A motorcycle is required to travel at a constant speed over an overbridge shaped as a circular arc of radius R and total length L . Assume the motorcycle begins at the highest point. Determine: (i) the maximum velocity it can have such that contact with the road is maintained at the highest point; (ii) the distance along the bridge from the highest point at which it will lose contact with the road if it travels at a

Step-by-step solution

At the highest point of the bridge, the normal force N is given by the equation of motion: mg - N = mv^2 R For contact to be maintained, N 0 , which implies: mg mv^2 R v Rg Thus, the maximum velocity at the highest point is v_ max = Rg . If the motorcycle travels at a speed v = v_ max 2 = Rg 2 , the normal force at an angular position from the highest point is: N = mg - mv^2 R The motorcycle loses contact when N = 0 : mg = m R ( Rg 2 ) = mg 2 = 1 2 = 3 The distance along the bridge from the highest point is s = R =