Abicyclist rides 3.44 km due east, while the resistive force from the air has a magnitude of 6.83 n and points due west. the rider then turns around and rides 3.44 km due west, back to her starting point. the resistive force from the air on the return trip has a magnitude of 6.83 n and points due east. find the work done by the resistive force during the round trip.

 W = -47 103 J

Explanation:

Work is the scalar product of force by distance, blacks indicate vectors

       W = F .d

       W = F d cos θ

Let's find the work of the two trajectories

Case 1. The force is directed to the west and the displacement to the east, therefore, the angle between the two is 180º and cos 180 = -1

      W₁ = 6.83 3.44 10³ cos 180

      W₁ = - 23.5 10³ J

Case 2. The force is directed to the east and displacement points to the west, again the angle is 180º

      W₂ = 6.83 3.44 cos 180

      W₂ = -23.5 103 J

The total work is the sum of each of the calculated jobs

     W = W₁ + W₂

     W = 2 (-23.5 103)

     W = -47 103 J

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3. dark matter

empty space could also be a simple vacuum