What is the formula for calculating the radius of a loop in a jet fighter?

[Karma]

A Jet Fighter is flying his Fighter, in a Loop the Loop path chasing the Red Baron. His instruments tell him that the plane is level (at the bottom of the loop) and traveling with a speed of 180km/h. He is sitting on a set of bathroom scales, and notes that they read four times the usual force of Gravity on him. What is the radius of the loop?

Can someone tell me what formula I should be using, and what things that I should be aware of? Thank You

 

[Arman_AAT_Khos]

For Bodies in Equilibrium The sum of the Forces is zero, viz. Newton's 1st law of motion: sum of unbalanced external forces contribute to motion of the object.

S := Summation

S ( F_y = 0 )

Force on him due to gravity is directed downwards away from the radius.
Force on him due to the centripedal Force is directed upwards towards the radius.

The Jet follows curvilinear motion and the acceleration has two components tangental and normal to the path, for computing Centripedal force, use the normal component of the acceleration.

F = m*a_n = m*v^2/r

be sure to convert the units of velocity from U.S. to SI

- Arman Khos

 

[Karma]

Thank you for the help but can you can you clearify on what this stands for
" _ ". Such as F=M*n_a

 

[Leong]

it is the net force acting on the person, m is his mass and n_a is the centripedal acceleration or normal acceleration according to Arman's explanation.

 

[carlz]

F = (mv^2)/r = ma

cancel out m

v^2/r = a

you have the velocity and a = 9.81 * 4

tada, that's the radius

 

[Karma]

v=50m/s
a=39.2
r=?
50^2/R=39.2
R=64
The answer I am supposed to get is 85.

 

[carlz]

made a mistake. Ok, when he is straight and level flight, the scale would already read 1g or 9.81ms-2.

So, when the scale reads 4g during the loop, we have to take into consideration the the 4gs is including gravity. so, 4-1=3. The centripretal force would be 3g.

Sub the a for 9.81 * 3

r = 84.947m

Sorry for the mistake above.

 

[Arman_AAT_Khos]

Yes, the "_" is a subscript to denote the normal component of acceleration.

The pilot is measuring the combined force of his weight with that of centripedal acceleration. So, S ( F_n ) = ma_n = F - mg substitute for F; 4W = ma_n + mg

Sorry for the confusion, S ( F_y = 0 ) describes the sum of forces on a body that prevent motion.