An airplane travels 80 m/s as it makes a horizontal circular turn which has a 0.8 km radius. What is the magnitude of the resultant force on the 75 kg pilot of this airplane?
To find the magnitude of the resultant force on the pilot, we need to consider two forces acting on the pilot: the gravitational force (weight) and the centripetal force.
1. Gravitational Force (Weight):
The weight of an object can be calculated using the formula: weight = mass × gravitational acceleration.
Given that the mass of the pilot is 75 kg, and the gravitational acceleration is 9.8 m/s², we can calculate the weight of the pilot:
Weight = 75 kg × 9.8 m/s² = 735 N.
2. Centripetal Force:
The centripetal force is the force that keeps an object moving in a circular path. It is directed toward the center of the circular motion. In this case, the centripetal force is provided by the resultant force acting on the pilot.
The centripetal force can be calculated using the equation: centripetal force = mass × centripetal acceleration.
The centripetal acceleration is given by the formula: centripetal acceleration = (velocity^2) / radius.
Given that the velocity of the airplane is 80 m/s and the radius of the circular path is 0.8 km (which is equivalent to 800 m), we can calculate the centripetal force:
Centripetal acceleration = (80 m/s)^2 / 800 m = 64 m/s².
Centripetal force = 75 kg × 64 m/s² = 4800 N.
Now, to find the magnitude of the resultant force, we need to add the weight and the centripetal force:
Resultant force = Weight + Centripetal force = 735 N + 4800 N = 5535 N.
Therefore, the magnitude of the resultant force on the 75 kg pilot of this airplane is 5535 N.