Calculating Normal Force on Pilot in Air Show Loop

[myoplex11]

Homework Statement

A 9940 kg plane in an air show completes a vertical loop of radius 596 meters at 155 m/s. What normal force does the airplane seat exert on the 92 kg pilot at the top of the loop and at the bottom of the loop.

Homework Equations

Top of loop
m(v^2/r)= Fnormal + mg
m(v^2/r)= Fnormal - mg

The Attempt at a Solution

should i use the mass of the pilot and the plane for this problem iam really stuck.

 

[alphysicist]

Hi myoplex11,

Homework Statement

A 9940 kg plane in an air show completes a vertical loop of radius 596 meters at 155 m/s. What normal force does the airplane seat exert on the 92 kg pilot at the top of the loop and at the bottom of the loop.

Homework Equations

Top of loop
m(v^2/r)= Fnormal + mg
m(v^2/r)= Fnormal - mg

The Attempt at a Solution

should i use the mass of the pilot and the plane for this problem iam really stuck.

It's asking about forces acting on the pilot, so begin with a free body diagram for the pilot. What mass would you use? What forces act on the pilot, and what is the pilot's acceleration?

 

[thomate1]

Yes, you should use the mass of the pilot and the plane for this problem. To calculate the normal force on the pilot, you will need to use the equation Fnormal = m(v^2/r) - mg, where m is the mass of the pilot, v is the velocity of the plane, and r is the radius of the loop. At the top of the loop, the normal force will be equal to the weight of the pilot, which is given by mg. At the bottom of the loop, the normal force will be equal to the sum of the weight of the pilot and the weight of the plane, which is given by m(v^2/r) + mg. Therefore, the normal force on the pilot at the top of the loop is 92 kg x (155 m/s)^2 / 596 m = 23,844 N, and the normal force on the pilot at the bottom of the loop is 92 kg x (155 m/s)^2 / 596 m + 9940 kg x 9.8 m/s^2 = 1,006,444 N.