H203 Dynamics - 1. Notes (1718) [For Upload]

DYNAMICS Content  Newton’s Law of motion  Linear momentum and its conservation Learning Outcomes Candidates should be able to: (a) state each of Newton’s laws of motion. (b) show an understanding that mass is the property of a body which resist s change in motion (inertia). (c) describe and use the concept of weight as the effect of a gravitational field on a mass. (d) define and use linear momentum as the product of mass and velocity. (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 simple 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 collision between two bodies, the relative speed of approach is e qual 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. References: Physics for Scientists and Engineers. Serway. College Physics. Sears and Zemansky. Useful applet: Url : http://iwant2study.org/lookangejss/02_newtonianmechanics_3dynamics/ejss_model_Momentum1D01 /Momentum1D01_Simulation.xhtml Look under Collision Carts, Atwood Machines, Newton Cradle Or https://phet.colorado.edu/en/simulation/legacy/collision-lab

Concept Map Newton’s Laws of Motion Newton’s 3rd Law Newton’s 1st Law 𝑭 𝒏𝒆𝒕 = ∆(𝒎𝒗 ) 𝒕 𝑭 𝒏𝒆𝒕 = 𝒎𝒂 𝑭 𝒏𝒆𝒕 = 𝟎 ⟺ ∆(𝒎𝒗) = 𝟎 Newton’s 2nd Law 𝒅𝑷 𝒅𝒕 ∝ 𝑭 𝒓𝒆𝒔𝒖𝒍𝒕𝒂𝒏𝒕 Inelastic Collisions Elastic Collisions Collisions 𝑽𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝒐𝒇 𝑨𝒑𝒑𝒓𝒐𝒂𝒄𝒉 = 𝑽𝒓𝒆𝒍𝒂𝒕𝒊𝒗𝒆 𝒐𝒇 𝑺𝒆𝒑𝒂𝒓𝒂𝒕𝒊𝒐𝒏 𝑷 𝒊 = 𝑷 𝒇 𝑬𝑲𝒊 = 𝑬𝑲𝒇 & 𝑷 𝒊 = 𝑷 𝒇 𝑬𝑲𝒊 > 𝑬𝑲𝒇 & Principle of Conservation of Momentum ∆𝑷 = 𝑭𝒏𝒆𝒕 dt

3.0 Introduction Dynamics is the branch of mechanics where the forces that act on a body are not in equilibrium. The vector sum of the forces gives a resultant force that causes the body to accelerate. This resultant force causes change in motion. In Kinematics, we learned how a body would move under constant acceleration, if we combine the knowledge from Dynamics and Kinematics, we will be able to predict the motion of a body when we know the forces acting on the body. In the seventeenth century, Sir Isaac Newton formulate d the three Newton’s laws of motion and it is the basis behind Newtonian Mechanics. Today, Newtonian mechanics is useful for many engineering efforts in our everyday scale, like how an artillery shell travels in air, and it explains many phenomena observed.