Newton’s 1 st Law of Mechanics A particle will continue is a straight line at constant speed unless acted upon by a net push or pull (i.e. force). The

Newton’s 1Newton’s 1stst Law of Mechanics Law of MechanicsA particle will continue is a straight line at constant A particle will continue is a straight line at constant

speed unless acted upon by a net push or pull (i.e. speed unless acted upon by a net push or pull (i.e.

force). force).

The property of a body to continue in a straight line at The property of a body to continue in a straight line at

constant speed is called constant speed is called InertiaInertia..

MassMass is the is the measuremeasure of a of a body’s inertiabody’s inertia. Thus, a 2 kilo-. Thus, a 2 kilo-

gram object has twice the inertia of a 1 kilo-gram gram object has twice the inertia of a 1 kilo-gram

object. object.

Newton’s 1Newton’s 1stst Law of Mechanics Law of MechanicsNewton’s 1Newton’s 1stst Law tells us a couple of things: Law tells us a couple of things:

1)1) The natural state of mater is a straight line at The natural state of mater is a straight line at

constant speed.constant speed.

2)2) If an object is not moving in a straight line and/or if If an object is not moving in a straight line and/or if it is speeding up or slowing down then a net push it is speeding up or slowing down then a net push or pull must be acting upon the body.or pull must be acting upon the body.

Newton’s 2Newton’s 2ndnd Law of Mechanics Law of MechanicsThe direction of the acceleration of a particle will be in The direction of the acceleration of a particle will be in

the direction of the net external force applied to the the direction of the net external force applied to the

particle. The magnitude of the particle’s acceleration particle. The magnitude of the particle’s acceleration

will be proportional to the magnitude of the net will be proportional to the magnitude of the net

external force applied to the particle and inversely external force applied to the particle and inversely

proportional to the mass of the particle.proportional to the mass of the particle.

A

F1

F2

F3 F1+F2+F3

Newton’s 2Newton’s 2ndnd Law of Mechanics Law of Mechanics

This is a vector equation. Each direction (x, y, and z) This is a vector equation. Each direction (x, y, and z)

can be solved independently!!can be solved independently!!

AmFExternal

zzyyxx AmFAmFAmF

Solving Newton’s 2Solving Newton’s 2ndnd Law LawThe mass of the particle is usually given or it can be The mass of the particle is usually given or it can be

obtained using a scale. Thus, in theory all problems in obtained using a scale. Thus, in theory all problems in

Newtonian Mechanics reduce to one of two types: Newtonian Mechanics reduce to one of two types:

1)1) You have the acceleration and solve Newton II for You have the acceleration and solve Newton II for

the forces.the forces.

2)2) You have the forces and solve Newton II for the You have the forces and solve Newton II for the

particle’s acceleration.particle’s acceleration.

Free Body DiagramsFree Body DiagramsSolving Newton’s 2Solving Newton’s 2ndnd Law often requires us to identify Law often requires us to identify

all of the forces acting upon a body. all of the forces acting upon a body.

Identifying the forces is not always obvious so Identifying the forces is not always obvious so

physicist have devised a physicist have devised a graphical trickgraphical trick called a called a

Free Body DiagramFree Body Diagram to to solvesolve the the left hand side of left hand side of

Newton’s 2Newton’s 2ndnd Law Law..

Drawing Free Body DiagramsDrawing Free Body Diagrams

Step 1: Step 1: Isolate the bodyIsolate the body

Step 2: Step 2: Inventory the forces using Inventory the forces using WANTfWANTf

Step 3: Step 3: Draw a coordinate axisDraw a coordinate axis

Step 4: Step 4: Identify any critical angles or dimensionsIdentify any critical angles or dimensions

(Our problems will generally have no angles or critical (Our problems will generally have no angles or critical

dimensions!!)dimensions!!)

Drawing Free Body DiagramsDrawing Free Body Diagrams

Step 1: Step 1: Isolate the bodyIsolate the body

Step 2: Step 2: Inventory the forces using Inventory the forces using WANTfWANTf

Step 3: Step 3: Draw a coordinate axisDraw a coordinate axis

Step 4: Step 4: Identify any critical angles or dimensionsIdentify any critical angles or dimensions

(Our problems will generally have no angles or critical (Our problems will generally have no angles or critical

dimensions!!)dimensions!!)

