An automobile of mass travels at a steady along a level circular track of radius
PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion
Problem
An automobile of mass 1.2×103kg travels at a steady 20m/s along a level circular track of radius 50m. Each of the four wheels has mass 12kg and radius 0.30m. The tires roll without slipping.
While negotiating the curve, engineers wish to analyse two separate questions:
• Question A – What horizontal static friction force must act on the pavement to provide the required centripetal acceleration of the car’s centre of mass?
• Question B – What total frictional torque must act on each wheel rim to keep the wheels from skidding relative to the pavement?
A group of students debates whether to model the car as a single object or to track the wheels as separate rigid bodies.
(a) For Question A, choose the more appropriate model and justify your choice in terms of the physical quantity being sought.
(b) For Question B, choose the more appropriate model and justify your choice.
(c) Suppose a student treats the entire car, including its wheels, as a single object when answering Question B. Qualitatively describe how this modeling error will affect the numerical value the student obtains for the required frictional torque, and explain the physical reason for the discrepancy.
(d) Using the correct model for Question B, derive an algebraic expression for the minimum magnitude of the static frictional force on the pavement in terms of the given symbols and any necessary geometric parameters, then calculate its value for one wheel.
(e) Explain how your answer in part (d) would change if the wheels were replaced by lighter alloy versions with half the mass but the same radius, all other conditions remaining identical.