Question

A civil engineer is to design a road curved at a 102 m radius to carry racing cars traveling at 19 m/s.

The acceleration of gravity is 9.8 m/s2 .

At what angle θ should it be banked for maximum control of the racing car?

Answer in units of ◦.

Car is 1.3 Mg

μ = 0.14

Answer 1

Given r =102m

Maximum speed ,v= 19m/s

mass of car =1.3Mg = 1300kg and

F_c =centripetal force =mv²/r

Take x axis parallel to inclined plane

Consider all forces in y direction

N - F_cSin - mgcos =0

N = F_cSin +mgcos

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Fr is the frictional force = = (F_cSin +mgcos)

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Consider all forces in x direction

F_cCos -mgsin -Fr =0

F_cCos -mgsin -(F_cSin +mgcos) =0

F_c(Cos -sin) -mg(Sin+Cos) =0

Divide by Cos

F_c(1 -tan) -mg(tan+) =0

F_c =mv²/r = 1300*19²/102 = 4600.98 N

mg =1300*9.81 = 12753 N

4600.98(1 -0.14*tan) -12753(tan+0.14) =0

0.361(1 -0.14*tan) = (tan+0.14)

0.361-0.051tan = (tan+0.14)

0.95tan = 0.221

tan = 0.233

ANSWER:

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