Newton’s LawsNewton’s Laws

Forces and MotionForces and Motion

Laws of MotionLaws of Motion

formulated by Issac Newton in formulated by Issac Newton in the late 17the late 17thth century century

written as a way to relate force written as a way to relate force and motionand motion

Newton used them to describe Newton used them to describe his observations of planetary his observations of planetary motion.motion.

HistoryHistory Aristotle was an ancient Greek Aristotle was an ancient Greek

philosopherphilosopher Based on his observations the common Based on his observations the common

belief was that in order for an object to belief was that in order for an object to continue moving, a force must be continue moving, a force must be exerted in the direction of the motionexerted in the direction of the motion

This lasted until Issac Newton This lasted until Issac Newton proposed his “Laws of Motion” based proposed his “Laws of Motion” based on observations made of bodies free on observations made of bodies free from earth’s atmosphere.from earth’s atmosphere.

Newton’s 1Newton’s 1stst Law LawInertiaInertia

An object at rest will stay at rest, An object at rest will stay at rest, and an object in motion will stay in and an object in motion will stay in motion at constant velocity unless motion at constant velocity unless acted on by an unbalanced force.acted on by an unbalanced force.

This statement contradicted Aristotle’s teaching and was considered a radical idea at the time. However, Newton proposed that there was, in fact, an unrecognized force of resistance between objects that was causing them to stop in the absence of an applied force to keep them moving. This new unseen resistance force became known as “friction”.

Newton’s 2Newton’s 2ndnd Law LawFFnetnet = ma = ma

If an unbalanced force acts on a If an unbalanced force acts on a mass, that mass will accelerate mass, that mass will accelerate in the direction of the force.in the direction of the force.

Newton’s 1st Law says that without an unbalanced force objects will remain at constant velocity (a=0)…so it seems logical to say that if we apply a force we will see an acceleration.

2 N 8 N

a

Since 8N is greater than 2N, the unbalanced force is to the right so the acceleration is to the right.

Newton’s 3Newton’s 3rdrd Law LawAction - ReactionAction - Reaction

For every action force there is an For every action force there is an equal and opposite reaction force. equal and opposite reaction force.

Example: If you punch a wall with your fist in anger, the wall hits your fist with the same force. That’s why it hurts!

Action-reaction forces cannot balance each other out because they are acting on different objects.

A Force is…A Force is…

A “push” or “pull”A “push” or “pull” Measured in Newtons (N) in the Measured in Newtons (N) in the

metric (SI) system and pounds metric (SI) system and pounds (lbs) in the English system(lbs) in the English system

A vector quantity requiring A vector quantity requiring magnitude and direction to magnitude and direction to describe itdescribe it

Represented by drawing arrows Represented by drawing arrows on a diagramon a diagram

Types of ForcesTypes of Forces Weight - force of gravityWeight - force of gravity Normal force – surface pushing back Normal force – surface pushing back Friction - resistance forceFriction - resistance force Applied force - force you exertApplied force - force you exert Tension - applied through a rope or chainTension - applied through a rope or chain Centripetal Force – any force that causes circular Centripetal Force – any force that causes circular

motionmotion Elastic Forces – applied force due to the stretch or Elastic Forces – applied force due to the stretch or

compression of a rubberband, bungee, or springcompression of a rubberband, bungee, or spring Drag Forces – any resistance force caused by fluids Drag Forces – any resistance force caused by fluids

(i.e. air resistance)(i.e. air resistance) Net force – total vector sum of all forcesNet force – total vector sum of all forces Balanced forces – equal and oppositeBalanced forces – equal and opposite Unbalanced forces – not equal and oppositeUnbalanced forces – not equal and opposite

WeightWeight

The force of gravity acting on a mass.The force of gravity acting on a mass.Weight always acts down!Weight always acts down!

*gF W m g Weight = mass (kg) * acceleration due to gravity

Weight is a force…so this is a special case of F=ma and the unit is a Newton.