WANTfWANTfWWeighteight

AApplied (springs, electric forces, etc.)pplied (springs, electric forces, etc.)

NNormal (Force of contact)ormal (Force of contact)

TTension (strings or ropes)ension (strings or ropes)

FFriction (sliding friction, air drag, etc.)riction (sliding friction, air drag, etc.)

These are the only type of forces that exist in These are the only type of forces that exist in

mechanics!!!mechanics!!!

Drawing Free Body DiagramsDrawing Free Body DiagramsExample: Example: Draw the free body diagram for a ball falling Draw the free body diagram for a ball falling

on the Earth with no air resistance.on the Earth with no air resistance.



Step 1: Isolate the body (Our body is a ball).Step 1: Isolate the body (Our body is a ball).



Step 1: Isolate the body (Our body is a ball)Step 1: Isolate the body (Our body is a ball)

Step 2: Inventory the forcesStep 2: Inventory the forces

W





Step 3: Draw a coordinate axisStep 3: Draw a coordinate axis

W

x

y





Step 3: Draw a coordinate axisStep 3: Draw a coordinate axis

Step 4: Critical Angles & Dimensions (None)Step 4: Critical Angles & Dimensions (None)

W

x

y

Reading Your Free Body DiagramsReading Your Free Body DiagramsExample: Example: UseUse your Free Body Diagram and your your Free Body Diagram and your

knowledge of falling bodies to find a formula relating knowledge of falling bodies to find a formula relating

weight and mass of an object.weight and mass of an object.

Solution:Solution:

From reading our Free Body Diagram, we haveFrom reading our Free Body Diagram, we have

We know that acceleration of a free falling object isWe know that acceleration of a free falling object is

yx AmW-Am0

gAy

Reading Your Free Body DiagramsReading Your Free Body DiagramsCombining our results, we haveCombining our results, we have

Thus, we have a relationship between the magnitude Thus, we have a relationship between the magnitude

of the weight of an object and the object’s mass:of the weight of an object and the object’s mass:

kilograms)in (mass)m/s(10gmW 2

gmWA0 x

Weight VS MassWeight VS MassAs we learned earlier, mass is an intrinsic property of a As we learned earlier, mass is an intrinsic property of a

body that describes a bodies resistance to body that describes a bodies resistance to

acceleration.acceleration.

Weight doesn’t belong to a body. It is a gravitational Weight doesn’t belong to a body. It is a gravitational

force of attraction between the Earth and the body.force of attraction between the Earth and the body.

Without the Earth, the ball would have no weight, but it Without the Earth, the ball would have no weight, but it

still would have mass!!still would have mass!!

Forces act upon bodies! They are not part of the body! Forces act upon bodies! They are not part of the body!

Drawing Weight ArrowsDrawing Weight ArrowsThe arrow should start in the center of the body (thisThe arrow should start in the center of the body (thispoint is called the “center of gravity”) and should point point is called the “center of gravity”) and should point straight downward toward the Earth.straight downward toward the Earth.

Drawing Normal Force ArrowsDrawing Normal Force ArrowsA normal force is a force of contact between two A normal force is a force of contact between two bodies. The force should be drawn on the free body at bodies. The force should be drawn on the free body at the contact interface and in the direction that would the contact interface and in the direction that would push the objects apart.push the objects apart.

ProblemsProblems1) A TSU dorm has caught fire and a TSU student is 1) A TSU dorm has caught fire and a TSU student is

headed for safety by climbing down a rope. If the headed for safety by climbing down a rope. If the

students is climbing down the rope as shown below at students is climbing down the rope as shown below at

a decreasing speeda decreasing speed

A.A. Draw the student’s Free Body DiagramDraw the student’s Free Body Diagram

B.B. Determine if the student’s weight is greater or less Determine if the student’s weight is greater or less than the force the rope applies on the studentthan the force the rope applies on the student

V

ProblemsProblems2) A bathroom scale actually reads the normal force 2) A bathroom scale actually reads the normal force

applied by the scale to you and not your weight. The applied by the scale to you and not your weight. The

reading on the scale is sometimes called your reading on the scale is sometimes called your

““apparent weight. apparent weight.

a)a) Describe a situation when the magnitude of your Describe a situation when the magnitude of your

apparent weight is more than the magnitude of your apparent weight is more than the magnitude of your

actual weight. actual weight.

b)b) Describe a situation when the magnitude of your Describe a situation when the magnitude of your

apparent weight is less than the magnitude of your apparent weight is less than the magnitude of your

actual weight. actual weight.

