Chapter 5 ForcesChapter 5 Forces

(Forces in One Dimension)(Forces in One Dimension)

Objectives for Section Objectives for Section 5.15.1

Describe how force affects the motion of Describe how force affects the motion of an object.an object.

Identify different types of forces.Identify different types of forces. Interpret and construct free-body Interpret and construct free-body

diagrams.diagrams. Explain the relationship between the Explain the relationship between the

motion of an object and the net external motion of an object and the net external force acting on the object.force acting on the object.

Calculate the net force.Calculate the net force. State Newton’s three laws of motion and State Newton’s three laws of motion and

how they are applied.how they are applied. Use Newton’s Second Law to calculate Use Newton’s Second Law to calculate

the acceleration of an object.the acceleration of an object.

A. Forces and Motion - study of A. Forces and Motion - study of dynamicsdynamics1.1. Force Force - a push or a pull it can - a push or a pull it can

change the motion of an object, start or change the motion of an object, start or stop movement, and change shape of stop movement, and change shape of objectobject

2. 2. Four basic types Four basic types

a. gravitational - weakest, a. gravitational - weakest, attractive attractive force between force between objects, acts over objects, acts over very very large distanceslarge distancesb. electromagnetic - results from basic b. electromagnetic - results from basic

property of particles. Large compared to property of particles. Large compared to gravitational, but over smaller distancesgravitational, but over smaller distances

c. strong nuclear forces - holds nucleus together, c. strong nuclear forces - holds nucleus together, limited in range to diameter of nucleuslimited in range to diameter of nucleus

d. weak nuclear forces - deals with d. weak nuclear forces - deals with radiation – radiation – alpha, beta, gammaalpha, beta, gamma

3. forces act & cause things to occur3. forces act & cause things to occur4. Forces can be in 4. Forces can be in contactcontact or act over or act over

distances - distances - field forcesfield forces ( (long-range forceslong-range forces)) a. a. contact forces – an object from the contact forces – an object from the external world touches a system and exerts external world touches a system and exerts a force on ita force on itb. field forces – an object is pushed or b. field forces – an object is pushed or pulled by a force without actual touching pulled by a force without actual touching (gravity, magnetic or electrostatic force)(gravity, magnetic or electrostatic force)

Force and MotionForce and Motion

What is a force? What is a force? A push or pull on an object (system)A push or pull on an object (system)

How does it affect the motion of the How does it affect the motion of the object it acts on? object it acts on? It changes it’s motion or shape (starts, It changes it’s motion or shape (starts,

stops, changes motion, it causes stops, changes motion, it causes acceleration)acceleration)

System: the object being manipulatedSystem: the object being manipulated Agent: cause of the forceAgent: cause of the force

Types of ForcesTypes of Forces

Contact forceContact force Example: Your book laying Example: Your book laying

on the deskon the desk

Field forceField force Example: You drop your Example: You drop your

textbook onto the floor.textbook onto the floor.

Free-body DiagramsFree-body Diagrams

Balanced & Unbalanced Balanced & Unbalanced ForcesForces

With a With a Balanced force Balanced force – opposite and equal forces acting on – opposite and equal forces acting on the same object result in NO motion of the objectthe same object result in NO motion of the object

Unbalanced forces Unbalanced forces – two or more forces of unequal – two or more forces of unequal strength or direction acting upon on an object strength or direction acting upon on an object results results in the motion of the objectin the motion of the object

A. ForceA. Force

Balanced Forces (Equilibrium)Balanced Forces (Equilibrium)

forces acting on an forces acting on an object that are object that are opposite in direction opposite in direction and equal in sizeand equal in size

no change in no change in velocityvelocity

A. ForceA. Force Net ForceNet Force

unbalanced forces that are not unbalanced forces that are not opposite and equalopposite and equal

velocity changes (object velocity changes (object accelerates)accelerates)

Ffriction

W

Fpull

Fnet

NN

Newton’s Laws of Newton’s Laws of MotionMotion

““If I have seen far, it is because I have stood on the If I have seen far, it is because I have stood on the shoulders of giants.”shoulders of giants.”

