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when we solve problems in mechanics can we take co-ordinate axes in any direction.for example:in inclined plane problems when we take x-axis along the incline and y-axis perpendicular to it value of normal force is mgcosx(x is anle of inclination)but if we take x-axis parallel to the ground and y-axis perpendicular to it value of normal force is mg/cosx.why does value of normal force depend on coordinate axes and which one is its correct value(give reasons).what coordinate axes should i take in case the inclined plane is moving(give reasons)
7 years ago
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Yes,co-ordinate axes could be taken in any direction as one wish...!!! Your analysis is right in the sense that value of normal force is different for both choice.But then you must divide acceleration down the incline also in two components for the second choice & solve accordingly. Why the first choice is always used then? For the obvious(bt not always seen !!!) reason that the block is constrained to move down the incline only.So you take x-axis down the incline to have acceleration in one direction only & u've simpler equations to solve as u don't have to break the normal force in 2 components with acceleration in that direction being zero. Also in second choice u've to considere hor. component of normal force as cause of acceleration in that direction & then vectorially add them to get net acceleration down the incline. In almost all dynamics problem (however complex it may seem) constraints make it possible to get the exact no. of equations as there are variables in problem.Once you identify all constraints & transform them in mathematical equations using concepts of physics, battle is won. So,now you understand that it doesn't matter in whichever direction you take your co-ordinate axis as long as you remain honest with your choice throughout your solving process.You get identical results nonetheless.
Yes,co-ordinate axes could be taken in any direction as one wish...!!!
Your analysis is right in the sense that value of normal force is different for both choice.But then you must divide acceleration down the incline also in two components for the second choice & solve accordingly.
Why the first choice is always used then?
For the obvious(bt not always seen !!!) reason that the block is constrained to move down the incline only.So you take x-axis down the incline to have acceleration in one direction only & u've simpler equations to solve as u don't have to break the normal force in 2 components with acceleration in that direction being zero.
Also in second choice u've to considere hor. component of normal force as cause of acceleration in that direction & then vectorially add them to get net acceleration down the incline.
In almost all dynamics problem (however complex it may seem) constraints make it possible to get the exact no. of equations as there are variables in problem.Once you identify all constraints & transform them in mathematical equations using concepts of physics, battle is won.
So,now you understand that it doesn't matter in whichever direction you take your co-ordinate axis as long as you remain honest with your choice throughout your solving process.You get identical results nonetheless.
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