Questions on friction

Type A. Questions On Coefficient of friction

1. A ball rolled on ice with a velocity of 14m s^- 1 comes to rest after travelling 40 m. Find the coefficient of friction. Given g = 9.8 m s ^- 2

[Ans. 0.25]

2. The coefficient of friction between a horizontal surface and a moving body is u. With what speed must a body of mass m be projected parallel to the surface to travel a distance S before stopping?

[Ans. (2μgS)^1/2 ]

3. An automobile is moving on a horizontal road with a speed v. If the coefficient of friction between the tyres and the road is μ , show that the shortest distance in which the automobile can be stopped in v²/2μ g.

4. A suitcase is gently dropped on a conveyor belt moving with a speed of 4.9 m s-¹. If the coefficient of friction between the belt and the suitcase is 0.7, how far will the suitcase move on the belt before coming to rest ?

[Ans. 1.75 m]

Type B. Questions On Angle of friction

5. If the coefficient of friction is 0.6, calculate the angle of friction.

[Ans. 31°]

6. A force of 5 kgf is just sufficient to pull a block of weight 8 kgf over a horizontal surface. Find the angle of friction.

[Ans. 32°]

Type C. Questions On Angle of repose

7. A cubical block rests on a plane of = 1/√3. Determine the angle through which the plane be inclined to the horizontal so that the block just slides down.

[Ans. 30°]

8. A mass of 4 kg rests on a horizontal plane. The plane is gradually inclined until at an angle 15 with the horizontal, the mass just begins to slide. What is the coefficient of static friction between the block and the surface?

[Ans. 0.268]

9. A mass of 100 kg is resting on a rough inclined plane of angle 30°. If the coefficient of friction is 1/√3, find the greatest and the least forces that acting parallel to the plane in both cases, just maintain the mass in equilibrium.

[Ans. 100 kgf, zero]

Type D. Questions On Motion against friction

10. A block of mass 2 kg rests on a plane inclined at 30° with the horizontal. The coefficient of friction between the block and the surface is 0.7. Calculate the frictional force acting on the block.

[Ans. 9.8 N]

11. A horizontal force of 1.2 kgf is applied to a 1.5 kgf block, which rests on a horizontal surface. If the coefficient of friction is 0.3; find the acceleration produced. Given, g = 9.8 m s-2.

[Ans. 4.9 m s^-2]

12. A body is in limiting equilibrium on a rough inclined plane inclined at an angle of 30° with the horizontal. Calculate acceleration with which the body will slide down, when inclination of the plane is changed to 45°.

Given g=9.8 m/s^2.

[Ans. 2.93 m/s²]

13. A metal block is placed on a metal plane inclined at an angle of 30°. If the mass of the block is 0.5 kg and coefficient of friction is 0.2, what force must be applied (a) to keep the body from sliding down the plane, (b) to move it up the plane, (c) to move it up with an acceleration of 0.2 m/s^-2.

[Ans. 1.60 N ; 3.30 N ; 3.40 N]

14. A block is gently placed at the top of an inclined plane 640 cm long. Find the time taken by the block to slide down to the bottom of the plane, which makes an angle of 30° with the horizontal. Coefficient of friction = 0.2 and

g = 980 cm/s^2,

[Ans. 2 s]

15. A block slides down an inclined plane having inclination of 30° with the horizontal. Starting from rest, it covers 13.5 m in the first three seconds. Find the coefficient of kinetic friction between the block and the inclined plane.

[Ans. 0.224]

16. A train of mass 150 metric ton is drawn up an incline of 1 in 100 at the rate of 36 km/h. If resistance due to friction is 12 newton per ton, calculate the power of the engine.

[Ans. 165 kW]

17. Calculate the power of the engine which can pull a train of mass 250 quintal up an incline of 1 in 100 at the rate of 108 km/h, the resistance due to friction being 20 newton per quintal.

[Ans. 224.1 kW]

18. A block of mass 0-1 kg is held against a wall by applying a horizontal force of 5 N on the block. If coefficient of friction between the wall and the block is 0.5, what is the magnitude of frictional force acting on the block?

Given, g = 9.8 m/s^2.

[Ans. 0.98 N]