A laboratory device delivers mechanical power to a flywheel according to the…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A laboratory device delivers mechanical power to a flywheel according to the following description of a power–time graph.
• From t=0 s to t=4 s the power remains constant at 40W.
• From t=4 s to t=8 s the power increases linearly, reaching 80W at t=8 s.
• From t=8 s to t=12 s the power drops suddenly and stays constant at 20W.
Answer the following questions about the work done on the flywheel during the 12-s interval.
(a) Describe qualitatively how the power delivered to the flywheel changes over the three time intervals specified.
(b) Without performing explicit numerical calculations, identify which of the three 4-s intervals results in the greatest amount of work done on the flywheel. Justify your answer using features of the power–time description.
(c) Explain, in words, why the work done on the flywheel during any time interval can be represented by the area enclosed by the power–time graph and the time axis over that interval.