Question

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a skateboarder wants to cross a large playground and notices that there are large shapes painted on its asphalt surface. one shape is a large circle that covers the entire playground. inscribed in that circle is a square, with one point at the skateboarders feet and the other at his destination. the surface is rough and, therefore, friction is present. what path does he follow in order to minimize the work done by nonconservative forces?
the square.
the circle.
the path does not matter.

Explanation:

The work - done by non - conservative forces (here friction) is given by \(W_{nc}=F_f d\), where \(F_f\) is the frictional force and \(d\) is the distance traveled. The frictional force \(F_f=\mu N\) is constant for a given surface and normal force. To minimize \(W_{nc}\), the distance \(d\) should be minimized. The shortest distance between two points is a straight line. In the given situation, the straight - line path is along the side of the square (since one point of the square is at the starting and the other at the destination). The circle has a larger perimeter than the side of the square for the same diameter and side - length relationship.

Answer:

The square.