A certain light truck can go around a flat curve having a radius of 150m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0m?

1 Answer
A08
Apr 26, 2018

Friction between the tires and the flat road provides the required centripetal acceleration for the truck to negotiate the curve safely without skidding.

#a_(c,max)=v_max^2/R # ......(1)

Inserting given values we get

#a_(c,max)=(32.0)^2/150=6.82bar6\ ms^-2 #

For a changed radius of the curve of #75.0\ m#, the maximum safe speed from (1) becomes

#v_("new",max)=sqrt(a_(c,max)R_"new") #
#v_("new",max)=sqrt(6.82bar6xx75.0) #
#v_("new",max)=22.6\ ms^-1 #, rounded to one decimal place.

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