A research team is testing a prototype winch designed for mountain rescue. During one run the team records the winch’s instantaneous power output at 1 s intervals as it raises a stretcher vertically upward. The data are shown in the table.
Time (s): 0, 1, 2, 3, 4, 5, 6
Power (kW): 0.0, 1.8, 3.6, 4.0, 3.2, 2.4, 2.0
Assume the power varies smoothly between the listed points and that losses are negligible.
a) Using the tabulated data, estimate the total mechanical work delivered by the winch during the 6 s interval. Clearly state and justify any numerical method you use.
b) From your result in part (a), determine the average power output of the winch over the 6 s interval and compare it to the maximum instantaneous power listed in the table.
c) The stretcher and patient together have a mass of 120kg. Assuming the work you calculated in part (a) is entirely converted into gravitational potential energy, determine the vertical distance the stretcher is raised during the test.