## Question

The pilot of an aircraft, who is not tied to his seat, can loop a vertical circle in air without falling out at the top of the loop. What is the minimum speed required so that he can successfully negotiate a loop or radius 4 km? Take *g* = 10 ms^{–2}. ^{ }

### Solution

The pilot does not drop down when he is at the top of the loop because his weight *mg* is less than the centripetal force *m* *v*^{2}/*R* required to keep him in the loop. The rest of the centripetal force is balanced by the reaction of the seat. Hence, he is stuck to the seat without being tied to it. If the speed of the aircraft is reduced so that *mg* > *mv*^{2}/*R*, he will fall off from his seat. Therefore, the minimum speed *v _{min}* required to successfully negotiate the vertical loop is given by

#### SIMILAR QUESTIONS

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