup$ Notice the weight of the object will by the definition of vertical always be along the vertical direction. You can, however, divide this vertical force into components along the slope and perpendicular to it. $\endgroup$– WouterDec 18, 2013 at 21:36
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2 Answers
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Let me give you an intuition of what components are and then I will answer your question:
I pull a dog on a leash with a tension of 5N at an angle of 53.1 degrees. This is equivalent to pulling the dog simultaneously horizontally with a rope with a force of 3N (5cosθ) and vertically with a rope with a tension force of 4N (5sinθ)
In both scenarios, the dog "feels" the same. In other words, the two components are equivalent to the single force of 5N at an angle of 53.1 degrees.
In your question, the weight only acts downwards. We can "break" the force down using a coordinate system and find two components which are equivalent to the weight. The vertical weight vector can be divided into components along the slope and perpendicular to it. By replacing the weight vector by these components, and dividing the other forces into the same coordinate system, we can determine the motion of the object along and perpendicular to the plane.
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I am not sure If I understand your question correctly.
The gravitational force in this problem acts only "downwards". However, to define a direction in two dimensions one needs two coordinates. In the conventional coordinate system the force acts in the $(0,1)^T$ direction, where $0$ and $1$ are the coordinates.
In the problem presented by you another choice of coordinate system is more practical, namely with one axis perpendicular to the slope and one tangential. In these coordinates the motion only takes plac ein one of the coordinates.
So separating the force in the two components is just a (arbitrary) choice of the coordinate system.
