UNIT XX: DYNAMICS AND NEWTON’S LAWS

•  DYNAMICS is the branch of mechanics concerned with the forces that cause motions of bodies

•  FORCE is a quantitative interaction between two (or more) objects. Forces push or pull. •  A contact force occurs when two or more bodies touch •  A “distance” force refers to phenomena like gravity or magnetism, where the force is exerted “at a distance” or through space.

•  Force is a vector.

•  The application of a force causes a change in an object’s acceleration. Force and acceleration are directly proportional.

•  Force is directly proportional to the mass of an object.

• Unbalanced forces CAUSE an object to accelerate (either speed up or slow down).

•  Balanced forces on an object mean acceleration = 0 m/s2

I. Definition of FORCE

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II. Types of forces and their symbolism

ContactForces

Fric'onal

Tension

Normal

AirResistance

Applied

Spring

DistanceForces

Gravita'onal

Electrical

Magne'c

FgravFfrictFtensFnorm

FairFapp

Fspring

Forces acting on an object are represented with vector arrows labeled with the appropriate force symbol

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Felectror E

B

III. Illustrating 1-dimensional forces with Free Body Diagrams

•  A FREE BODY DIAGRAM is a drawing that illustrates the forces acting on an object •  Free-body diagrams must show all the forces which exist for the object in the given situation. •  A 1-dimensional force means that the force acts either vertically (up or down) or horizontally (left or right)

Situation: Box resting on a table

Fnorm

Fgrav

The normal force is a force that exists when two objects are in contact. The box pushes down on the table but the table exerts an upward force on the box “Normal” means “perpendicular to”. The normal force will be perpendicular to the surface applying the force.

Gravitational force always points down. The weight of an object quantifies the force due to gravity.

THESE FORCES ARE BALANCED. ACCELERATION IS ZERO. NOTICE THE VECTORS HAVE THE SAME LENGTH (MAGNITUDE) BUT WORK IN OPPOSING DIRECTIONS.

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Situation: Box pushed to the right, with friction

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Situation: Rain drop falling from the sky, no air resistance

Fgrav

Situation: Rain drop falling from the sky, with air resistance

Fgrav

Fair

Fnorm

Fgrav

FappFfrict

air resistance is a frictional force that pushes against a moving object.

UNBALANCED FORCE

ACCELERATING BODY

UNBALANCED FORCE

ACCELERATING BODY

The frictional force works against the applied force used to slide the box. If the applied force exceeds the frictional force, forces are unbalanced and the box will accelerate. Later we will distinguish between sliding and static friction.

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Can a moving object have balanced forces?

YES, as long at the object is not accelerating (this is was one of Newton’s “breakthrough” ideas, not intuitive, and we will discuss it more later). If the object IS accelerating, the forces acting on it are unbalanced.

Situation: Box was pushed to the right, no friction or air resistance

Fnorm

Fgrav

The box was pushed from the left. It is moving to the right. It will move at constant velocity (zero acceleration) until an unbalanced force changes its acceleration.

Situation: Rain drop falling from the sky, with air resistance = gravity force

Fgrav

FairBALANCED FORCE

MOVING YET NON-ACCELERATING BODY

A falling object eventually encounters enough air resistance that its velocity stops increasing. That’s terminal velocity. At that point, the forces on the moving body are balanced.

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Situation: Picture hanging on a single wire

Situation: Picture hanging on 2 wires

Fgrav

Ftens

Fgrav

Ftens FtensTension force is directed along the length of a wire, rope, etc. It pulls the object it is attached to and the object pulls back with equal force. So the force on each end of the wire is the same.

2 wires share the tension force equally.

2Ftens = Fgrav

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IV. NET FORCE

•  The net force is the vector sum of all the forces acting on an object.

