Jet Pilot Loop: Solve 2 Physics Problems in 1 Hour

[RileyAllen]

A jet pilot takes his aircraft in a vertical loop

a. If the jet is moving at a speed of 1300 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.7 g's.

b. Calculate the 75-{\rm kg} pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed).


I need much help! This is one of only 2 problems I can not figure out. Due in one hour.

 

[Delphi51]

For part (a), you must use the centripetal force formula
F = m*(v^2)/r
Replace F with ma.
Convert your speed into m/s.

 

[nlightner]

I understand the urgency of solving problems within a given time frame. I will do my best to guide you through the problem and provide a solution within the given time limit.

a. To solve this problem, we need to use the equation for centripetal acceleration, which is a = v^2/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the circle. We also know that 6.7 g's is equivalent to 65.7 m/s^2. Therefore, we can set up the equation as follows:

65.7 m/s^2 = (1300 km/h)^2/r

To solve for r, we need to convert the velocity from km/h to m/s and square it. The conversion factor for km/h to m/s is 1 km/h = 0.2778 m/s. Therefore, the equation becomes:

65.7 m/s^2 = (1300 km/h * 0.2778 m/s)^2/r

Solving for r, we get a minimum radius of 153.3 meters.

b. To calculate the pilot's effective weight, we need to use the equation W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. We also know that the pilot's mass is 75 kg and the acceleration due to gravity is 9.8 m/s^2. Therefore, we can set up the equation as follows:

W = 75 kg * 9.8 m/s^2

This gives us a weight of 735 N at both the bottom and top of the circle.

I hope this helps you solve the problems within the given time frame. Remember to always double check your calculations and units to ensure accuracy. Good luck!