HCI 03 Dynamics Lecture Notes

Hwa Chong Institution (College) H2 Physics C1 2023 1 Chapter 3 Dynamics “Although you can get a strike by hitting the head pin square-on, it is not a very high percentage shot. Hitting the pins in "the pocket", which is the gap between the head pin and the next pin on the right (the 3-pin) for right handed bowlers, and the next pin to the left (the 2-pin) for lefties, will strike with the most consistency.” (Neil Lazarski, “How to Raise Your Bowling Average”)

Hwa Chong Institution (College) H2 Physics C1 2023 2 H2 Physics Syllabus 9749 Topic 3: Dynamics Content  Newton’s laws of motion  Linear momentum and its conservation Learning Outcomes Students should be able to: (a) state and apply each of Newton’s laws of motion. (b) show an understanding that mass is the property of a body w hich resists change in motion (inertia). (c) describe and use the concept of weight as the force experie nced by a mass in a gravitational field. (d) define and use linear momentum as the product of mass and v elocity. (e) define and use impulse as the product of force and time of impact. (f) relate resultant force to the rate of change of momentum. (g) recall and solve problems using the relationship F = ma, appreciating that resultant force and acceleration are always in the same direction. (h) state the principle of conservation of momentum. (i) apply the principle of conservation of momentum to solve si mple problems including inelastic and (perfectly) elastic interactions between two bodies in one dimension. (Knowledge of the concept of coefficient of restitution is not required.) (j) show an understanding that, for a (perfectly) elastic colli sion between two bodies, the relative speed of approach is equal to the relative speed of separation. (k) show an understanding that, whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place. Topic 4: Forces (Part) Learning Outcomes Students should be able to: (b) describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate. (c) show a qualitative understanding of normal contact forces, frictional forces and viscous forces including air resistance. (No treatment of the coefficients of friction and viscosity is required.) (d) show an understanding that the weight of a body may be take n as acting at a single point known as its centre of gravity.

Hwa Chong Institution (College) H2 Physics C1 2023 3 Contents 3.1  Introduction ....................................................................................................................................... 4  3.1.1  Types of Forces ........................................................................................................................... 4  3.1.2  Weight .......................................................................................................................................... 5  3.1.3  Contact Forces ............................................................................................................................. 6  3.1.4  Tension ........................................................................................................................................ 7  3.2 Newton’s Laws of Motion .................................. ............................................................................... 8  3.2.1  Newton's 1st Law ......................................................................................................................... 8  3.2.2  Linear Momentum ........................................................................................................................ 8  3.2.3  Newton's 2nd Law ...................................................................................................................... 10  3.2.4  Impulse ....................................................................................................................................... 11  3.2.5  Newton’s 2nd Law for Constant Mass ......................................................................................... 13  3.2.6  Newton’s 3rd Law ........................................................................................................................ 16  3.3   Principle of Conservation of Linear Momentum ............................................................................. 18  3.3.1  Two-body Systems ..................................................................................................................... 20  3.3.2   Types of Collisions ..................................................................................................................... 21 Appendix A: Static and Kinetic Friction ..................................................................................................... 27  Appendix B: Newton’s Law in Car Safety ................................................................................................. 28 Tutorial 3: Dynamics ................................................................................................................................. 29  Self-Review Questions ................................................................................................................................. 29  Discussion Questions ................................................................................................................................... 31  Videos of Lecture Examples can be found at https://youtube.com/playlist?list=PL_b5cjrUKDlYDkaMJ2sKNvZNiASvpiSfT

Hwa Chong Institution (College) H2 Physics C1 2023 4 3.1 Introduction Dynamics is the branch of classical mechanics concerned with the study of forces and their effects on motion. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion. 3.1.1 Types of Forces Broadly speaking, forces may be categorized into two kinds: contact forces and non-contact forces. 3.1.1.1 Contact Forces Forces acting between two bodies that are in physical contact. Contact forces Description Friction Force that resists the relative motion or the tendency for relative motion between two surfaces that are in contact. Normal contact force Net electrostatic repulsion between two surfaces that are in contact. Contact force Vector sum of friction and normal contact force, meaning the total contact force. Spring force Force exerted by one end of a spring when the spri ng is extended or compressed from its natural length. The spring forces acts throughout a spring, in both directions. Tension Force exerted by one end of a string/rope which is bein g pulled taut. The tension is constant throughout the string/rope and acts in both directions. Upthrust Net upward force exerted by the fluid on a body fully or partially submerged in the fluid. Viscous drag force Force that resists a body moving relative to a fluid. Air resistance Drag force exerted by air on a body moving in ai r. Air resistance is a specific form of drag. 3.1.1.2 Non-contact Forces Forces acting between two bodies which are NOT in physical contact (separated by a distance). This characteristic of the force is described as action-at-a-distance. Non-contact forces Description Physical property of a body on which the force acts on. Gravitational force Attractive force exerted between masses. Ma ss Electric force Attractive/repulsive force exerted between elect rically charged bodies. Electric charge Magnetic force Force exerted between currents Moving charges

Hwa Chong Institution (College) H2 Physics C1 2023 5 3.1.2 Weight The weight of a body is due to the body being in a gravitationa l field. In most cases, the object of interest is close to the Earth and its