- Sir Isaac Newton - Sir Isaac Newton (referring to Galileo)(referring to Galileo)

A. Newton’s First LawA. Newton’s First Law

Newton’s First Law of MotionNewton’s First Law of Motion An object at rest will remain at rest An object at rest will remain at rest

and an object in motion will and an object in motion will continue moving at a constant continue moving at a constant velocity unless acted upon by a net velocity unless acted upon by a net force.force.

Newton’s 3 Laws of Newton’s 3 Laws of MotionMotion

Newton’s 1st Law of MotionNewton’s 1st Law of Motion: : AKA AKA The Law of Inertia The Law of Inertia

which states which states an object at rest will remain at rest, and an an object at rest will remain at rest, and an object in motion will remain in motion at a constant velocity object in motion will remain in motion at a constant velocity until acted on by another force.until acted on by another force.

Remember: The greater the mass of an object the greater the inertia

Newtons’s 1Newtons’s 1stst Law and Law and YouYou

Don’t let this be you. Wear seat belts.Don’t let this be you. Wear seat belts.

Because of inertia, objects (including you) Because of inertia, objects (including you) resist changes in their motion. When the resist changes in their motion. When the car going 80 km/hour is stopped by the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 brick wall, your body keeps moving at 80 m/hour.m/hour.

22ndnd Law Law

Newton’s Second LawNewton’s Second Law

The acceleration of an object is The acceleration of an object is equal to the sum of the forces acting equal to the sum of the forces acting on the object (the net force) divided on the object (the net force) divided by the mass of the object.by the mass of the object.

a = F / ma = F / mF = ma

Newton's Second Law:Newton's Second Law: aa.. F = m aF = m a but more easily but more easily understood understood byby

a = F / ma = F / mb.b. Acceleration is directly Acceleration is directly

proportional to force and inversely proportional to force and inversely proportional to mass of an objectproportional to mass of an object

c.c. Second law is a vector Second law is a vector equation - direction of acceleration equation - direction of acceleration is the same direction as the is the same direction as the netnet forceforce

d. Greater the force, the greater is d. Greater the force, the greater is the the acceleration the mass acceleration the mass experiencesexperiences

Unit of Force is the Newton Unit of Force is the Newton (N)(N)

One newton is the force required One newton is the force required to give a mass of one kilogram an to give a mass of one kilogram an acceleration of one meter per acceleration of one meter per second squared.second squared.

1 N = 1 kg-m/s1 N = 1 kg-m/s2 2 (a derived (a derived unit)unit)

Net ForceNet Force

Sum of all forces acting on Sum of all forces acting on an objectan object

Equilibrium (when the net Equilibrium (when the net forces balance or equal forces balance or equal zero)zero)

Can you have equilibrium Can you have equilibrium when an object is moving?when an object is moving?

Combine all forces acting on object Combine all forces acting on object to determine the to determine the net forcenet force acting on acting on the objectthe object

(1) sum of all forces is the net force.(1) sum of all forces is the net force. (2) net force can replace all forces (2) net force can replace all forces

acting on object and have the same acting on object and have the same resultresult

(3) forces added using vector math – (3) forces added using vector math – more later on the processmore later on the process

(4) net force will have magnitude and (4) net force will have magnitude and direction – critical to rememberdirection – critical to remember

(5) Net force - combination of all (5) Net force - combination of all forces acting on an objectforces acting on an object

Calculating Net ForceCalculating Net Force

Check Your Check Your UnderstandingUnderstanding

1. What acceleration will result when a 12 N net 1. What acceleration will result when a 12 N net force applied to a 3 kg object? force applied to a 3 kg object?

12 N = 3 kg x 4 m/s/s12 N = 3 kg x 4 m/s/s

2. A net force of 16 N causes a mass to accelerate 2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/sat a rate of 5 m/s22. Determine the mass.. Determine the mass.

16 N = 3.2 kg x 5 16 N = 3.2 kg x 5 m/s/sm/s/s  

3. How much force is needed to accelerate a 66 3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?kg skier 1 m/sec/sec?

66 kg-m/sec/sec or 66 N66 kg-m/sec/sec or 66 N

4. What is the force on a 1000 kg elevator that is 4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?falling freely at 9.8 m/sec/sec?

  9800 kg-m/sec/sec or 9800 N9800 kg-m/sec/sec or 9800 N

Newton’s Third LawNewton’s Third Law

Newton’s Third Law of MotionNewton’s Third Law of Motion When one object exerts a force on a When one object exerts a force on a

second object, the second object second object, the second object exerts an equal but opposite force on exerts an equal but opposite force on the first.the first.

