Question

ENGINEERING MECHANICS ?-ESC204-DYNAMICS TEST Freeman Summer 2018 Problem 3 (15 points) (chapter 13 problem) A 400-kg motorcycle (cyclist included) is driving on hlly terrain where the radii of curvature are 60 m at A and 40 m at B. For safety, the cyclist must not leave the ground at A or experience more than 3 g's at B. What is the top constant speed for the cyclist to safely cross the terrain? Hint: What does it mean to leave the ground? One g is equivalent to the acceleration due to gravity.

Answer 1

Mass of motorcycle= 400 kg

Radius of curvature at A= 60m

Radius of curvature at B= 40

For the cyclist not leave the ground at A, the centrifugal force experienced at A, which tends to push the motorcycle away from the ground, should be less than or equal to weight of the motorcycle, which implies that

Now at point B, cyclist should not experience more than 3 g's, which means the centrifugal force plus the weight of the motorcycle should give acceleartion less than 3 g.

This means the top velocity of the motorcycle can be equal to $\sqrt{60g}$ .