Mass is…Mass is…

The amount of matter an object The amount of matter an object is made up of.is made up of.

Measured in kilograms.Measured in kilograms. A universal value, independent A universal value, independent

of the influences of gravity.of the influences of gravity. NOTNOT a force. a force.

Normal Force (FNormal Force (FNN)) Defined as the force of a surface Defined as the force of a surface

pushing back on an object.pushing back on an object. Always directed perpendicular to the Always directed perpendicular to the

surface.surface. This is a contact force. No contact…This is a contact force. No contact…

no normal force.no normal force. NOTNOT always equal to weight. always equal to weight.

Examples: FN

Table

Wa l l

FN

FrictionFriction A resistance force usually caused by A resistance force usually caused by

two surfaces moving past each other.two surfaces moving past each other. Always in a direction that opposes the Always in a direction that opposes the

motion.motion. Measured in NewtonsMeasured in Newtons Depends on surface texture and how Depends on surface texture and how

hard the surfaces are pressed together.hard the surfaces are pressed together. Surface texture determines the Surface texture determines the

coefficient of friction (coefficient of friction (μμ) which has no ) which has no units. units.

Normal force measures how hard the Normal force measures how hard the surfaces are pressed together. surfaces are pressed together.

Types of frictionTypes of friction

Static friction is the force an object Static friction is the force an object must overcome to must overcome to startstart moving. moving.

Kinetic friction is the force an object Kinetic friction is the force an object must overcome to must overcome to keepkeep moving. moving.

Static friction is always greater Static friction is always greater than kinetic friction!than kinetic friction!

Calculating the Force of FrictionCalculating the Force of Friction

k k Nf F

Nf FWhere f is the force of friction, μ is the coefficient of friction, and FN is the normal force

For kinetic friction:

s s Nf FFor static friction:

Drag ForcesDrag Forces

Deriving expressions for drag forces Deriving expressions for drag forces such as air resistance will be the such as air resistance will be the topic of an entire powerpoint of its topic of an entire powerpoint of its own.own.

Stay tuned for more to come to an AP Stay tuned for more to come to an AP Physics class near you.Physics class near you.

May theMay the Net Force Net Force be with yoube with you

Total force acting on an objectTotal force acting on an object Vector sum of all the forcesVector sum of all the forces The unbalanced force referred to in The unbalanced force referred to in

Newton’s Law of MotionNewton’s Law of Motion Net force is equal to the mass of an object Net force is equal to the mass of an object

times the acceleration of that object.times the acceleration of that object.

netF F ma

Force DiagramsForce Diagrams Force diagrams must include the Force diagrams must include the

object and all forces acting on it. object and all forces acting on it. The forces must be attached to the The forces must be attached to the

object.object. No other vectors may be attached to No other vectors may be attached to

the object.the object. Components of forces, axis systems, Components of forces, axis systems,

motion vectors and other objects or motion vectors and other objects or surfaces may be included in force surfaces may be included in force diagrams.diagrams.

Force DiagramForce DiagramProblem: A 10 kg crate with an applied force of 100 N slides across a

warehouse floor where the coefficient of static friction is 0.3 between the crate and the floor. What is the acceleration of the crate.

Weight = Fg = (10 kg)*(9.81m/s2)

Fapplied = 100 N10 kg

FN

f = μFN

To Solve the ProblemTo Solve the ProblemNow that you have the force diagram!Now that you have the force diagram!

, xnet x x appliedF F F friction ma

Problem: A 10 kg crate with an applied force of 100 N slides across a warehouse floor where the coefficient of static friction

is 0.3 between the crate and the floor. What is the acceleration of the crate.

Fapplied = 100 N10 kg

FN

f = μFN

Weight = Fg = (10 kg)*(9.81m/s2)

Write the Newton’s 2nd Law equation for the x- and y- directions.

a

,net y y n g yF F F F ma Now plug in what you know and solve for what you don’t. Algebra…YUK!!

