When we solved the problem of a block sliding down an inclined plane we chose ou

Question

When we solved the problem of a block sliding down an inclined plane we chose our coordinate system such that one axis was parallel to the plane and one was perpendicular. This choice differed from the "horizontal-vertical" system we often think of. Using the defition of work, explain why the parallel-perpendicular choice provides the solution whereas the horiztonal-vertical choice does not. Consider the forces acting on the block, and indicate which force(s) is(are) capable of doing work as the block slides down the plane.

Explanation / Answer

As a matter of fact, you can solve the problem using either of the two systems. However, using the parallel-perpendicular system will simplify the solution procedure.

Of all the forces on the block, the applied force, the friction force and the wight do work, while the normal support force does not do work. Using the parallel-perpendicular system, it is easy to calculate the work done by the friction, as the force multiplying the distance along the inclined plane. If you use the vertical-horizontal system, you need to calculate the work done by the two components of the friction force, which is a little bit tedeious.

The other advantage is that it is easy to determine the support and friction forces using the parallel-perpendicular system. If you use the vertical-horizontal system, you need to solve a systwm of two equations for the support force and friction force.

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