Forces and the Laws of Motion

Force

That which accelerates a mass

Non-zero forces always associated with a mass

Net force: vector sum

Balanced: vector sum is zero

Definitions

Contact force: requires contact between objects to act

Noncontact force: acts through force fields 

First Law of Motion

Inertia: a property of matter

Resist change in velocity (accelerations)

Equal to Mass of Object

Does not vary with location

The First Law

Motion constant unless acted on by a net force

Second Law of Motion

Net Force changes motion

Change in motion is proportional to the net force

Newton defined the change in motion as mass x velocity

We call this momentum

Second Law of Motion (cont.)

F = Dmv/Dt

Dv/Dt is acceleration (a)

F = ma

Unit: kg • m/s2 = Newton (N)

Internal vs External Forces

External: from environment

Internal: contained in object

temperature

Only external forces affect motion

Free Body Diagrams

Show all forces acting on body

Isolate body and align to geometry of problem

Draw forces as vectors. Show components if needed.

Free Body Diagrams (2)

Indicate a coordinate system, the frame of reference

Show the positive direction

Problem Solution

Draw diagrams

Whole problem

Freebody diagram for each object

Show forces as vectors

Concept: F = ma

Problem Solution (2)

Determine components of forces affecting motion

Combine forces as needed

Substitute values and solve

Third Law of Motion

For each force on an object, the object exerts an equal but opposite force

Must be in contact

Effect of force determined by mass

Fundamental Forces

Five Fundamental Forces

Electromagnetic Force

Strong Force

Weak Force

Gravity

Dark (antigravity)

Relative strength

Strong: 1

EMF: 10-2

Weak: 10-13

Gravitational: 10-38

Dark: 10-?

Fundamental Forces

Gravity

attractive force between masses

dependent on mass of body

follows inverse square rule

weakest force

mechanism unknown

Newton and Gravity

Force on a planet is proportional to the square of its distance from the sun

derived from Kepler’s 1st law

F = constant • m/r2

(r is distance from center of Sun)

Newton and Gravity (2)

Observation of falling objects led to the conclusion that force was proportional to the mass of the object

 

F a m

Newton and Gravity (3)

Realized both objects attract

Combined observations

F a m1m2/r2

(r is distance between centers)

Added proportionality constant to calculate force

F = G(m1m2/r2)

Newton and Gravity (4)

Provided the 1st unification of theory

Kepler’s 3rd law can be derived from Newton's Law of Gravitation

Mass vs. Weight

Mass:

property of matter

amount of matter in object

does not vary with location

Mass vs. Weight

Weight:

force of gravity on mass

acts toward center of Earth

vary inversely with distance

vary directly with mass

Determination of g

W = GMem/r2

W also is ma. g used to represent acceleration from gravity \ mg = GMem/r2

g = GMe/r2

g = 9.80 m/s2

Types of Mass

Gravitational: Balance mass against known weight

Inertial: move the mass and find ratio of unbalanced forces

Types of Mass

Sixth Force:

Recent experiments find denser materials fall faster

Hypothesize a repellent force exists to account for difference

Electromagnetism

Interaction between charged particles

Like - repel; unlike - attract

1036 times as strong as gravity

positives and negatives balance

Electromagnetism (2)

Responsible for:

strength

flexibility

support

combination of atoms

Force carrier: photon

Electromagnetism (3)

Normally the number of protons is balanced by the number of electrons.

2 people next to each other with 1% more e- generate enough force to lift mass of earth.

Strong Force

Between Quarks and Baryons

Holds protons and neutrons together

Leftover strong force holds nucleus together

 

Strong Force

Decreases rapidly, mostly felt by adjacent particles

Force carrier: gluon

Strong Force (2)

When number of protons too large:

repellent force of protons overcomes strong force

energy of strong force released as nuclear power

Weak Force

Interaction of particles in nuclear decay

Felt only by particles in decay

Force Carrier: W+, W-, Z

Related to electromagnetic force

Dark Force

Produced by dark energy (quintessence)

Has a negative pressure

Constant, equally distributed

Works against gravity

Described by some as negative from of gravity (symmetry w/other forces)

Dark Force Effects

Universe starts expanding (Big Bang), Matter density is high

Gravity slows expansion

As universe expands matter density decreases

Dark Force accelerates expansion

Other Forces and Effects

Normal Force

Force surface exerts on an object placed on it

Act perpendicular to surface

Requires contact

Third Law Impact

Weight of object pushes on surface

Surface pushes back with FN

FN depends on fraction of W perpendicular to surface

Slanted Surface

FN still perpendicular to surface

W is directed toward center of Earth, only portion is perpendicular

Multiply W by sine or cosine to find FN

Apparent Weight

Weight is the effect of gravity

Apparent weight is FN

Acceleration inline with gravity changes FN

FN = mg + ma

Force of Friction

Friction (1)

A force on object by surface, parallel to surface

Surfaces must be in contact

Resists motion

Cause of Friction

Read Scientific American article on friction

Answer questions on the worksheet

Static Friction

Resists start of motion

Depends on:

Normal forces

Coefficient of Static Friction (ms)

Ff = msFN

Kinetic Friction

Between moving surfaces

Resists motion, slows an object

Weaker than static friction

Depends on:

Normal force

Coefficient of kinetic friction

Tension Force (T)

A pull on an object

Magnitude equal in both directions

T applied to a rope is passed to object

T is not affected by pulleys

Forces and Equilibrium

System (object) has no acceleration

No net forces

SFx and Sfy are zero

Analyzing Equilibrium Situations

Select the "system"

Object about which the most information is known.

If two or more objects are connected, it may be necessary to treat each object separately

Draw a free-body diagram

Be sure to include only forces that act on the system.

Do each object separately

Do not include forces that the object exerts on its environment.

Choose a set of x, y axes

Resolve forces into components along axes

Apply equations 4.9a and 4.9b

Solve the equations for the unkowns

Non-Equilibrium Situations

Net force is present

Follow same steps except

SFx = max

SFy = may

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