Phy 201: General Physics I

Chapter 4: Forces & Newton’s Laws of Motion

Lecture Notes

Newton’s 1st Law

• Also known as the “Law of Inertia” • Key Points:

– When an object is moving in uniform linear motion it has no net force acting on it

– When there is no net force acting on an object, it will stay at rest or maintain its constant speed in a straight line

• This property of matter to maintain uniform motion is called inertia

• Stated a simpler way: Nature is lazy! {i.e. matter resists changes in motion}

F=0 a = 0 {v = constant}

Every object continues in its state of rest, or of motion unless compelled to change that state by forces impressed upon it.

Newton’s 2nd Law• When a net force is exerted on an object its velocity will

change:

• The time rate of change of motion (acceleration) is related to:– Proportional to the size of the net force– Inversely proportional to the mass of the object (i.e. its inertia)

• The relationship between them is

or

• The direction of will always correspond to the direction of

ˆ ˆx y

F 1a= = F x + F y

m m

ˆ ˆ

x yF = ma= m a x + a y

...1 2 3F=F F F dv

dt

a

F

Newton’s 3rd LawWhen an object exerts a force on a second object, the second

object exerts an equal but oppositely directed force on the first object

where:

Consequences:• Forces always occur in action-reaction pairs (never by themselves)• Each force in an action-reaction pair acts on a different object

Important: • Newton’s 3rd law identifies the forces produced by interactions

between bodies• Newton’s 2nd law defines the accelerations that each object

undergoes

1 on 2FBody 1 Body 2

2 on 1F

2 on 1 1 on 2F F

Free-Body Diagrams• Simplified drawing of a body with only the forces acting on

it specified• The forces are drawn as vectors• Free-Body diagrams facilitate the application of Newton’s

2nd Law

Examples:

Joey

W

Joey in “Free Fall”

Joey

W

floorF

Joey standing on a floor

Joey

W

floorF

Joey getting slapped while standing on a floor

slapF

Types of Forces

Non-Contact:• Gravitational• Electric• Magnetic

Contact:• Normal• Frictional• Tension

In our world, forces can be categorized as one of 2 types:

• Non-Contact: force is exerted over a distance of space with out direct contact (a.k.a. “action-at-a-distance” forces)

• Contact: forces is exerted due to direct contact

(Note: at the microscopic level, ALL forces are non-contact)

• In either case, Newton’s 3rd law still applies to the forces present

Examples of each type of force:

Mass vs. Weight• The “weight” of an object is the gravitational force

exerted on it by the gravitational attraction between the object and its environment:

• On the surface of the Earth, the gravitational force is referred to as weight:

• Mass is a measure of an object’s inertia (measured in kg)

– Independent of object location• Weight is the effect of gravity on an object’s mass

(measured in N)– Determined by the local gravitational acceleration

surrounding the object

ˆG G G G G G GF =ma =ma y F =m a F =ma

ˆG GF = W = (-mg)y F = W = mg

Notes:• Mass is a measure of an object’s inertia (measured in kg)

– Independent of object location• Weight is the effect of gravity on an object’s mass (measured in N)

– Determined by the local gravitational acceleration surrounding the object

Normal Force

• The “support” force between 2 surfaces in contact• Direction is always perpendicular (or normal) to the plane of the

area of contactExample: the force of floor that supports your weight

Consider standing on a scale on the floor of an elevator. The reading of the scale is equal to the normal force it exerts on you:Task: Construct free body diagrams for the scale:

1. At rest2. Constant velocity3. Accelerating upward4. Accelerating downward

Examples of Normal Force

Surface Frictional Forces• When an object moves or tends to move along a surface, there

is an interaction between the microscopic contact points on the 2 surfaces. This interaction results in a frictional force, that is– parallel to the surface– opposite to the direction of the motion

• There are 2 types of surface friction:– Static (sticking)– Kinetic (sliding)

Static Friction• Static (or sticking) friction ( ) is the frictional force

exerted when the object tends to move, but the external force is not yet strong enough to actually move the object.

• Increasing the applied force, the static frictional force increases as well (so the net force is zero) . The force just before breakaway is the maximum static frictional force.

• The direction of the static friction force is always in opposition to the external forces(s) acting on the body

• The magnitude of the maximum static friction force is:

Where:– is the coefficient (maximum) of static friction– FN is the normal force

max maxs s Nf =μ F

sf

maxsμ

Kinetic Friction• Kinetic frictional force ( ) is the frictional force exerted by the

surface on an object that is moving along the surface• Kinetic frictional force:

– always opposes the direction of the motion– the direction is along the surface (parallel to the surface)

• The magnitude of the kinetic frictional force depends only on the normal force and the properties of the 2 surfaces in contact

Where:– k is the coefficient of kinetic friction– FN is the normal force

Notes:– Kinetic friction is independent to the rate of travel of the sliding body– Kinetic friction is independent to the surface area of contact

k k Nf =μ F

kf

Tension Force

• Force applied through a rope or cable• When the rope or cable is mass-less (negligible

compared to the bodies it is attached to) it can be treated as a connection between 2 bodies– No mass means no force needed to accelerate rope– Force of pull transfers unchanged along the rope – Action force at one end is the same as the Reaction

force at the other end

• When attached to a pulley the tension force can be used to change the direction of force acting on a body

• Calculation of a tension force is usually an intermediate step to connecting the free-body diagrams between 2 attached objects

Tension Applications

• With Pulley (flat surface):

• Inclined Plane:

• Atwood Machine:

M1

M2

M1

M2

M1 M2

Sir Isaac Newton (1642-1727)• Greatest scientific mind of the late 17th century• Invented the “calculus” (independently but

simultaneously with Gottfried Wilhelm Leibnitz)

• Among his accomplishments included:– A Particle Theory Light & Optics– A Theory of Heat & Cooling

• Established 3 Laws of Motion• Proposed the Law of Universal Gravitation (to

settle a parlor bet proposed by Christopher Wren!!)– The competition was actually between Edward

Haley & Robert Hooke– This theory successfully explained planetary motion

and elliptical orbits

“If I have seen further it is by standing on the shoulders of giants.”