An Indy car has a mass of approximately 715 kg and wide racing slick tires that

Question

An Indy car has a mass of approximately 715 kg and wide racing slick tires that have a coefficient of friction with the road equal to 0.8. In an effort to spruce up the racing scene, organizers have decided to have races wiht the tracks tilted 90 degrees to a normal road (see picture). Indy car's can reach speeds of 230 mph, and you can assume they are at maximum speed before they enter the sideways track.

a. If the race organizers want to build a track with the largest radius possible, how large can they build it and still have an Indy car be able to stay on the track?

b. It begins raining, lowering the coefficient of friction to 0.7. If the track is 20m wide and cars start at the very top of the track, will they be able to complete one full revolution before sliding off the track? Justify.

Explanation / Answer

here,

mass of the car , m = 715 kg

coefficient of friction , u = 0.8

speed of car , v = 230 mph

v = 102.82 m/s

a.

let the radius of the track be r

to mave the car in circular track,

m*g - u * m*v^2/r = 0

715 * 9.8 - 0.8 * 715 *102.82^2/r

r = 863.02 m

the largest radius of the track possible is 863.02 m

b.

the resultant downward accelration be a

u = 0.7

a = g - u * v^2/r

a = 9.8 - 0.7 * 102.82^2/863.02

a = 1.225 m/s^2

the time taken to complete one revolution, t = 2*pi*r/v

t = 2*pi*863.02/102.82

t = 52.71 s

let the time taken to silde of the trak be t'

width of track , w = 20 m

using seccond equation of motion

w = u*t + 0.5 * a*t'^2

20 = 0 + 0.5 * 1.225 * t'^2

t' = 5.71 s

t' <t

therefore the car will not be able to complete one full revolution before sliding off the track

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