Question

A circular racetrack of
radius 300 m is banked at an angle of 15°
If the coefficient of friction between the
wheels of a race-car and the road is 0.2
what is the (a) optimum speed of the race-
car to avoid wear and tear on its tyres, and
(b) maximum permissible speed to avoid
slipping?​

Answer 1

(a) Optimum speed of car is

tanθ=

rg

v

2

v

2

=rgtanθ

=10×300×tan15

v

2

=780m/s

v=28m/s

(b) Maximum permissible speed to avoid slipping is

v

m

=

Rg(

1−μtanθ

μ+tanθ

)

=

300×10(

1−0.2tan15

0.2+tan15

)

=

1458.7

=38.19m/s

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Answer 2

Answer in attachment

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