Newton’s Laws Newton’s Laws

Divisions of PhysicsDivisions of Physics

2 Divisions of Physics2 Divisions of Physics– Classical Mechanics (Newtonian Physics)Classical Mechanics (Newtonian Physics)

Treats energy and matter as separate entitiesTreats energy and matter as separate entities Uses Newton’s three Laws to predict motionUses Newton’s three Laws to predict motion Accurately predicts and describes the behavior of Accurately predicts and describes the behavior of

large scale objectslarge scale objects Connects acceleration and forceConnects acceleration and force

– Quantum Mechanics Quantum Mechanics Studies motion and energy of atoms and subatomic Studies motion and energy of atoms and subatomic

particlesparticles Studies microscopic objects that move at the speed Studies microscopic objects that move at the speed

of light (c=c 3.00 x 10of light (c=c 3.00 x 1088 m/s) m/s)

Newton’s 1Newton’s 1stst Law Law

Newton uses 3 Laws to predict force Newton uses 3 Laws to predict force and motion interactions for and motion interactions for macroscopic objectsmacroscopic objects

“ “ an object at rest or in uniform motion an object at rest or in uniform motion will remain at rest or in motion will remain at rest or in motion unless acted on by an external force”unless acted on by an external force”

The First Law is often interpreted as The First Law is often interpreted as saying that saying that objects resist changes objects resist changes in motionin motion. This resistance to motion . This resistance to motion changes is often given the name changes is often given the name inertiainertia. Objects with large inertia . Objects with large inertia resist changes in motion better than resist changes in motion better than objects with small inertia. objects with small inertia.

Newton’s 2Newton’s 2ndnd Law Law

“ “ the acceleration of a body is directly the acceleration of a body is directly proportional to the net force acting on it proportional to the net force acting on it and inversely proportional to its mass”and inversely proportional to its mass”

a = Fa = Fnetnet / m or F / m or Fnetnet =ma =ma

where – Fwhere – Fnetnet = net force (N) = net force (N)

m = mass (kg)m = mass (kg)

a = acceleration (m/sa = acceleration (m/s22))

Newton’s 3Newton’s 3rdrd Law Law

““When an object exerts a force on a When an object exerts a force on a second object, the second object second object, the second object exerts a force on the first that is exerts a force on the first that is equal in magnitude but opposite in equal in magnitude but opposite in direction”direction”

““for every action there is an equal and for every action there is an equal and opposite reaction”opposite reaction”

action – reaction pairaction – reaction pair

Determining Net ForceDetermining Net Force

Force in Two DimensionsForce in Two Dimensions

Sometimes the direction of the net Sometimes the direction of the net force is not clear. You must find the force is not clear. You must find the magnitude and direction of the net magnitude and direction of the net force by adding vectorsforce by adding vectors

Sample problem – page 172Sample problem – page 172

Multi-mass ProblemsMulti-mass Problems

Tension in ropes and cablesTension in ropes and cables

When a force is exerted on one end of a When a force is exerted on one end of a cable, each particle in the cable exerts and cable, each particle in the cable exerts and equal force on the next particle in the equal force on the next particle in the cable, creating tension through the cable. cable, creating tension through the cable. TensionTension is the magnitude of the force is the magnitude of the force exerted on and by a cable.exerted on and by a cable.

To avoid complicated mathematics we make To avoid complicated mathematics we make several assumptions about cables and ropes:several assumptions about cables and ropes:

The mass of the rope or cable is so much smaller The mass of the rope or cable is so much smaller than the mass of the load that it does not than the mass of the load that it does not significantly affect the motion or forces involvedsignificantly affect the motion or forces involved

The tension is the same at every point in the rope The tension is the same at every point in the rope or cableor cable

If the rope or cable passes over a pulley, the If the rope or cable passes over a pulley, the direction of the tension forces changes, but the direction of the tension forces changes, but the magnitude stays the same. (pulley is frictionless magnitude stays the same. (pulley is frictionless and its mass ins negligible.and its mass ins negligible.

Assigning Direction to the motion of Assigning Direction to the motion of Connected Objects:Connected Objects:

When two objects are attached as in an Atwood machine, they are running When two objects are attached as in an Atwood machine, they are running in two different directions. However, connected objects move as a unit. in two different directions. However, connected objects move as a unit.

