A daredevil rider has to complete a vertical loop of radius 25 m on a motorcycle. What is the minimum speed he can go at?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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When the daredevil rider is riding his motorcycle in a vertical loop, there are two forces that contribute to the centripetal acceleration of the rider at any point. One of them is the gravitational force of the Earth equal to m*g. The other is the normal force of the surface the rider is riding his motorcycle on. At any point N + m*g = m*v^2/r where v is the velocity of the rider and r is the radius of the circular path. At the highest point the normal force is 0 and the centripetal force is contributed only by the gravitational force else the rider will fall down.

m*g = m*v^2/r

=> v^2 = g*r

=> v = sqrt(9.8*25)

=> v = 15.652 m/s

The motorcycle rider has to ride at a minimum speed of 15.652 m/s to be able to complete a vertical loop of radius 25 m without falling.