Chapter 6

Forces (Newton’s Laws of Motion)

6.1: Force and Motion• A force is an interaction between one object and

another (push/pull has both magnitude and direction = vector quantity)

When you push on a wall, the wall pushes back on you!

Environmental Forces• Contact force:

– Acts on object by touching it– Ex. Force of hand on ball, elbows on desk

• Long-range force– Exerted without contact

Examples of contact and action-at-distance

Contact Forces Long Range ForcesFrictional Force Gravitational ForceTension Force Electrical ForceNormal Force Magnetic ForceAir Resistance ForceApplied ForceSpring Force

Forces have “Agents”

• That are not so secret • Agent = specific cause of force (if you can’t

identify the cause then the force does not exist)– Ex. My hand causes a force upward on a baseball,

my hand = Agent – Force of gravity: Agent = mass of Earth

Common Types of Forces• Friction: Ff Due to surface bumps and “stickiness” of the atoms on the

surfaces of materials. ALWAYS acts opposite of direction of motion

• Weight: Fg Force due to gravitational attraction between 2 objects, usually earth and an object

• Normal: FN The force that supports an object against gravity

• Spring: Fsp Restoring force (push/pull) exerted by a spring

• Tension: FT Pull exerted by a string, rope or cable

• Thrust: Fthrust Force that moves objects such as rockets, planes, cars and people

If the Normal Force is less than the Weight, what happens?

Defining YOUR System

• System = portion of the universe chosen for studying the changes that take place within it

• EXAMPLES: a planet, and/or the liquid within a glass. YOU DEFINE YOUR SYSTEM (my definition differs a little from your text)

Examples of Systems

1. A book is at rest on a tabletop. Diagram the forces acting on the book.

2. An egg is free-falling from a nest in a tree. Neglect air resistance. Diagram the forces acting on the egg as it is falling.

3. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. Diagram the forces acting on the squirrel.

4. A force is applied to the right to drag a sled across loosely packed snow with a rightward acceleration. Diagram the forces acting upon the sled.

Draw Systems w/ bodies and w/o

Diagram of System Free-body Diagram

How objects move: Newton’s 2nd Law• The acceleration produced by a net force on an

object is directly proportional to the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.– Units

• Mass: kg• Acceleration: m/s2

• Force = N

• Recall: Velocity vs. time slope = acceleration• Force vs. Acceleration slope = mass

Net Force• Net Force: Combination of all forces on an object

• Vector Quantities: Forces shown by arrows– Have both magnitude (how much)

and direction (which way)

Adding Vectors• Resultant: Sum of two or more vectors

– Same direction, add– Opposite direction, subtract

Complicated by angles (Ch. 7)

Newton’s First Law of Motion• Every object continues in its state of rest, or a

uniform speed in a straight line, unless acted on by a nonzero force– Restating Galileo’s concept of Inertia

When you pull out a tablecloth, the dishes are left in their initial state of rest.

When a driver slams on the breaks, the car stops faster than the driver’s body, which causes the body to lurch forward causing whiplash.

The Equilibrium Rule• When the net force on something is equal to zero

Tension = Stretching Force

Is this diagram in equilibrium?

Equilibrium of Moving Things• Equilibrium = state of no change• An object moving at a constant speed in a straight

line is in equilibrium

• Friction: Force that occurs opposite of motion when objects are in contact

6.2: Using Newton’s Laws

Recall Newton’s 2nd Law• The acceleration produced by a net force on an

object is directly proportional to the net force, is in the same direction as the net force, and is inversely proportional to the mass of the object.– Units

• Mass: kg• Acceleration: m/s2

• Force = N

Mass – A Measure of Inertia• Amount of Inertia (resist in change of motion) depends on

amount of mass– Mass: Amount of matter in an object; measured in kilograms (kg)– DIFFERENT THAN WEIGHT!

• Weight: Force on an object due to gravity

– Weight and mass are directly proportional • Double the Mass, Double the Weight!

Which bucket would be harder to push? WHY?

Newton’s Second Law of Motion

If the mass increases, to produce the same amount of acceleration, what must you do to the force?

If the force on an object doubles and the mass does not change, what happens to the acceleration?

Dynamic Cart Demo

• 2 Volunteers of obviously different mass/weight

Pg. 128-129 Example problem

Lifting a Bucket:A 50 kg bucket is being lifted by a rope. The rope is guaranteed not to break if the tension is 500 N or less. The bucket started at rest, and after being lifted 3.0 m, it is moving at 3.0 m/s. Assuming that the acceleration is constant, is the rope in danger of breaking?

