## Problems Banking of a Road:

### Formulae Conversions 1. A coin kept on a horizontal rotating disc has its centre at a distance of 0.1 m from the axis of rotation of the disc. If the coefficient of friction between the coin and the disc is 0.25, find the speed of the disc at which the coin would be about to slip off.
2. A coin kept on a horizontal rotating disc has its centre at a distance of 0.25 m from the axis of rotation of the disc. If m = 0.2, find the angular velocity of the disc at which the coin is about to slip off. ( g = 9.8 m/s²)
3. A coin just remains on a disc rotating at 120 r.p.m. when kept at a distance of 1.5 cm from the axis of rotation. Find the coefficient of friction between the coin and the disc.
4. With what maximum speed a car can be safely driven along a curve of radius 40 m on a horizontal road, if the coefficient of friction between the car tyres and road surface is 0.3 ? ( g = 9.8 m/s²)
5. A coin just remains on a disc rotating at a steady rate of 180 rev/min if kept at a distance of 2 cm from the axis of rotation. Find the coefficient of friction between the coin and the disc.
6. A coin kept with its centre at a distance of 9 cm from the axis of rotation of a disc starts slipping off when the disc speed reaches 60 r.p.m. Up to what speed will the coin remain on the disc if its centre is 16 cm from the axis of rotation of the disc?
7. A coin placed on a turn table rotating at 30 r.p.m. revolves with the table without slipping provided it is not more than 12 cm away from the axis. How far from the axis can the coin be placed so that it revolves with the turn table without slipping if the speed of rotation is 45 r.p.m.?
8. Find the maximum speed at which a car can be safely driven along a curve of 100 m radius. The coefficient of friction between tyres and surface of road is 0.2.
9. A car travelling at 18 km/h just rounds a curve without skidding. If the road is plane and the coefficient of friction between the road surface and the tyres is 0.25, find the radius of the curve.
10. A car can just go around a curve of 20 m radius without skidding when travelling at 36 km/h. If the road is plane, find the coefficient of friction between the road surface and tyres.
11. To what angle must a racing tract of radius of curvature 600 m be banked so as to be suitable for a maximum speed of 180 km/h?
12. A curve in the road is in the form of an arc of a circle of radius 400 m. At what angle should the surface of road be laid inclined to the horizontal so that the resultant reaction of the surface acting on a car running at 120 km/h is normal to the surface of road?
13. A vehicle enters a circular bend of radius 200 m at 72 km/h. The road surface at the bend is banked at 10°. Is it safe? At what angle should the road surface be ideally banked for safe driving at this speed ? If the road is 5m wide, what should be the elevation of the outer edge of road surface above the inner edge?
14. Find the minimum radius of an arc of a circle that can be negotiated by a motorcycle riding at 21 m/s if the coefficient of friction between the tyres and the ground is 0.3. What is the angle made with the vertical by the motorcyclist? g=9.8 m/s² .
15. What is the angle of banking necessary for a curved road of 50 m radius for safe driving at 54 km/h? If the road is not banked, what is the coefficient of friction necessary between the road surface and tyres for safe driving at this speed?
16. A train of mass 105 kg rounds a curve of radius 150 m at a speed of 20 m/s. Find the horizontal thrust on the outer rail if the track is not banked. At what angle must the track be banked in order that there is no thrust on the rail? g= 9.8 m/s².
17. The radius of curvature of a metre gauge railway line at a place where the train is moving at 36 km/h is 50 m. If there is no side thrust on the rails find the elevation of the outer rail above the inner rail.
18. Find the angle of banking of the railway track of radius of curvature 3200 m if there is no side thrust on the rails for a train running at 144 km/h. Find the elevation of the outer rail above the inner one if the distance between the rails is 1.6 m.
19. A metre gauge train is moving at 60 km/hr along a curved rod of radius of curvature 500 m at a certain place. Find the elevation of outer rail over the inner rail, so that there is no side pressure on the rail. (g = 9.8 m/s²)
20. A coin is placed at a distance 10 cm from the centre of a turntable of radius 1 m just begins to slip, when the turn table rotates at a speed of 90 r.p.m. Calculate the coefficient of static friction between the coin and the turntable.
21. A motor cyclist at a speed of 5 m/s is describing a circle of radius 25 m. Find his inclination with the vertical. What is the value of coefficient of friction between the road and tyres.
22. A motor van weighing 4400 kg rounds a level curve of radius 200 m on unbanked road at 60 km/hr. What should be the minimum value of the coefficient of friction to prevent skidding? At what angle the road should be banked for this velocity?
23. A circular road course track has a radius of 500 m and is banked to 10°. If the coefficient of friction between the road and tyre is 0,25. Compute (i) the maximum speed to avoid slipping (ii) optimum speed to avoid wear and tear of the tyres.
24. A rotor has a diameter of 4.0 m. The rotor is rotated about central vertical axis. The occupant remains pinned against the wall. When the linear velocity of the drum is 8 m/s. Compute the coefficient of static friction between the wall of the rotor and the clothings of occupant. Also calculate the angular velocity of the drum. How many revolution it will make in a minute?

1. 0.495 m/s
3. 0.2415
4. 10.84 m/s
5. 0.7249
6. 45 r.p.m.
7. 5.33 cm
8. 14m/s
9. 10.2m
10. 0.5102
11. 23° 18’
12. 15° 49’
13. Unsafe; 11° 32’ ; 1 m
14. 150 m; 16° 42’
15. 24° 40’; 0.4592
16. 2.67 x 105 N; 15° 13’
17. 0.2 m
18. 2°55’; 81 mm
19. 0.0567 m
20. 0.9055
21. 5°49’, 0.1020
22. 0.1418, 8°4’
23. 46.70 m/s, 29.39 m/s
24. 0.3063, 4 rad/s, 38.19 r.p.m.