System – working with more that one object at a timeSystem – working with more that one object at a time

Internal forces - the forces exerted through the rope or the cable, between Internal forces - the forces exerted through the rope or the cable, between any two objects in the system. any two objects in the system. Internal forces do not affect the Internal forces do not affect the motion of the systemmotion of the system..

External forces -External forces - forces such as gravity, or friction that affects the whole forces such as gravity, or friction that affects the whole system. system. External forces do affect the motion of the system.External forces do affect the motion of the system.

When you set up the system you must assign direction from one side of the When you set up the system you must assign direction from one side of the cable to the other. Left is often negative and right is positive.cable to the other. Left is often negative and right is positive.

Now you are ready to do some multi-massed questionsNow you are ready to do some multi-massed questions

MomentumMomentum

In a very simplistic (and non-physics) In a very simplistic (and non-physics) fashion, fashion, momentummomentum can be can be described as the amount of "oomph" described as the amount of "oomph" an object has. A slowly moving bus an object has. A slowly moving bus and a speeding bullet are very and a speeding bullet are very different objects, but you wouldn't different objects, but you wouldn't want to be hit by either one! The want to be hit by either one! The momentum of an object is defined as momentum of an object is defined as the the product of its mass and product of its mass and velocityvelocity, ,

MomentumMomentum

pp = = mvmv

pp is the object's momentum is the object's momentum mm is its mass (kg) is its mass (kg)vv is its velocity (m/s) is its velocity (m/s)

The units of momentum are simply kg m/sThe units of momentum are simply kg m/s

A very important point is that A very important point is that momentum is a momentum is a vectorvector. It has direction. Another point is that the . It has direction. Another point is that the momentum discussed in this section is more momentum discussed in this section is more specifically specifically linear momentumlinear momentum....

MomentumMomentum The changes in an object's momentum could arise because its The changes in an object's momentum could arise because its

velocity changes. velocity changes. Of course, its mass may change, but you will learn more about Of course, its mass may change, but you will learn more about that later. Anytime that later. Anytime the velocity of an object changes, there must be acceleration and, the velocity of an object changes, there must be acceleration and, as Newton pointed out, as Newton pointed out, acceleration is a result of a net forceacceleration is a result of a net force. . If you put all this together:If you put all this together:

ImpulseImpulse – the product of the force exerted on an object and time – the product of the force exerted on an object and time interval over which the force actsinterval over which the force acts

JJ = F = FΔΔtt

JJ – impulse (Ns) – impulse (Ns)F – force (N)F – force (N)T – time interval (s)T – time interval (s)

Do questions 29-32 page 199Do questions 29-32 page 199

The Impulse – Momentum The Impulse – Momentum TheoremTheorem

We use the average force because when We use the average force because when impulse is calculated over a very short impulse is calculated over a very short time interval, force changes continually time interval, force changes continually throughout the few milliseconds of contact throughout the few milliseconds of contact of the two objectsof the two objects

It is not always easy to calculate impulse It is not always easy to calculate impulse in these situations so …..an alternate in these situations so …..an alternate method is to analyze the monentum method is to analyze the monentum before and after an interaction between before and after an interaction between tow objectstow objects

FFΔΔt = t = ΔΔpp FFΔΔt = pt = pbb – p – paa

FFΔΔt = m(vt = m(vff –v –vii))

Impulse and Auto SafetyImpulse and Auto Safety

One of the most practical and One of the most practical and important applications of impulse is important applications of impulse is the design of automobiles and their the design of automobiles and their safety equipmentsafety equipment

Collisions –mass stays the sameCollisions –mass stays the same

-momentum goes to zero-momentum goes to zero

Can not reduce the change in momentum Can not reduce the change in momentum therefore can not reduce the impulsetherefore can not reduce the impulse

F F ΔΔt = t = J (constant)J (constant)

If you increase the time interval of interaction the If you increase the time interval of interaction the average force exerted on the car occupants is average force exerted on the car occupants is reducedreduced

Enter – crumple zones – see diagram pg. 203Enter – crumple zones – see diagram pg. 203Other examples of increased time intervals in order Other examples of increased time intervals in order

to decrease Force – lining of safety helmets that to decrease Force – lining of safety helmets that compress relatively slowcompress relatively slow

Conservation of MomentumConservation of Momentum

The total momentum before the The total momentum before the collision equal the total momentum collision equal the total momentum after the collisionafter the collision

ppii = p = pff

mm11vv11 +m +m22vv22 = m = m11vv11’ +m’ +m22vv22’’