FRICTION

• http://www.youtube.com/watch?v=1hhW76BIwP4&feature=player_embedded

Friction ForceFRICTION: Force between 2 surfaces that opposes motion• Static Friction (Fs):

Force that must be overcome to move an object at rest

• Kinetic Friction (FK):

Force of friction that opposes a moving object

Friction Equations

• Kinetic friction is weaker than static friction fk < fs

• Force of friction = coefficient of friction times the normal force (supporting force)

• Coefficient of Friction (μ): measure of “roughness”– Relates texture of surfaces in contact– Calculated in lab

• Static friction: Fs = μsFN

• Kinetic friction: FK = μkFN

Example Problem: Balanced Friction Forces (pg. 131)

• You push a 25 kg wooden box across a wooden floor at a constant speed of 1.0 m/s. How much force do you exert on the box?

Ex. Problem: Unbalanced Friction Forces (Pg. 132)

• If the force you exert on the box is doubled, what is the resulting acceleration of the box?

When acceleration is gFree Fall

• Free fall: When the force of gravity is the only force acting on an object (air resistance is negligible)

a = g = 9.8m/s2

• Objects of different masses fall at the same rate

The elephant has a greater gravitational attraction than the person. BIGGER “F”.

BUT, the elephant also has a bigger mass proportional to that BIGGER F. BIGGER “m”.

That means that the BIGGER “F” cancels the BIGGER “m” and the objects fall at the same acceleration.

When acceleration is less than gNon-Free Fall

• Most of the time, air resistance is NOT negligible.– Air resistance/ Air Drag

• Force of friction acting between object and air• Depends on SPEED and SURFACE AREA• When Drag Force = Force of gravity = no net force =

TERMINAL VELOCITY

Increase Speed, increase air resistance/ drag force

Increase Surface Area, increase air resistance

Gliding Increase Surface Area in Nature

“Flying” squirrels have large flaps of skin

Increase Surface Area, Increase Air Drag, Slow Your Fall!

“Flying dragons” (lizards in genus Draco) have long ribs that support gliding membranes

“Flying” frogs have very large toes with webbing between them

Non-Free Fall• Air resistance decreases the acceleration due to

gravity– Terminal velocity: Object is no longer accelerating

downward – falling at a constant rate• Human skydiver: 150 – 200km/hr• Parachute increases surface area, which slows terminal

speed to 15-25km/hr

Removing Air Resistance• Air Resistance:

– Coin falls faster than feather because the feather has less mass and greater surface area

• Remove Air Resistance (Vacuum)– Coin and feather fall at the same

rate

Periodic Motion•A motion that repeats itself in equal intervals of time is Periodic Motion.•Simple harmonic motion (SHM): a type of periodic motion where the restoring force is directly proportional to the displacement

Describing SHM• Periodic Motion/ SHM results from net forces trying

to obtain re-establish EQUILIBRIUM• Period (T): time (in seconds) needed to repeat one

complete cycle of motion• Amplitude: Maximum distance (in meters) the

object moves from equilibrium

The Mass on a Spring• Period of Oscillation, T, depends on the mass

of the block and the strength of the spring but not on the amplitude of the motion

The Pendulum

• Period depends only on The Length (L) of the string/ pendulum and on the force of gravity, not on the mass of the “bob” or the amplitude of oscillation

Resonance• Vibrations produced by one object align with

another object • The power of resonance can be as gentle as an

adult pushing a child on a swing, or as ferocious as the force that toppled what was once the world's third-longest suspension bridge.

• Resonance helps explain all manner of familiar events, from the feedback produced by an electric guitar to the cooking of food in a microwave oven.

6.3: Interaction Forces

Newton’s Third Law of Motion• Whenever one object exerts a force on a second

object, the second object exerts an equal an opposite force on the first– Action and Reaction Forces

• Equal in strength, opposite in direction

When a boxer hits a bag, he exerts a force on the bag. The bag exerts an equal force on the boxer opposite the original force

Boxer = Action Force

Bag = Reaction Force

Newton’s Third Law of MotionYou swing an ax and get

it stuck in a stump…

What was the Action Force?

What was the Reaction Force?

Action and Reaction on Different Masses

• Falling objects pull upward on Earth with as much force as the Earth pulls downward on it!

Because the Earth has such a great mass, we can’t see the acceleration

Action and Reaction onDifferent Masses

• When you fire a cannon, the cannonball exerts and equal an opposite force on the cannon.

Why does the cannon move very little, but the cannonball flies very far?

The cannon has a large mass, the cannonball has a small mass.

Defining Your System• Since action and reaction forces are equal and

opposite, why don’t they cancel to zero?– When we have action and reaction systems, they are

isolated from other forces. These other forces can cause acceleration!

The Four Fundamental Forces

• Gravity: affects all masses (infinite range), force carrier, Gravitons

• Weak Interaction: Small short range, forces caused by bosons, in atomic nucleus, cause of radioactive decay

• Electromagnetism: Large range, acts on charged particles through photons

• Strong Interaction: works primarily on subatomic particles but range is theoretically infinite. Works through gluons, which hold protons and neutrons together.

Weakest

Strongest

When Newton’s Laws are not valid• Objects moving near the

speed of light

• Objects that are very small – on the scale of an atom

• Objects under the influence of very strong gravitation forces