Chapter 5 The Laws of Motion

Chapter 5 Intro We’ve studied motion in terms of its position, velocity and acceleration, with respect to time. We now need to look at what causes motion, and changes to it. To do so, we will utilize three simple laws penned more than 300 years ago, by Sir Isaac Newton.

5.1 Force What is a force? – Any interaction that causes a change to an objects motion (acceleration) – Vector Quantity Dir, or unit vector notation) – Dimensions MLT -2, Units N (newtons) = kg m/s 2 Net Force- the vector sum of all forces acting on an object. (Total, resultant, unbalanced) Net force = zero, forces are balanced, a = 0. – Equilibrium (constant speed/rest)

5.1 Force Classes – Contact- forces enacted through physical contact between objects (applied, normal, friction etc.) – Field- forces enacted through empty space between objects (gravity, electric, magnetic) Should be noted that there is technically no such thing as a contact force -> electric force between charged subatomic particles (refer to atomic model) For the macroscopic level of classical physics, contact forces are sufficient.

5.1

Fundamental Forces – Gravitational (between objects with mass) – Electromagnetic (between charged particles) – Strong Nuclear Force (between protons/neutrons) – Weak Nuclear Force (involved in radioactive decay) Remember- rules for vector addition apply when finding Net Force (ΣF)

5.2 Newton’s 1 st Law and Inertial Frames Inertial Frame of Reference – A F.o.R. from which an object with zero interactions would seem to have zero acceleration – Ex: Train – Non Inertial FoR would observe an acceleration

5.2 Newton’s 1 st Law- – “In the absence of a net force, and view from an inertial reference frame, an object at rest remains at rest, and an object in motion continues in motion with constant velocity.” – An object’s tendency to resist changes to its rest/motion is called Inertia Quick Quiz Pg. 115

5.3 Mass Mass- quantification of Inertia – The more matter contained within an object the greater its resistance to changes in motion. (The greater the mass, the lesser the acceleration for a given force) – Scalar Quantity (no direction) – Fundamental Dimension M, units kg – Mass ≠ Weight

5.4 Newton’s 2 nd Law Newton’s 2 nd Law explains what happens to an object when a force acts on it. – “When observed from an Inertial reference frame, the acceleration of an object is proportional to the net force acting on it, and inversely proportional to its mass.” – – Broken into component equations

5.4 Quick Quizzes Pg 117 Example 5.1

5.5 Gravitational Force & Weight Gravitational Force – Local Force of Attraction to the Earth – F g = mg (from 2 nd Law applied to free fall) – Weight (magnitude of F g ) – m in this equation is called gravitational mass due to difference in behavior from inertial mass. (though they are equivalent in value in Newtonian dynamics) Quick Quizzes p. 119 Example 5.2, p. 120

5.6 Newton’s 3 rd Law “When two objects interact, the force (F 12 ) exerted by object 1 on object 2, is equal in magnitude and opposite in direction to the force (F 21 ) exerted by object 2 on object 1.” – Forces always occur in pairs – Force pairs always act on different objects.

5.6 Normal Force- (n or F n ) – Force of support provided to an object resting on a surface – Always perpendicular (normal) to the surface Free-body Diagrams- – Showing all of the forces acting only on a single object – Object often represented as a dot

5.6 Quizzes p. 122 Example 5.3

5.7 Applications of Newton’s Laws When we apply Newton’s Laws, we are only interested in external forces on a the object. – FBD only shows the forces acting on a single object. – Separate FBD for each object. Equilibrium- ΣF = 0 – Static Eq. ΣF = 0 while at rest – Dynamic Eq. ΣF = 0, while at constant velocity

5.7 Examples p – Equilibrium – Inclines – Multiple Objects – Non Inertial RF – Atwood/Pulley Systems

5.8 Friction When an object is in motion along a surface or through a viscous medium, there is resistance to the motion due to the interaction. – Friction- resistive force against the direction of motion (slippage). Static Friction- resists impending motion – Matches net force applied up to F s,max F s ≤ μ s F n Kinetic Friction- resists actual motion – Generally less than Fs, max F k = μ k F n

5.8

normal force is needed to calculate friction. – Fn is not always equal to mg Quick Quizzes Pg 133 Example Problems Pg