Q37 of 42 Page 35

A racing car travels on a track (without banking) ABCDEFA (Fig. 5.10). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is μ = 0.1. The maximum speed of the car is 50 m s-1. Find the minimum time for completing one round.


To find the total time, we find the time of each segments.

Segment:ABC


Here, the frictional force is



And the centripetal force is



Therefore,




Segment:DEF


Again, the centripetal force is equal to friction.




Now, the time taken is distance/speed.


For ABC, the distance is



And for DEF we have



Therefore,



Hence the time taken is 86.3 seconds.


More from this chapter

All 42 →
35

When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.

 36

Figure 5.9 shows (vx ,t ),and( (vy ,t) diagrams for a body of unit mass. Find the force as a function of time.


 38

The displacement vector of a particle of mass m is given by r (t) = î A cos ωt + ĵ B sin ωt.

(a) Show that the trajectory is an ellipse.


(b) Show that F = −mω2r


 39

A cricket bowler releases the ball in two different ways

(a) giving it only horizontal velocity, and


(b) giving it horizontal velocity and a small downward velocity. The speed vs at the time of release is the same. Both are released at a height H from the ground. Which one will have greater speed when the ball hits the ground? Neglect air resistance.