Forces and the Laws of Motion Chapter 4. 4-1 Changes in Motion Objectives Describe how force affects the motion of an object Interpret and construct

Forces and the Laws of Motion

Chapter 4

4-1 Changes in Motion

ObjectivesDescribe how force affects the motion of an

object Interpret and construct free-body diagrams

Changes in Motion

Dynamics is an area of mechanics which seeks to explain why objects move as they doThis involves studying how forces affect

motion force – an action exerted on an object that

may change the object’s state of rest or motion

Changes in Motion

Often times a force acting on an object will cause the object’s velocity to change with respect to time – it’s accelerating Examples: throwing a baseball vs. catching a

baseball

Changes in Motion

A newton is the SI unit of forcenewton (N) – the amount of force required to

accelerate a 1 kg mass at 1 m/s2

Therefore, 1 N = 1 kg x 1 m/s2

Changes in Motion

Forces can act through contact or at a distanceContact forces are forces that result from the

physical contact between objects (push/pulls) Examples: pushing a cart, kicking a football, etc.

Field forces are force that do not involve the physical contact between objects

Examples: gravitational force, electromagnetic force, etc.

Force / Free-body Diagrams

Force is a vector quantityBoth the magnitude and the direction of the

force will influence how it affects the motion of an object.

The acceleration will be in the same direction as the force.

Force / Free-body Diagrams

Drawing Free-body Diagrams

Drawing Free-body Diagrams1) Identify the forces acting on the object and

the direction of the forces.

2) Draw a diagram to represent the isolated object.

3) Draw and label vector arrows for all external forces acting on the object.

4-2 Newton’s First Law

Objectives:Explain the relationship between the motion of

the object and the net force acting on the object

Determine the net force acting on an objectCalculate the force required to bring an object

to equilibrium

Newton’s First Law

It is a common misconception that if there are no forces acting on an object it will be at restConsider what happens when push a book

along a table vs. pushing it along a sheet of ice.

What happens? Why?


Galileo correctly concluded that it is an object’s nature to maintain its state of motion or rest

Newton further developed this idea into what has come to be known Newton’s First Law of Motion


Newton’s First Law of Motion: An object at rest remains at rest, and an

object in motion continues in motion with constant velocity (constant speed in a straight line) unless the object experiences a net external force.Sometimes referred to as the law of inertia


inertia – the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction

Mass is a measure of inertia of a bodyThe more mass that an object has, the harder

it is to change its state of motion (requires a greater force)

Pushing a car vs. a truck (starting from rest) Stopping a baseball vs. a bowling ball (same velocity)


Any object that is accelerating has to have a net force acting on it net force (ΣF) – the vector sum of all of the forces

acting on an object

If the net force is equal to zero, the object will have a constant velocity (acceleration = 0) Example: a book being slid at a constant velocity –

Why is it not accelerating?



Objects that are either at rest or moving with a constant velocity are said to be in equilibriumequilibrium – the state in which the net force

on an object is zero


4-3 2nd & 3rd Laws of Motion

Objectives:Describe an object’s acceleration in terms of

its mass and the net force acting on it.Calculate the direction and magnitude of the

acceleration caused by a known net force. Identify action-reaction pairs

Newton’s Second Law

Newton’s Second Law of Motion:

The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass.

Equation: ΣF = ma

net force = mass x acceleration


Acceleration is inversely proportional to mass. If the same force is applied to objects of

different masses: The object with the greater mass will experience a

smaller acceleration. The object with less mass will experience a greater

acceleration.


Acceleration is directly proportional to net force.When mass is constant:

Increasing the force increases the acceleration by the same factor.

Decreasing the force decreases the acceleration by the same factor.


Sample Problem C:

Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book toward Roberto. If the net force acting on the book is 1.6 N to the right, what is the book’s acceleration?


U: a (m/s2)

K: m = 2.2 kg

ΣF = 1.6 N to the right

ΣF = ma

1.6 N = (2.2 kg)a

a = 0.73 m/s2 to the right

Newton’s Third Law

Newton recognized that a single isolated force cannot existConsider what happens when a person

wearing ice skates pushes on the wall of an ice rink…

Forces always exist in pairs – Newton described this in his third law of motion


Newton’s Third Law of Motion:

Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object.Equal magnitude, opposite direction


Generally stated: For every action there is an equal and opposite reaction.The objects exerting the forces on each other

are referred to as the action-reaction pair These forces occur at the same time and act on

different objects


Consider the following examples:What are the action-reaction forces involved

when a person hammers a nail into a piece of wood?