Ftens = 20N

Fgrav = −20N

Fnet = Ftens + Fgrav = 20N + (−20N ) = 0N

Fnorm = 10N

Fgrav = −10N

Fapp = 25NFfrict = −5N

Fnet = Ftens + Fgrav + Ffrict + Fapp =20N + (−20N ) + (−5N ) + 25N = +20N

REMEMBER, the signs just indicate the DIRECTION of the force vector

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V. Newton’s 1st LAW

•  Here’s the usual way it is written:

Everyobjectinastateofuniformmo6ontendstoremaininthatstateofmo6onunlessanexternalforceisappliedtoit.

•  Remember that a state of motion also includes no motion, or rest

•  The really big deal contained in this law is that a continuous force is NOT necessary to KEEP an object moving. Once moving, an object keeps moving until an unbalanced force acts to change its acceleration.

•  This law is sometimes called the Law of Inertia.

•  A force must overcome the inertia of an object to get it to accelerate.

A . INTRODUCTION

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B. INERTIA

•  Inertia is the tendency of an object to resist a change in its acceleration.

•  Inertia is related to the amount of mass an object contains.

•  The higher the mass, the larger the inertia. More massive objects resist changes in their state of motion.

•  How the mass is distributed in an object can affect its inertia.

•  Galileo is credited with developing the concept of inertia.

ONCE AN OBJECT’S INERTIA IS OVERCOME, IT WILL REMAIN IN THE NEW STATE OF MOTION UNTIL ANOTHER FORCE ACTS ON IT.

CONTINUOUS APPLICATION OF A FORCE IS NOT REQUIRED TO KEEP AN OBJECT MOVING.

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VI. NEWTON’S 2nd LAW

•  The usual way the 2nd Law is stated:

F= ma

•  The force is directly proportional to the object’s acceleration or mass. •  The force and acceleration vectors point in the same direction •  If sufficient force is applied in the + direction, the object accelerates in the + direction.

THIS LAW ALLOWS US TO CALCULATE HOW VELOCITES CHANGE WHEN FORCES ARE APPLIED TO AN OBJECT

F= ma

unbalanced force change in acceleration

the SI unit for F is the Newton, N

N =kgims2

A. DESCRIPTION

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F= ma

for constant m,

LARGE F means LARGE a

SMALL F means SMALL a

for constant F,

LARGE m means SMALL a

SMALL m means LARGE a

for constant a,

LARGE F means LARGE m

SMALL F means SMALL m

F is directly proportional to m and a

a is inversely proportional to m

a=Fm

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Let’s apply the previous information to free fall (remember, motion due to the force of gravity, ignoring air resistance)

acceleration due to gravity has the symbol g and is a CONSTANT equal to 9.8 m/s2

F= mg If it’s true that g is a constant, then

we can see why objects, no matter what the mass, hit the ground at the same time when dropped together.

g=F

m

if m is LARGE, free fall F is correspondingly LARGE which keeps g constant

if m is SMALL, free fall F is correspondingly SMALL which keeps g constant

In other words, objects accelerate due to gravity at the same rate regardless of mass. Force required to accelerate an object depends on its inertia (mass). More massive objects require more force. In free fall, the RATIO of force to mass is constant

F

m=

F

msmall mass object large mass object

B. 2nd LAW and FREE FALL

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F= ma

Let’s make a substitution…

Recall…

a=Δv

Δt

F= m

Δv

ΔtThis shows how force is related to velocity

Lot’s of motion dynamics problems can be solved using Newton’s 2nd law.

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VII. NEWTON’S 3rd LAW

The 3rd LAW is usually stated like this:

Foreveryac6onthereisanequalandoppositereac6on.

•  Forces come in pairs. An object exerting a force on another object experiences an equal force. The two forces are in opposite directions.

•  The MAGNITUDE of the force pair is the same. The directions are opposing.

Here’s an example of action-reaction force pairs:

air exiting an open balloon air rushes down, pushing against the atmosphere

balloon is pushed up

If the pin exerts the same force on the ball, why doesn’t ball stop…or roll backwards?