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 =mv^{2}/r

Take x axis parallel to inclined plane

Consider all forces in y direction

N - F_{c}Sin
- mgcos
=0

N = F_{c}Sin
+mgcos

----------------------------

Fr is the frictional force =
=
(F_{c}Sin
+mgcos)

------------

Consider all forces in x direction

F_{c}Cos
-mgsin
-Fr =0

F_{c}Cos
-mgsin
-(F_{c}Sin
+mgcos)
=0

F_{c}(Cos
-sin)
-mg(Sin+Cos)
=0

Divide by Cos

**F _{c}(1 -tan)
-mg(tan+)
=0**

F_{c} =mv^{2}/r = 1300*19^{2}/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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