The magnitudes of the forces are The magnitudes of the forces are always equal. The two forces are always equal. The two forces are know as action-reaction forces or know as action-reaction forces or action-reaction pairs.action-reaction pairs.

Newton’s 3Newton’s 3rdrd Law of Motion Law of Motion:: For every action there is an equal & opposite reaction.For every action there is an equal & opposite reaction.

If an object is not in motion, then all forces acting on it are balanced and the net force is zero!If an object is not in motion, then all forces acting on it are balanced and the net force is zero! Friction – the force that one surface exerts on another when the two rub against each other.Friction – the force that one surface exerts on another when the two rub against each other.

Newton’s 3 Laws of Newton’s 3 Laws of MotionMotion

Sliding friction

Rolling friction

Fluid friction

5.1 Concept Review5.1 Concept Review You exert a force on a black box and You exert a force on a black box and

measure its acceleration and then exert the measure its acceleration and then exert the same force on a brown box and find its same force on a brown box and find its acceleration is three times greater. What acceleration is three times greater. What can you conclude? can you conclude? Mass of the brown box is 1/3 that of the black boxMass of the brown box is 1/3 that of the black box

What is a Newton?What is a Newton? Force require to accelerate 1 kg by 1m/sForce require to accelerate 1 kg by 1m/s22

1 N = 1 kg-m/s1 N = 1 kg-m/s22

How can you feel the inertia of a pencil How can you feel the inertia of a pencil or your text book? or your text book? By changing it’s motion (accelerating it)By changing it’s motion (accelerating it)

Objectives for Section Objectives for Section 5.25.2

Describe the relationship between the Describe the relationship between the mass and weight of an object using mass and weight of an object using Newton’s 2Newton’s 2ndnd Law Law

Demonstrate an understanding of Demonstrate an understanding of frictional forces and the use of frictional forces and the use of coefficients of frictioncoefficients of friction

Be able to calculate acceleration based Be able to calculate acceleration based on net forceon net force

Define free fall and terminal velocity due Define free fall and terminal velocity due to air resistanceto air resistance

Weight ForceWeight Force

Using Newton’s Second Law you can Using Newton’s Second Law you can derive the formula for weight force.derive the formula for weight force.

Mass and WeightMass and Weighta. weight - due to gravitational forcea. weight - due to gravitational force

(1)(1) w = m g (F = m a)w = m g (F = m a) (2)(2) direction is downwarddirection is downward

b. b. mass - amount of matter in an mass - amount of matter in an object. object. c. c. gravitational massgravitational mass

(a) measured using a balance to (a) measured using a balance to compare weights of two objectscompare weights of two objects

(b) unknown mass on one side, (b) unknown mass on one side, known known mass on the othermass on the other

d. Inertial mass: measured by the force is d. Inertial mass: measured by the force is required to accelerate the mass: m = F/arequired to accelerate the mass: m = F/a

e.e. weight is a vector, mass is a weight is a vector, mass is a scalarscalar

Friction is the name given to the force that acts between materials that touch as they move past each other.

• Friction is caused by the irregularities in the surfaces of objects that are touching.

• Even very smooth surfaces have microscopic irregularities that obstruct motion.

• If friction were absent, a moving object would need no force whatever to remain in motion.

Friction

More on Friction……………

1. Force that opposes motion between two surfaces in contact.

2. Amount depends on:

a. Kinds of surfaces in contact – this determines the coefficient of friction ()

b. Amount of force pressing surfaces together – the normal force (More weight more friction)

3. Expressed as Ff = FN

3. Friction is caused by 3. Friction is caused by microweldsmicrowelds

4. Types of friction:

a. Static (usually the greatest)

b. Sliding

c. Rolling (usually the least)

d. Fluid Friction (air or water resistance)

Drag ForceDrag Force

The friction force exerted by a fluid The friction force exerted by a fluid on the object moving through the on the object moving through the fluid.fluid.

