Answer:
A) r= 4081.63m
B) Fc= 519.205 kN
Explanation:
Given
[tex]m=60.000 lf *\frac{1kg}{0.453lb}=13245.033 Kg[/tex]
[tex]V=400\frac{m}{s}[/tex]
[tex]a=4*g=4*9.8\frac{m}{s^{2}}=39.2\frac{m}{s^{2}}[/tex]
A)
The radius of the circle is:
[tex]a_{c}=\frac{V^{2}}{r}\\r=\frac{V^{2}}{a_{c}}\\r=\frac{(400)^{2}}{39.2\frac{m}{s^{2}}}\\r=4081.63 m[/tex]
B)
The centripetal force
[tex]F_{c}=m*a_{c}\\F_{c}=13245.033kg*39.2\frac{m}{s^{2}}\\F_{c}=519205.29N\\F_{c}=519.205 kN[/tex]
C)
The force of lift according to Bernoulli law the force of lift is equal to the force make the F-14 jet flying
Equation:
[tex]F_{lift}=\frac{1}{2}*A*p*(V)^{2}[/tex]
p=density of the air in the moment the jet in flying ≅1-1.5 and the area is going to be the area of the wings where is the force of lift acting have to be more that Fc
a) The radius of the circle is 4078.719 meters.
b) The centripetal force is 1066217.04 newtons.
c) The force of lift on the wings there is 1332771.3 newtons.
a) Let suppose that the F-14 jet is experimenting a uniform circular motion, the centripetal acceleration ([tex]a[/tex]), in meters per square second, by the jet is described by the following expression:
[tex]a = \frac{v^{2}}{R}[/tex] (1)
Where:
If we know that [tex]a = 4\cdot g[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]v = 400\,\frac{m}{s}[/tex], then the radius of the circle is:
[tex]R = \frac{v^{2}}{a}[/tex]
[tex]R = \frac{v^{2}}{4\cdot g}[/tex]
[tex]R = \frac{\left(400\,\frac{m}{s} \right)^{2}}{4\cdot \left(9.807\,\frac{m}{s^{2}} \right)}[/tex]
[tex]R = 4078.719\,m[/tex]
The radius of the circle is 4078.719 meters.
b) The centripetal force ([tex]F[/tex]), in newtons, of the aircraft is equal to the product of the F-14 mass ([tex]m[/tex]), in kilograms, and the acceleration ([tex]a[/tex]), that is to say:
[tex]F = m\cdot a[/tex] (2)
If we know that [tex]m = 27180\,kg[/tex] ([tex]60000\,lb[/tex]), [tex]a = 4\cdot g[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], then the centripetal force is:
[tex]F = (27180\,kg)\cdot 4\cdot \left(9.807\,\frac{m}{s^{2}} \right)[/tex]
[tex]F = 1066217.04\,N[/tex]
The centripetal force is 1066217.04 newtons.
c) At the bottom of the circle, the lift force ([tex]L[/tex]), in newtons, is the sum of the weight of the aircraft ([tex]W[/tex]), in newtons, and the centripetal force ([tex]F[/tex]). By the Newton's Laws of motion, we get the following expression:
[tex]L = F + W[/tex] (3)
If we know that [tex]F = 1066217.04\,N[/tex], [tex]W = m\cdot g[/tex], [tex]m = 27180\,kg \,(60000\,lb)[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] , then the lift force on the wings is:
[tex]L = 1066217.04\,N + (27180\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)[/tex]
[tex]L = 1332771.3\,N[/tex]
The force of lift on the wings there is 1332771.3 newtons.
We kindly invite to check this question on centripetal forces: https://brainly.com/question/1869806
