So I already got the answer for the first part:
An airplane is flying in a horizontal circle at a speed of 102 m/s. The 80.0 kg pilot does not want the centripetal acceleration to exceed 6.18 times free-fall acceleration.
Find the minimum radius of the plane's path. The acceleration due to gravity is 9.81 m/s2.
The answer is 171.79
The second part is what I need help with:
At this radius, what is the magnitude of the net force that maintains circular motion exerted on the pilot by the seat belts, the friction against the seat, and so fourth. Answer in units of N.
Please explain how you got your answer. Thanks so much!
To find the magnitude of the net force exerted on the pilot by the seat belts, friction against the seat, and other forces, we can use the equation for centripetal force.
The centripetal force is the force directed towards the center of the circle that keeps an object moving in a circular path. It is given by the equation:
Fc = m * ac
Where Fc is the centripetal force, m is the mass of the pilot, and ac is the centripetal acceleration.
In this case, we know the mass of the pilot is 80.0 kg and the maximum acceptable centripetal acceleration is 6.18 times the acceleration due to gravity, which is 9.81 m/s^2.
Now, we can find the required centripetal acceleration:
ac = (6.18 * 9.81 m/s^2) = 60.46 m/s^2
Next, we can calculate the centripetal force:
Fc = (80.0 kg) * (60.46 m/s^2) = 4836.8 N
Therefore, the magnitude of the net force exerted on the pilot by the seat belts, friction against the seat, and other forces is 4836.8 N (rounded to the nearest one decimal place).
Please note that in reality, there could be additional forces involved such as gravity, air resistance, and other forces that vary depending on the specific situation. However, for the purpose of this calculation, we are only considering the centripetal force.