Walker, Halliday & Resnick — Force and Motion-II: Problem 54

54 In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass \( m \) riding around a horizontal circle of radius \( r \) at speed \( v \). What is the variation \( dF \) in the net force magnitude for (a) a variation \( dr \) in the radius with \( v \) held constant, (b) a variation \( dv \) in the speed with \( r \) held constant, and (c) a variation \( dT \) in the period with \( r \) held constant?