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Nerd Bling

UNIVERSITY PHYSICS

Chapter 5 NEWTON’S LAWS OF MOTION

Monday: • Newton’s Three Laws of Motion• FREE BODY DIAGRAMS• Inclined planesWednesday:• Action-Reaction forces• Pulleys and Ropes

Man of the MillenniumSir Issac Newton

(1642 -1727)

1687 Published Principia•Invented Calculus•3 Laws of Motion•Universal Law of Gravity

© 2013 Pearson Education, Inc.

A force is a push or a pull. A force acts on an object. Pushes and pulls are applied to

something. From the object’s perspective, it

has a force exerted on it. Contact forces are forces

that act on an object by touching it at a point of contact.

Long-range forces are forces that act on an object without physical contact. (gravity, electricity,etc)

What Is a Force?

Slide 5-18

Forces are InteractionsEarth on Rock Rock on EarthF F= −


Every force has an agent which causes the force. Forces exist at the point of contact between the agent and the

object (except for the few special cases of long-range forces). Forces exist due to interactions happening now, not due to

what happened in the past. Consider a flying arrow. A pushing force was

required to accelerate the arrow as it was shot.

However, no force is needed to keep the arrow moving forward as it flies.

It continues to move because of inertia.

Thinking About Force

Slide 5-75

The natural motion of a body is to remain in

whatever state of motion it is in unless

acted upon by net external forces.

Galileo Challenged The DogmaOf Aristotle’s Natural Motion

(Forces are needed for any motion)

Newton’s First Law(Law of Inertia)

An object will remain at rest or in a constant state of motion unless acted upon by external net forces.

Net Force

Direction of applied forces matters!!!Opposite forces cancel!

InertiaThe resistance of an object to change its state of motion. A measure of mass or how much stuff an object has.

A hollow tube lies flat on a table. A ball is shot through the tube. As the ball emerges from the other end, which path does it follow?

QuickCheck 5.10

Slide 5-76

CA hollow tube lies flat on a table. A ball is shot through the tube. As the ball emerges from the other end, which path does it follow?

QuickCheck 5.10

Slide 5-77

Mass & WeightW mg=

29.8 /g m s=

Calculate your weight in N.1 lb = 4.45 N

Calculate your mass in Kg.

(g is a scalar!)

F ma=

Moon MassThe acceleration due to gravity on the surface of the

moon is only 1/6 as it is on the Earth. What is the weight of a 10-kg object on the moon and on the Earth?

What is its mass on each?

Mass is the same everywhere in the universe! 10 kg!

210 9.8 / 98E EW mg kg m s N= = ⋅ =

1 1 98 16.36 6E M E

W mg m g N N= = = =M

Perception of WeightThe perception of weight comes from the support force acting

back on you. If you are in free fall you feel weightless.

Galileo Challenged Aristotle PhysicsIn a vacuum, all objects fall with the same

acceleration due to gravity: 9.80 m/s2, independent of their weight.

The Weight to Mass Ratio of ALL objects always equals g!

The force of gravity – the weight of an object – is greater for a larger mass, but the larger mass has greater INERTIA and resists a change in motion more so that the ratio of weight to

mass is a universal constant.

Finding little g

2E

E

GMaR

=

Calculate the acceleration of gravity acting on you at the surface of the Earth. What is g?

2you E

E

Gm MF

R= youF m a=

( )( )( )

11 2 2 24

26

6.673 10 / 5.98 10

6.38 10

−

=x Nm kg x kg

ax m

29.81 /a m s=

Source of the Force Reaction to the Force

= g!

Rock & FeatherA rock and feather fall with the same acceleration due to gravity in

a vacuum. Is the force of gravity acting on them the same?

Newton’s First Law(Law of Inertia)

IF an object remains at rest or in a constant state of motion the net

external forces are zero! EQUILIBRIUM!!

Newton’s First Law 0 => No Change in MotionIf F =∑

Dynamic Equilibrium Static Equilibrium

Static Equilibrium

0xF =∑Forces up equal the forces down. Forces sideways cancel too.

