Static and Kinetic Friction, Rolling Friction - UNSOLVED PRACTICE SET

Q7. Distinguish between static friction, limiting friction, and kinetic friction. Draw a graph showing how friction varies with applied force.

Q8. State the laws of limiting friction. How does the coefficient of friction depend on the nature of surfaces?

Q9. Why is it easier to roll a barrel than to slide it? Explain the origin of rolling friction.

Q10. In your school, a student pushes a 20 kg desk across the floor. The desk doesn't move until the applied force reaches 60 N. Once moving, it can be kept moving with 40 N. Calculate μₛ and μₖ. (Take g = 10 m/s²)

Q11. A block is placed on an inclined plane. The angle is gradually increased until the block just begins to slide. If this angle is 30°, calculate the coefficient of static friction.

Q12. Why are ball bearings used in bicycle wheels and machine parts? Explain in terms of friction.

Q13. Explain the different types of friction with examples:

(i) Static friction

(ii) Limiting friction

(iii) Kinetic (sliding) friction

(iv) Rolling friction

Discuss the laws of friction and explain why rolling friction is much smaller than sliding friction. Include a graph showing the variation of friction with applied force.

Q14. A block of mass 10 kg is placed on a rough horizontal surface (μₛ = 0.6, μₖ = 0.4).

(a) Calculate the limiting friction.

(b) A horizontal force of 40 N is applied. Does the block move? Calculate the friction force.

(c) A horizontal force of 70 N is applied. Calculate the acceleration.

(d) Once moving, if the force is reduced to 50 N, what is the new acceleration?

(e) Calculate the minimum force required to keep the block moving at constant velocity.

Q15. Discuss the motion of a body on an inclined plane:

(a) Smooth inclined plane: derive expressions for acceleration and time of descent

(b) Rough inclined plane: derive the condition for the body to just begin sliding

(c) Show that the angle of repose equals the angle of friction

(d) A body is projected up a rough inclined plane: derive the expression for the distance travelled before coming to rest

Q16. A 5 kg block is placed on a rough inclined plane of angle 37° (sin 37° = 0.6, cos 37° = 0.8). The coefficient of static friction is 0.5 and kinetic friction is 0.4.

(a) Calculate the component of weight down the plane.

(b) Calculate the maximum static friction up the plane.

(c) Will the block slide down? If yes, calculate its acceleration.

(d) Calculate the force required up the plane to keep the block stationary.

(e) If projected up the plane at 5 m/s, how far will it travel before stopping?

Q17. A car of mass 1000 kg is moving at 20 m/s on a level road. The coefficient of kinetic friction between the tyres and the road is 0.8.

(a) Calculate the braking force required to stop the car.

(b) Calculate the minimum stopping distance.

(c) If the road is wet (μₖ = 0.3), calculate the new stopping distance.

(d) Explain why anti-lock braking systems (ABS) are designed to prevent wheel lock.

(e) Calculate the stopping distance on an upward incline of 10° (μₖ = 0.8).

Q18. In a school experiment, students measure the coefficient of friction between a wooden block and different surfaces.

(a) Describe an experiment to measure μₛ using an inclined plane.

(b) Describe an experiment to measure μₖ using a horizontal surface and ticker timer.

(c) A student records the following data: For wood on wood, limiting friction = 12 N, normal reaction = 30 N. Calculate μₛ.

(d) For the same surfaces, the student finds μₖ = 0.3. Explain why μₖ < μₛ.

(e) Suggest two methods to reduce friction in practical applications.