Circular Motion: Plane does a loop

[thussain93]

Homework Statement

A Jet pilot takes his aircraft in a vertical loop. if the jet is moving at a speed of 700km/hr at the bottom of the loop, determine the minimum radius of the loop if the acceleration at the lowest point doesn't exceed 6.0g's (this means 6.0 x acceleration due to gravity on earth)

Homework Equations

Fcentripital = MV^2/R

The Attempt at a Solution

All i know is that 700km/hr is 194.44m/s
and i also know that the Fg at the bottom would be -58.8N
I'm totally stuck, help me out thanks

 

[tiny-tim]

Welcome to PF!

Hi thussain93! Welcome to PF!

(try using the X² tag just above the Reply box )

It just means find R such that the centripetal acceleration is 6 times 9.8.

 

[kerimek]

I would approach this problem by first understanding the concept of circular motion. When an object moves in a circular path, it experiences a centripetal force directed towards the center of the circle. This force is given by the equation Fcentripetal = MV^2/R, where M is the mass of the object, V is its velocity, and R is the radius of the circle.

In this case, the jet pilot is experiencing a centripetal force at the bottom of the loop, which is equal to the sum of two forces: the force of gravity (Fg) and the normal force (Fn) from the wings of the jet. Since the acceleration at the lowest point of the loop is limited to 6.0g's, we can set the centripetal force equal to 6 times the force of gravity, or 6Fg.

Using the given speed of 700km/hr (194.44m/s) and the equation Fcentripetal = MV^2/R, we can set up the following equation:

6Fg = M(194.44m/s)^2/R

We also know that Fg = Mg, where g is the acceleration due to gravity on Earth (9.8m/s^2). Substituting this into our equation, we get:

6Mg = M(194.44m/s)^2/R

Solving for R, we get:

R = (M(194.44m/s)^2)/(6Mg)

R = 588.23m

Therefore, the minimum radius of the loop is 588.23m. This means that the jet pilot must maintain a circular path with a radius of at least 588.23m in order to not exceed 6.0g's of acceleration at the bottom of the loop.