Find Minimum Radius for Safe Vertical Looping | Jet Pilot in 1400 km/h Loop

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To determine the minimum radius for a safe vertical loop at 1400 km/h, the centripetal acceleration must not exceed 6.0 g's, equivalent to 58.8 m/s². The speed of the jet is converted to 389 m/s, and the formula for centripetal acceleration, a_c = v²/r, is applicable. The discussion clarifies that the mass of the jet is not necessary for this calculation, as the focus is on the relationship between speed and radius. The key takeaway is to use the centripetal acceleration formula directly without needing to sum forces. Understanding this allows for the correct calculation of the minimum radius required for safe looping.
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A jet pilot takes his aircraft in a vertical loop

(a) If the jet is moving at a speed of 1400 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 6.0 g's.


I am having some trouble here. I converted the speed to be 389 m/s. I thought i would use the equation F=m(v^2/r) Then F would equal the normal force minus mg. But this does not seem to work out since we do not know the mass. I am a little confused. So any help would be great. Thanks
 
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F = ma.. Fcent = m*Acent
 
vsage said:
F = ma.. Fcent = m*Acent

i don't understand what you are saying
 
I'm saying the question is asking for centripetal acceleration which is given by v^2/r. You don't need to sum the forces just the accelerations.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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