A bicyclist rides 5.0 km due east, while the resistive force...

A bicyclist rides $5.0 \mathrm{km}$ due east, while the resistive force from the air has a magnitude of $3.0 \mathrm{N}$ and points due west. The rider then turns around and rides $5.0 \mathrm{km}$ due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of $3.0 \mathrm{N}$ and points due east. (a) Find the work done by the resistive force during the round trip. (b) Based on your answer to part (a), is the resistive force a conservative force? Explain.

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Key Concepts

Conservative vs Non-conservative Forces

Conservative forces are those for which the total work done in moving an object around any closed path is zero, meaning they have an associated potential energy that is independent of the path taken. In contrast, non-conservative forces, such as resistive forces, dissipate energy and yield a net work that is not zero over a closed path, emphasizing the path-dependent nature of the energy transfer they produce.

Work

Work is a measure of energy transfer that occurs when a force causes an object to move. In physics, work is calculated as the dot product of a force vector and a displacement vector, meaning only the component of the force parallel to the displacement contributes to the work. When a force acts opposite to the displacement, the work done is negative, indicating energy is taken away from the system.

Resistive (Non-conservative) Forces

Resistive forces, such as friction or air resistance, act to oppose the motion of an object and convert mechanical energy into other forms like heat. These forces are classified as non-conservative because the work done by them depends on the path taken by the object rather than only its initial and final positions. As a result, the net work done by a resistive force over a closed path is not zero.

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