How does a rocket work?


Field forces also exist in pairsWhen an apple falls from a tree it accelerates

toward the Earth because the Earth exerts a gravitational force on the apple.

If this is the action force, what is the reaction force?

4-4 Everyday Forces

Objectives:Explain the difference between mass and

weight.Find the direction and magnitude of normal

forces.Describe air resistance as a form of friction.Use coefficients of friction to calculate

frictional force.

Weight

weight (Fg) – a measure of the magnitude of the gravitational force exerted on an objectSince weight is the magnitude of the

gravitational force acting on an object, it is a scalar quantity

Will the weight of an object be constant?

Weight vs. Mass

Since the gravitational force between objects varies by location, weight will vary by an object’s location.

Mass does not vary by location - it is an inherent property of the object.Example: A 1.5 kg hammer will have a weight

of 14.7 N near the Earth’s surface, but it will weigh 2.4 N on the Moon (it’s mass is 1.5 kg in both locations)

Weight

The force of gravity can be calculated by the following equation:

Fg = mag

ag represents the acceleration due to gravity Near Earth’s surface ag = g = 9.8 m/s2, so:

Fg = mg

Weight

What is the weight of an astronaut on Earth (g = 9.8 m/s2) and on the Moon

(ag = 1.6 m/s2) if the astronaut’s mass is 81.6 kg?

The Normal Force

A television set is at rest on a table.The force of gravity is constantly acting on the

TV. Is the TV in equilibrium? If so, how is it in

equilibrium?

The Normal Force

normal force (Fn) – a force that occurs when objects come in contact with each other and acts perpendicular to the shared surface In the absence of other forces, Fn is equal

and opposite to the component of Fg that is perpendicular to the contact surface.

Fn = mg cos θ

The Normal Force

The Force of Friction

Friction is a force that resists motion (static friction) or opposes the motion of objects that are in contact (kinetic friction)

Is there any friction actingon the jug of orange juicepictured to the right?


static friction (Fs) – the force that resists the initiation of sliding motion between two surfaces that are in contact and at rest


When a force is applied to an object that remains at rest, the Fs is always equal an opposite to the component of the applied force that is parallel to the surface If the applied force increases, Fs increases

If the applied force decreases, Fs decreases

The Force of Friction Once the applied force is as great as it

can be without causing the object to move, the static friction is at its maximum value (Fs,max)

Increasing the applied force further will cause the object to move and it then be experiencing kinetic friction


kinetic friction (Fk) – the force that opposes the movement of two surfaces that are in contact and are sliding over each otherThe force of Fk is less than Fs,max

The net force acting on the object is equal to the difference between the applied force and the force of kinetic friction

ΣF = Fapplied - Fk


The force of friction is approximately proportional to the normal forceExample: It is easier to push a chair across

the floor at a constant speed than it is to push a heavier desk at the same speed


The force of friction can only be approximately calculated

This is because it is a macroscopic

effect caused by a complex interaction

of forces at the microscopic level.


In addition to the Fn, the force of friction also depends on the surfaces in contactThe quantity that expresses this concept is the

coefficient of friction

coefficient of friction (μ) – the ratio of the magnitude of the force of friction between two objects in contact to the magnitude of the normal force acting on the objects


The force of friction can be calculated with the following equations:

Static Friction: Fs ≤ μsFn

Kinetic Friction: Fk = μkFn


Air Resistance

Whenever an object moves through a fluid substance, such as air or water, the fluid provides a force that opposes the objects motion

Air resistance will increase on an object in free fall as the objects speed increases When the upward force of air resistance is equal in

magnitude to the downward force of gravity the object reaches terminal velocity

Fundamental Forces

The four fundamental forces are all field forcesElectromagnetic ForceGravitational ForceStrong Nuclear ForceWeak Nuclear Force

Fundamental Forces

The strong and weak nuclear forces have very small ranges and are not directly observable

The electromagnetic and gravitational forces act over long rangesThe strong nuclear force is the strongest of

the fundamental forces; gravity is the weakest

Documents

Forces and the Laws of Motion Chapter 4. 4-1 Changes in Motion Objectives Describe how force affects the motion of an object Interpret and construct