A car is traveling around a circular portion of road banked at an incline of 35 degrees to the horizonal. If the radius ofthe turn is 100 m and the coefficient of static friction is 0.60A) What is the minimum speed the car can take the turn without losing traction?B) At what speed would the static friction be zero?

Question
Asked Oct 15, 2019

A car is traveling around a circular portion of road banked at an incline of 35 degrees to the horizonal. If the radius of
the turn is 100 m and the coefficient of static friction is 0.60
A) What is the minimum speed the car can take the turn without losing traction?
B) At what speed would the static friction be zero?

check_circleExpert Solution
Step 1

The free body diagram for the above question is given below,

 

Je
FREE BODY DIA GRAM OF THE
CAR ON A BANKED ROAD
FOR THE GIVEN SCENARIO
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Je FREE BODY DIA GRAM OF THE CAR ON A BANKED ROAD FOR THE GIVEN SCENARIO

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Step 2

a)

 

The direction of the static frictional force fs is pointing upwards the slope since the car is maintaining just enough speed vmin to stop itself from sliding down.

The self-adjustable static frictional force fs will prevent the the car from losing traction and will point upwards the slope.

The equations governing the motion of the car on the banked circular road from the free body diagram are,

From the Newton’s second law of motion, it can be inferred that,

mv
Ση-
F
ΣΕ-0
F 0
II
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mv Ση- F ΣΕ-0 F 0 II

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Step 3

The frictional force fs  is expres...

N
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N

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