Calculating Minimum Radius for a Stunt Plane Dive

AI Thread Summary
To calculate the minimum radius for the stunt plane's circular motion at a speed of 100 m/s without exceeding an acceleration of 3.00 g, the relationship between acceleration, speed, and radius must be understood. The pilot experiences an upward force as she transitions from a vertical dive to circular motion, resulting in a sensation of sinking into her seat due to Newton's third law. The discussion highlights the importance of maintaining a specific radius to ensure safe maneuvering during the stunt. Understanding these dynamics is crucial for stunt pilots to avoid excessive forces during aerial maneuvers. The calculation ultimately ensures the pilot's safety while performing complex aerial stunts.
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Homework Statement



A 56.0 {\rm kg} stunt pilot who has been diving her airplane vertically pulls out of the dive by changing her course to a circle in a vertical plane.

Q? If the plane's speed at the lowest point of the circle is 100 {\rm m}/{\rm s}, what should the minimum radius of the circle be in order for the acceleration at this point not to exceed 3.00 g?
 
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Well, what is he relationship between the pilot's acceleration, speed and radius of circular motion?
 
thx 4 tryin but i got the answer thx... i still don't get the question tho...
 
The pilot is diving downwards towards the Earth and then exits the dive by turning into a circle. When the direction of motion is changed she will experience an accelerating force from her seat pushing her upwards. According to N3 she pushes just as hard downwards on the seat, so she will descibe it as sinking into the seat.
 
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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