An airplane has a mass of 3.41 × 104 kg and takes off under the influence of a constant net force of 2.57 × 104 N. What is the net force that acts on the plane's 78.8-kg pilot?

The acceleration 'a' of the plane equals the acceleration of the pilot, since they travel together.

a = 2.57*10^4/3.41*10^4 = 0.754 m/s^2\ = Fpilot/Mpilot = Fpilot/78.8
Fpilot = 59.4 Newtons

This rather small force causes acceleration along the flight path. The pilot's weight is cancelled by the force exerted on him by the seat cushion.

To find the net force acting on the pilot, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. Mathematically, it can be expressed as:

Net force = mass × acceleration

In this case, we are given the mass of the airplane (3.41 × 104 kg) and the net force acting on it (2.57 × 104 N). We need to find the net force acting on the pilot, who has a mass of 78.8 kg.

Let's assume that the acceleration of the airplane and the pilot are the same, since they are both part of the same system. Therefore, we can set up an equation to solve for the acceleration:

Net force = mass × acceleration

2.57 × 104 N = (3.41 × 104 kg + 78.8 kg) × acceleration

Note: We add the mass of the airplane and the pilot because the net force is acting on both of them.

Now, we can solve for the acceleration by rearranging the equation:

acceleration = Net force / (mass of airplane + mass of pilot)
acceleration = 2.57 × 104 N / (3.41 × 104 kg + 78.8 kg)

After calculating the value of acceleration, we can use it to find the net force acting on the pilot:

net force on pilot = mass of pilot × acceleration
net force on pilot = 78.8 kg × acceleration