The sign of many physical quantities depends on the choice of coordinates. For example, a y for free-fall motion can be negative or positive, depending on whether we choose upward or downward as positive. Is the same true of work? In other words, can we make positive work negative by a different choice of coordinates? Explain.

Solution 1DQ Introduction In this problem we have to see if work depends on the choice of coordinate system. Solution The work is given by W = F · d Where F is the force and d is the displacement. Now, as we know from vector algebra, the dot product can be written as F · d = |F||d|cos Where theta is the angle between the applied force and the displacement. So from the equation we can see that work depends on the angle between the force and the displacement. If the angle lies between 0rad to /2 rad then the work done is positive and if the angle lies between /2 rad and rad then the angle work done will be negative. If we change the coordinate system, the sign of both force and displacement will change and hence the sign of the product will remain unchanged. Hence it is clear that the work does not depends on the choice of coordinate system.