Final answer:
The net work done on the plane as it accelerates upward can be found using the work-energy principle. By calculating the final kinetic energy of the plane and subtracting the initial kinetic energy (which is 0 since it starts from rest), we can determine the net work done. The net work done on the plane is equal to 1.274 x 10^6 J.
Step-by-step explanation:
To find the net work done on the plane, we can use the work-energy principle. The work done is equal to the change in kinetic energy of the plane. The initial kinetic energy of the plane is 0 since it starts from rest. The final kinetic energy can be calculated using the equation:
K.E. = (1/2)mv^2
where m is the mass of the plane and v is the final velocity. We can find the final velocity using the equation of motion:
v^2 = u^2 + 2as
where u is the initial velocity of the plane (0 m/s in this case), a is the acceleration, and s is the distance traveled. Plugging in the values, we get:
a = 1.4 m/s^2
s = 31.0 m
Substituting these values into the equation, we find v = 14.6 m/s. Now we can calculate the final kinetic energy:
K.E. = (1/2)(7.7 x 10^3)(14.6^2)
Simplifying and calculating, we find K.E. = 1.274 x 10^6 J. Since the initial kinetic energy is 0, the net work done on the plane is equal to the final kinetic energy:
Net work done = 1.274 x 10^6 J