0yF =∑

Newton’s 2nd Law

The acceleration of object is directly related to the net forces acting on it and

inversely proportional to its mass.

netFam

=

F ma=∑

Newton’s 2nd Law

[ ] 2mkg Ns = =

Units

F ma=∑

Acceleration is in the direction of the net Force but not necessarily

in the direction of velocity.

netFam

=

Newton’s 3rd Law

To every force there is an equal but opposite reaction force.

hand on wall wall on handF F= −

Newton’s 3 Laws of Motion

2. Change in motionnetF ma= →

1. If 0 No change in motion= →∑F

1 on 2 2 on 13. F F= −

More on N3 Wednesday

Force Components

x x y yF ma F ma= =∑ ∑Newton’s Second Law is a Vector equation that can be broken

down into scalar components. Since x and y directions are independent, Newton’s Second Law can be expressed as

independent x and y equations.

F ma=∑

Force Vector DiagramsAlign axes to simplify the problem!

Show all the External forces acting ON the body only.

Statics Problem

W

T2T143 55

Find the tensions in the wires.+y

+x

Show all the External forces acting ON the body only.

Force Vector DiagramsDraw free-body diagrams for every object!

Solving Force Problems

1. State the knowns and desired unknowns.2. Draw a force vector diagram, label everything and define direction.3. Solve for the components of each force.4. Use Fnet = ma on each direction to generate equations.5. Derive a solution in terms of the given knowns.6. Enter the numbers and solve for the desired unknown.

x xF ma=∑

Starting from rest, Sally pulls Billy on the sled (total mass = 60kg) with a total force of 100 N at an angle of 40 degrees above the horizontal, as shown. After 5 seconds, how fast is the sled moving and how far has it traveled from where it started?

Problem

cos xF maθ =cos =x

Fam

θ

0cos 100 cos 40 5 6.38 /

60fF Nv v at t s m s

m kgθ

= + = = =

0fv v at= +

ProblemThe magnitude of F1 is 75.0N and F2 is 50.0N. Ignore

friction. What is the acceleration of the block?

At an instant when a 4.0-kg object has an acceleration equal to (5i + 3j) m/s2, one of the two forces acting on the object is known to be (12i + 22j) N. Determine the magnitude of the other force acting on the object.a. 2.0 Nb. 13 Nc. 18 Nd. 1.7 Ne. 20 N

The Inclined PlaneOrient your axes relative to the plane!!!

Why is the angle of the incline here? Prove it.

FIGURE 5.22

FIGURE 5.23

Incline Plane ProblemDraw a free-body diagram of a block which slides down a frictionless plane having an inclination of = 15.0°. If the block starts from rest at the top and the length of the incline is 2.00 m, find (a) the acceleration of the block and (b) its speed when it reaches the bottom of the incline.

Newton’s 3rd Law



Newton’s 3rd Law

You can’t TOUCH without being TOUCHED back!!


Newton’s 3rd Law



Newton’s 3rd Law

This is an INTERACTIVE Universe.


Gravity is an InteractionEarth on Rock Rock on EarthF F= −

Gravity is an InteractionThe Earth pulls on you, you pull on the Earth.You fall to the Earth, the Earth Falls to you.

You accelerate towards the Earth with g =9.8m/s2.With what acceleration is the Earth falling towards you?

Earth on You You on EarthF F= −

E Emg M a= −

EE

mgaM

=

222 2

24

(65 )(9.8 / ) 1.1 10 /5.98 10Ekg m sa x m s

x kg−= =

This is your weight:

Force is not AccelerationForce is the Same!

Acceleration is NOT!

Earth on You You on EarthF F= −

Earth to You You to Eartha a= −

Gun Pushes Bullet out.Bullet Pushes back on Gun (& Man)

kick

An interaction requires a pair of forces acting on two objects.

Action Reaction Pairs

Gun Pushes Bullet out.Bullet Pushes back on Gun (& Man)

kick

Rocket Thrust

Rocket Pushes Gas Out.Gas Pushes Back on Rocket.

