Laws of Motion

Kinematics describes motion, but it does not explain what causes it. This chapter answers that question through Newton's three laws of motion. It begins with Aristotle's mistaken idea that a force is needed to keep a body moving and Galileo's concept of inertia. Newton's first law states that a body continues in its state of rest or uniform motion unless an external force acts on it. The second law relates force to the rate of change of momentum, F = dp/dt = ma, and leads to the idea of impulse. The third law states that to every action there is an equal and opposite reaction, acting on a different body. You will study the conservation of momentum, with examples such as the recoil of a gun and rocket motion. The chapter covers the equilibrium of a particle under concurrent forces, common forces in mechanics, static and kinetic friction, and rolling friction. It also explains the dynamics of uniform circular motion, including a car on a level road and on a banked road.

Detailed Worksheet: Laws of Motion Section A - Definitions (10 marks) 1. State Newton's first law of motion and define inertia. (2 marks) 2. Define impulse and write its SI unit. (2 marks) 3. Why does a cricketer draw his hands back while catching a fast ball? (2 marks) 4. State the law of conservation of linear momentum. (2 marks) 5. Define the angle of repose and relate it to the coefficient of static friction. (2 marks) Section B - Calculations and Applications (15 marks) 6. A 0.15 kg ball moving at 12 m/s is hit back along its line of approach at 12 m/s. Find the impulse given to the ball. (3 marks) 7. A 4 kg gun fires a 0.02 kg bullet at 400 m/s. Find the recoil speed of the gun. (3 marks) 8. A man of mass 60 kg stands on a weighing scale in a lift. Find the reading when the lift moves up with an acceleration of 2 m/s^2 and when it falls freely. Take g = 9.8 m/s^2. (3 marks) 9. A 20 kg block is pushed along a horizontal floor by a force of 100 N. If the coefficient of kinetic friction is 0.3, find its acceleration. (3 marks) 10. A stone of mass 0.25 kg tied to a string 1.5 m long is whirled in a horizontal circle at 40 rev/min. Find the tension in the string. (3 marks) Section C - Diagrams (10 marks) 11. Draw the free-body diagram of a block resting on a rough inclined plane. (4 marks) 12. Draw the forces acting on a car taking a turn on a banked road. (3 marks) 13. Draw the free-body diagrams of two masses hanging over a frictionless pulley (Atwood machine). (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. State Newton's second law and derive F = ma from it. Show that the first law is contained in the second law. (5 marks) 15. Two masses of 8 kg and 12 kg are connected by a light string over a frictionless pulley. Find the acceleration of the masses and the tension in the string. Take g = 10 m/s^2. (5 marks) 16. Derive the expression for the maximum safe speed of a car on a banked road with friction. Find the optimum speed on a road of radius 300 m banked at 15 degrees, taking tan 15 = 0.268 and g = 9.8 m/s^2. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Take g = 9.8 m/s^2 unless stated otherwise. Draw free-body diagrams where helpful.