Preview Activity 13.2.1.
Recall from Section 9.3 that the work done by a force \(\vF\) on an object that moves with displacement vector \(\vv\) is \(\vF\cdot \vv\text{.}\) In this Preview Activity, we consider the work done by wind on a helicopter at various stages of its journey.
(a)
Our intrepid pilot flies for some time and finds that they are 30 km from where they started at a heading of 20 ° degrees east of due north. During this portion of the trip, the wind is exerting a force of 100 N on the helicopter in the due east direction. Find the work the wind has done on the helicopter during the flight.
(b)
Our pilot sees a storm ahead and changes their direction. Some time later, the pilot determines that they are 25 km due north of where they previously checked thier position. The wind is still exerting a force on the helicopter of 100 N in the due east direction. Find the work done by the wind on the helicopter during the second part of the flight.
(c)
Find the helicopters’s displacement from its original position after the first two parts of its flight and use that to find the work done by the wind on the helicopter during the first two parts of flight.
(d)
(e)
In order to get further away from the storm, the pilot turns and flies 45 ° west of due north for 50 km. The storm the pilot was avoiding has caused the wind to change as well. For this portion of the flight, the wind is exerting a force on the helicopter of 125 N in the south direction. Find the work done by the wind on the helicopter during this part of the flight.
(f)
Explain why you cannot take the total displacement of the three parts of the helicopter flight and calculate the total work done by the wind on the helicopter.
