Question

If the jet is moving at a speed of 1140 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 7.0 g's?Calculate the 69-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)?

Answer 1

To solve this problem we will apply the concepts related to the centripetal Force and the Force given by weight and formulated in Newton's second law. Through the two expressions we can find the radius of curve made in the hand. To calculate the normal force, we will include the concepts of sum of forces to obtain the net force on the body at the top and bottom of the maneuver. The expression for centripetal force acting on the jet is

$F_c = \frac{mv^2}{r}$

According to Newton's second law, the net force acting on the jet is

F = ma

Here,

m = mass

a = acceleration

v = Velocity

r = Radius

PART A ) Equating the above two expression the equation for radius is

$\frac{mv^2}{r} = ma$

$r = \frac{v^2}{a}$

Replacing with our values we have that

$r = \frac{(1140km/hr[\frac{1000m}{1km}\frac{1hour}{3600s}])^2}{7(9.8m/s^2)}$

$r = 1.462*10^3m$

PART B )

- The expression for effective weight of the pilot at the bottom of the circle is

$N = mg +\frac{mv^2}{r}$

$N = (69kg)(9.8m/s^2)+\frac{(69)(1140km/hr[\frac{1000m}{1km}\frac{1hour}{3600s}])^2}{1.462*10^3m}$

$N = 5408.87N$

Note that the normal reaction N is directed upwards and gravitational force mg is directed downwards. At the bottom of the circle, the centripetal force is directed upwards. So the centripetal force is obtained from the gravitational force and the normal reaction.

- The expression for effective weight of the pilot at the top of the circle is

$N = mg -\frac{mv^2}{r}$

$N = (69kg)(9.8m/s^2)-\frac{(69)(1140km/hr[\frac{1000m}{1km}\frac{1hour}{3600s}])^2}{1.462*10^3m}$

$N = 4056.47N$

Note that at the top of the circle the centripetal force is directed downwards. So the centripetal force is obtained from normal reaction and the gravitational force.