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 (mag @ Dir, or unit vector notation)– Dimensions MLT-2 , Units N (newtons) = kg m/s2

• 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

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 1st 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 1st 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 2nd Law

• Newton’s 2nd 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

aF m

xx maF yy maF zz maF

5.4

Quick Quizzes Pg 117Example 5.1

5.5 Gravitational Force & Weight

• Gravitational Force– Local Force of Attraction to the Earth– Fg = mg (from 2nd Law applied to free fall)

– Weight (magnitude of Fg)– 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. 119Example 5.2, p. 120

5.6 Newton’s 3rd Law

• “When two objects interact, the force (F12) exerted by object 1 on object 2, is equal in magnitude and opposite in direction to the force (F21) 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 Fn) – 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 124-130– 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 Fs,max

Fs ≤ μsFn

• Kinetic Friction- resists actual motion– Generally less than Fs, max

Fk = μkFn

5.8

5.8

• normal force is needed to calculate friction.– Fn is not always equal to mg

Quick Quizzes Pg 133Example Problems Pg 134 - 136