ProblemsProblems3)3) When a rock falls near the Earth its speed will When a rock falls near the Earth its speed will

increase until it reaches some maximum value called increase until it reaches some maximum value called

its terminal speed. After this time the air drag will its terminal speed. After this time the air drag will

prevent the rock from gaining speed. prevent the rock from gaining speed.

a)a) Draw a Free Body diagram for a rock that is falling Draw a Free Body diagram for a rock that is falling

at its terminal speed. at its terminal speed.

b)b) Determine the air drag if the rock has a mass of Determine the air drag if the rock has a mass of

2.5 kg.2.5 kg.

ProblemsProblems5) Use Newton’s 25) Use Newton’s 2ndnd Law to determine what the scale Law to determine what the scale

will read in each of the problems below:will read in each of the problems below:

a)a)

b)b)

2 kg 2 kg

2 kg

Newton’s 3Newton’s 3rdrd Law of Mechanics Law of MechanicsIf body A applies a force of If body A applies a force of some typesome type upon body B upon body B

then body B then body B mustmust apply the apply the same typesame type of force upon of force upon

body A that is body A that is equal in magnitudeequal in magnitude and and opposite inopposite in

directiondirection..

FBA FAB

Body A Body B

Newton’s 3Newton’s 3rdrd Law of Mechanics Law of MechanicsForces always come in pairs!! Forces always come in pairs!!

If we take the entire universe as our system then the If we take the entire universe as our system then the

sum of these forces always adds up to zero!!!sum of these forces always adds up to zero!!!

Thus, the total motion of the universe is always Thus, the total motion of the universe is always

conserved. conserved.

Physicists call this quantity related to motion the Linear Physicists call this quantity related to motion the Linear

Momentum which is defined by the equation:Momentum which is defined by the equation:

vmp

Conservation of Linear MomentumConservation of Linear MomentumThe linear momentum of a system is conserved (i.e. The linear momentum of a system is conserved (i.e.

constant) if the system is isolated (i.e. there is no net constant) if the system is isolated (i.e. there is no net

external force) or if the time in which any forces occur external force) or if the time in which any forces occur

is approximately zero (collisions, and explosions)!!is approximately zero (collisions, and explosions)!!

Δt

pΔ

Δt

vΔm

Δt

vΔmF

tFpΔ

Conservation of Linear MomentumConservation of Linear MomentumExample: A gun with a mass of two kilograms fires a Example: A gun with a mass of two kilograms fires a

bullet of mass 0.005 kg with a speed of 180 m/s as bullet of mass 0.005 kg with a speed of 180 m/s as

seen by an observer. What is the speed of the seen by an observer. What is the speed of the

recoiling gun as seen by the observer?recoiling gun as seen by the observer?

Solution: Considering the gun + bullet as the system, Solution: Considering the gun + bullet as the system,

the linear momentum just before and after the firing of the linear momentum just before and after the firing of

the gun is conserved.the gun is conserved.

x

y

Initially Final

Conservation of Linear MomentumConservation of Linear MomentumSolution (continued):Solution (continued):

The initial linear momentum in the x-direction isThe initial linear momentum in the x-direction is

The final linear momentum is found byThe final linear momentum is found by

x

y

Initially Final

m/skg0.0m/s)0.0(kg0.0052.0kgpx

m/skg0.0m/s180kg0.005vkg2.0p gx

Conservation of Linear MomentumConservation of Linear MomentumSolution (continued):Solution (continued):

m/s180kg0.005vkg2.0 g

m/s0.45

kg2.0

m/s180kg0.005vg

Documents

Newton’s 1 st Law of Mechanics A particle will continue is a straight line at constant speed unless acted upon by a net push or pull (i.e. force). The