Newton’s 3rd LawExploding Systems


The propulsion force on a car is due to

A. Static friction.B. Kinetic friction. C. The car engine.D. Elastic energy.

Reading Question 7.3

Slide 7-14


The propulsion force on a car is due to

A. Static friction.B. Kinetic friction. C. The car engine.D. Elastic energy.


Slide 7-15

In order to get an object moving, you must push harder on it than it

pushes back on you.

A) True B) False

QuestionYou push a heavy car by hand. The car, in turn, pushes back with an opposite but equal force on

you. Doesn’t this mean the forces cancel one another, making acceleration impossible?

How is it that the car moves?

Action-Reaction forces act on different objects.For F = ma, the forces must act on ONE object: the system.

The System

Interacting Objects

If object A exerts a force on object B, then object B exerts a force on object A.

The pair of forces, as shown, is called an action/reaction pair.

Slide 7-23

The three blocks are pushed across a rough surface by a 40-N force. If the coefficient of kinetic friction between each of the blocks and the surface is 0.20, determine the magnitude of the force exerted by m2 on m3.

a) 20 Nb) 30 Nc) 10 Nd) 15 Ne) 25 N

Problem1 2 32 , 3 , 5m kg m kg m kg= = =

Boxes A and B are sliding to the right on a frictionless surface. Hand H is slowing them. Box A has a larger mass than B. Considering only the horizontal forces:

QuickCheck 7.6

Slide 7-67

A. FB on H = FH on B = FA on B = FB on AB. FB on H = FH on B > FA on B = FB on AC. FB on H = FH on B < FA on B = FB on AD. FH on B = FH on A > FA on B


Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1?

A. Greater than rope 2.B. Less than rope 2.C. Equal to rope 2.


Slide 7-16


Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1?

A. Greater than rope 2.B. Less than rope 2.C. Equal to rope 2.


Slide 7-17

Tension ForcesTension forces are transmitted undiminished through the rope.

Different TSame T


Boxes A and B are being pulled to the right on a frictionless surface. Box A has a larger mass than B. How do the two tension forces compare?

QuickCheck 7.5

Slide 7-61

A. T1 > T2B. T1 = T2C. T1 < T2D. Not enough information to tell.


Boxes A and B are being pulled to the right on a frictionless surface. Box A has a larger mass than B. How do the two tension forces compare?

QuickCheck 7.5

Slide 7-62

A. T1 > T2B. T1 = T2C. T1 < T2D. Not enough information to tell.


All three 50-kg blocks are at rest. The tension in rope 2 is

QuickCheck 7.7

Slide 7-71

A. greater than the tension in rope 1.

B. equal to the tension in rope 1.

C. less than the tension in rope 1.


A. greater than the tension in rope 1.

B. equal to the tension in rope 1.C. less than the tension in rope 1.

All three 50-kg blocks are at rest. The tension in rope 2 is

QuickCheck 7.7

Slide 7-72

Each block is in static equilibrium, with .


Find the acceleration and tension of the system.


Pulleys

Block B drags block A across a frictionless table as it falls.

The string and the pulley are both massless. There is no friction where the pulley turns on its axle. Therefore, TA on S = TB on S.

Slide 7-69


Pulleys

Since TA on B = TB on A, we can draw the simplified free-body diagram on the right, below.

Forces and act as if they are in an action/reaction pair, even though they are not opposite in direction because the tension force gets “turned” by the pulley.

Slide 7-70


Pulleys, Masses, StringsWhat is the acceleration of the system?

(If they are connected, it is the same for both masses!)What is the tension in the string?

1. If it falls from rest2. If it is dragged to the left3. If the string is cut

FIRST: Draw free-body diagrams for each mass!!!

ProblemA force F = 40 N pulls the two masses. If the table is

frictionless, find the tension in the string.

a) 13 Nb) 36 Nc) 23 Nd) 15 Ne) 28 N

1 23 , 1.5m kg m kg= =


The top block is accelerated across a frictionless table by the falling mass m. The string is massless, and the pulley is both massless and frictionless. The tension in the string is

QuickCheck 7.10

Slide 7-78

A. T < mg.B. T = mg.C. T > mg.


The top block is accelerated across a frictionless table by the falling mass m. The string is massless, and the pulley is both massless and frictionless. The tension in the string is

QuickCheck 7.10

Slide 7-79

A. T < mg.B. T = mg.C. T > mg Tension has to be less than mg for

the block to have a downward acceleration.

