Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
905 views
in Physics by (19.1k points)

A car (mass m) is traveling with constant velocity  v along a banked circular curve (radius r, angle of slope α), The coefficient of static friction µ0 between the tires of the car and the surface of the road is given

 Determine the region of the allowable velocities so that sliding (down  or up the slope ) not take place.

1 Answer

+1 vote
by (10.1k points)
selected by
 
Best answer

 We model the car as a point mass and express the acceleration vector in terms of the Serret-Frenet frame. Then the equation of motion in the direction of the normal vector is (see the free -body diagram)

man=N SIN α+H cos α

Since the car does not move in the vertical direction we can apply the equilibrium condition 

We now solve these two equations for the normal force N and the force of static friction H:

H = man cosα −mg sin α , 

N = man sin α +mg cosα .

The car does not slide if the condition of static friction

is satisfied. With an = v2/r this leads to the allowable region of the velocity:

This is displayed for µ = 0.3 as a function of the angle α in the figure.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...