A race car accelerates uniformly as it leaves the pit area, going from rest to 3

Question

A race car accelerates uniformly as it leaves the pit area, going from rest to 300 km/h in a semicircular arc (i.e. 1/2 of a circle) with a radius of 196 m. Determine the tangential acceleration of the car when it is halfway through the turn (i.e. 1/4 of a circle), assuming constant tangential acceleration. Correct: Your answer is correct. m/s2 Determine the radial acceleration of the car at this time (when it has traveled 1/4 of a circle). m/s2 If the curve were flat, what would the minimum coefficient of static friction between the tires and the roadbed have to be in order to provide the total acceleration with no slipping or skidding when the car has traveled halfway through the turn?

Explanation / Answer

speed v=300 km/h =83.33 m/sec

raius r=195 m

a)

distance travelled is d=2pi*r/4

d=(pi*r/2)

d=(pi*195/2)=306.3 m

now,

v^2=2*a*d

83.33^2=2*a*306.3

tangential acceleration a=11.33 m/sec^2

b)

radial acceleration a=v^2/r

a=83.33^2/(195)

a=35.6 m/sec^2

c)

net acceleration a_net=sqrt(11.33^2+35.6^2)

a_net=37.34 m/sec^2

now,

m*a=f

m*a=us*mg

a=us*g

37.34=us*(9.8)

===>

coefficient of static friction=3.81

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