The two masses are at rest. The pulleys are frictionless. The scale is in kg. The scale reads

QuickCheck 7.8

Slide 7-73

A. 0 kg.B. 5 kg.C. 10 kg.

The two masses are at rest. The pulleys are frictionless. The scale is in kg. The scale reads

QuickCheck 7.8

Slide 7-74

A. 0 kg.B. 5 kg.C. 10 kg.


Pulleys, Masses, StringsWhat is the acceleration of the system?

(If they are connected, it is the same for both masses!)What is the tension in the string?

1. If it falls from rest2. If it is dragged to the left3. If the string is cut

FIRST: Draw free-body diagrams for each mass!!!

ProblemA constant force F pulls the system as

shown. The pulleys are frictionless. The coefficient of kinetic friction between the block and the table is µ.

a) Draw free body diagrams for both masses.

b) Find an expression for the acceleration in terms of the given variables.


An object on a rope is lowered at constant speed. Which is true?

A. The rope tension is greater than the object’s weight.

B. The rope tension equals the object’s weight.

C. The rope tension is less than the object’s weight.

D. The rope tension can’t be compared to the object’s weight.

QuickCheck 5.8

Slide 5-68


An object on a rope is lowered at constant speed. Which is true?

A. The rope tension is greater than the object’s weight.

B. The rope tension equals the object’s weight.C. The rope tension is less than the object’s weight.

D. The rope tension can’t be compared to the object’s weight.

Constant velocityZero acceleration

QuickCheck 5.8

Slide 5-69

Nerd BlingSlide Number 2Man of the Millennium�Sir Issac NewtonWhat Is a Force?Forces are InteractionsSlide Number 6Thinking About ForceThe natural motion of a body is to remain in whatever state of motion it is in unless acted upon by net external forces.Slide Number 9Net ForceInertiaQuickCheck 5.10QuickCheck 5.10Mass & WeightMoon MassPerception of WeightGalileo Challenged Aristotle Physics�In a vacuum, all objects fall with the same acceleration due to gravity: 9.80 m/s2, �independent of their weight.The Weight to Mass Ratio of ALL objects always equals g!�The force of gravity – the weight of an object – is greater for a larger mass, but the larger mass has greater INERTIA and resists a change in motion more so that the ratio of weight to mass is a universal constant. Finding little gRock & FeatherSlide Number 21Newton’s First LawStatic EquilibriumSlide Number 24Slide Number 25Acceleration is in the direction of the net Force but not necessarily in the direction of velocity.Slide Number 27Slide Number 28Force Components Force Vector DiagramsSlide Number 31Force Vector DiagramsSolving Force ProblemsProblemProblemSlide Number 36The Inclined PlaneFigure 5.22Figure 5.23Slide Number 40Incline Plane ProblemSlide Number 42Slide Number 43Slide Number 44Slide Number 45Slide Number 46Gravity is an InteractionGravity is an InteractionForce is not Acceleration�Force is the Same!�Acceleration is NOT!An interaction requires a pair of forces acting on two objects.Action Reaction PairsRocket Thrust Newton’s 3rd Law�Exploding SystemsSlide Number 54Slide Number 55In order to get an object moving, you must push harder on it than it pushes back on you. ��A) TrueB) FalseQuestionInteracting ObjectsProblemSlide Number 60Slide Number 61Slide Number 62Slide Number 63Tension ForcesSlide Number 65Slide Number 66Slide Number 67Slide Number 68Slide Number 69PulleysPulleysPulleys, Masses, StringsProblemSlide Number 74Slide Number 75Slide Number 76Slide Number 77Pulleys, Masses, StringsProblemQuickCheck 5.8QuickCheck 5.8

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