Centripetal ForceCentripetal Force Any force that causes an object to travel in a Any force that causes an object to travel in a

circular pathcircular path Always toward the center of the circular pathAlways toward the center of the circular path Any of the forces we have identified could be Any of the forces we have identified could be

the centripetal force, most commonly… gravity the centripetal force, most commonly… gravity (weight), tension, friction, & elastic forces(weight), tension, friction, & elastic forces

r

mFc

v

r

mvFc

2

Note: an object’s velocity is tangent to the curved path it takes, so perpendicular to the centripetal force, acceleration and radius

Centripetal Forces in horizontal Centripetal Forces in horizontal circles with tensioncircles with tension

mFc

v

Top view

θT

Fg=mg

r

Fc

m

L

When the plane of the circle traced out by the object is horizontal, gravity is perpendicular to the motion so the velocity remains constant. However, since the object will always hang below the point of support, only the component of the tension that is parallel to the plane of the circle can be considered as the centripetal force.

r

mvT

2

sin

mgT cos

Side view

Centripetal forces Centripetal forces

in in verticalvertical circles circles

Fc

v

v

v

v

FT

Fc

Fc

Fc

FT

FT

FT

Fg

Fg

Fg

Fg

At the top of the circle: -velocity is the lowest -centripetal force is a combination of the tension and gravitational forces

In a vertical circle, gravity does have an effect on the speed at different points on the circular path.

At the sides: -velocity is vertical and changing with the acceleration due to gravity -centripetal force is supplied by the tension alone since the gravitational force is perpendicular.At the bottom:

-velocity is the maximum -centripetal force is a combination of the tension and gravitational forces

gTc FFF

Tc FF

gTc FFF

Gravity as the Centripetal ForceGravity as the Centripetal ForceSatellite Motion Satellite Motion (assuming circular orbits)(assuming circular orbits)

m

Fg

v

r

RE

ME

In the case of a satellite orbiting a planet, the centripetal force (net force required to keep the object moving in the circular path) is provided by the gravitational force (weight). Of course at orbital altitudes we can no longer use Fg=mg to calculate weight of the satellite, so…

2

2

r

MmG

r

mv

FF

E

gc

We can solve this for v to get the orbital velocity associated with that particular radius.

r

GMv E

Note the orbital radius is measured to the center of the circular path of the orbit so … r = RE + H

H

Friction as the centripetal forceFriction as the centripetal forceA car going around a curveA car going around a curve

mFc

v

For a car going around a curve on a road, the force that keeps the car in the circular path (Centripetal force) is the friction of the road pushing the tires in toward the center of the circle.

NFr

mv

fFc

2

Note: This is for a flat curve. If the curve is banked, the problem is a little trickier. Draw the force diagram and be careful about the components. It combines the best of Centripetal Motion and Inclined Planes…lots of vectors!

Normal Force as the centripetal forceNormal Force as the centripetal forceAmusement Park RidesAmusement Park Rides

mFc

v

Top view

r

FN

Fg

fs

Nc

gs

FF

Ff

In a ride where the rider is stuck to the wall due to the spinning motion while the floor drops away the Normal force provides the Centripetal Force to keep the rider moving in circular path. Meanwhile, static friction between the wall and the rider is the force that balances gravity allowing the rider to “hang” on the wall.

Elastic Forces and Hooke’s LawElastic Forces and Hooke’s Law When a spring is When a spring is

stretched or compressed stretched or compressed it exerts a restoring it exerts a restoring force. force.

That force depends on That force depends on the stiffness of the the stiffness of the spring and the amount of spring and the amount of deformation (stretch or deformation (stretch or compression)compression)

The direction of the force The direction of the force is always opposite to the is always opposite to the direction of deformation.direction of deformation.

mk

m

x

kxF Hooke’s Law states:

Where: F is the restoring force,

k=spring constant (stiffness), x=stretch (or compression)

Spring force as centripetal forceSpring force as centripetal force