The takeoff runway on carriers is much too short for a modern jetplane to take off on its...

The takeoff runway on carriers is much too short for a modern jetplane to take off on its own. For this reason, the takeoff of carrier planes is assisted by hydraulic catapults (Fig. A). The catapult system is housed below the deck except for a relatively small shuttle that slides along a rail in the middle of the runway (Fig. B). The front landing gear of carrier planes is equipped with a tow bar that, at takeoff, is attached to the catapult shuttle (Fig. C). When the catapult is activated, the shuttle pulls the airplane along the runway and helps the plane reach its takeoff speed. The takeoff runway is approximately 300 ft long, and most modern carriers have three or four catapults.

Figure P5.7

In a catapult-assisted takeoff, assume that a 45,000 lb plane goes from 0 to 165 mph in 2 s while traveling along a rectilinear and horizontal trajectory. Also assume that throughout the takeoff the plane’s engines are providing 32,000 lb of thrust.

(a) Determine the average force exerted by the catapult on the plane.

(b) Now suppose that the takeoff order is changed so that a small trainer aircraft must take off first. If the trainer’s weight and thrust are 13,000 and 5850 lb, respectively, and if the catapult is not reset to match the takeoff specifications for the smaller aircraft, estimate the average acceleration to which the trainer’s pilots would be subjected and express the answer in terms of g. What do you think would happen to the trainer’s pilot?