Example: Air resistanceExample: Air resistance

Air resistance (drag force)

1. Force that opposes motion of objects through air

2. Pushes up on falling objects

3. Affected by object’s speed, size, shape

4. Without drag force, all objects fall at the same rate

5. Terminal velocity is the max speed at which an object can fall

Objects with similar air resistance fall at the same rate. Everything falls at the same rate of

speed in a vacuum. That rate is the gravitational constant.

On earth (-9.8 m/sec²)

Video! Falling Objects, Gravity, Air Resistance, on the moon with Apollo. http://www.youtube.com/watch?v=KDp

1tiUsZw8

Terminal VelocityTerminal Velocity

The constant velocity that is reached The constant velocity that is reached when the drag force equals the force when the drag force equals the force of gravity.of gravity.

What reaches a terminal velocity What reaches a terminal velocity faster, a heavy, compact object or a faster, a heavy, compact object or a light object with larger surface area?light object with larger surface area?

Objectives for Section 5.3 Objectives for Section 5.3 Net ForcesNet Forces

Identify forces acting on an object Identify forces acting on an object and calculate net forcesand calculate net forces

Determine acceleration based on the Determine acceleration based on the net forcenet force

Find the direction and magnitude of Find the direction and magnitude of normal forces.normal forces.

B. Using Newton’s Second LawB. Using Newton’s Second Law

1. Free body diagrams - critical for 1. Free body diagrams - critical for solving problemssolving problems

a. Sketch object under a. Sketch object under considerationconsideration

b. Draw and label all external forces b. Draw and label all external forces acting on objectacting on object

c. Assume a direction for each c. Assume a direction for each force. If force. If your selection ends up your selection ends up negative(-) means it goes the other negative(-) means it goes the other wayway

Combine all forces acting on object to Combine all forces acting on object to determine the determine the net forcenet force acting acting

on the objecton the object (1) (1) sum of all forces is the net force.sum of all forces is the net force. (2) (2) net force can replace all forces net force can replace all forces

acting acting on object and have the same on object and have the same resultresult

(3) (3) forces added using vector math forces added using vector math (4) (4) net force will have magnitude and net force will have magnitude and

direction – critical to rememberdirection – critical to remember (5) (5) Net force - combination of all Net force - combination of all

forces acting on an objectforces acting on an object

Tension ForceTension Force

Practice ProblemPractice ProblemA 50.0 kg bucket is being lifted by a rope. A 50.0 kg bucket is being lifted by a rope. The rope will not break if the tension is The rope will not break if the tension is 525 N or less. The bucket started at rest, 525 N or less. The bucket started at rest, and after being lifted 3.0 m, it is moving at and after being lifted 3.0 m, it is moving at 3.0 m/s. If the acceleration is constant, is 3.0 m/s. If the acceleration is constant, is the rope in danger of breaking? the rope in danger of breaking? Remember FRemember Fgg = = mg = 50kg(9.8m/smg = 50kg(9.8m/s2 2 )= 490N)= 490N

FFnetnet = F = Ftensiontension – F – Fg g or For Ftensiontension = F = Fnetnet + F + Fgg

FFnetnet = ma; use V = ma; use Vff22 = V = Vii

22+2ad or a = V+2ad or a = Vff22-V-Vii

22/2d/2d

a = (3m/s)a = (3m/s)22-(0m/s)-(0m/s)22/2(3m) = 1.5m/s/2(3m) = 1.5m/s22

FFnetnet = 50kg(1.5m/s = 50kg(1.5m/s22) = 75N) = 75N

FFtensiontension = F = Fnetnet + F + Fg g = 75N + 490N = 565 N, yes it is in = 75N + 490N = 565 N, yes it is in danger!danger!

Ftension

Fg

The Normal ForceThe Normal Force

Weight & Normal Force In which figure is the box’s weight equal

to the normal force in magnitude? The weight of the box and the magnitude

of the normal force are equal in Figure a. In which figure is the magnitude of the

normal force greater than the weight of the box?

The magnitude of the normal force is greater than the weight of the box in Figure b.

Are mass and gravity the only factors that contribute to the normal force of an object?

External forces other than gravity and the mass of the object may change the normal force that an object exerts.

In which figure (or figures) does the box have an apparent weight different from that caused by its mass and the effect of gravity alone?

The box’s apparent weight is different from the weight caused by its mass and gravity in Figures b and c.

Practice ProblemPractice Problem

Poloma hands a 13 kg box to a 61 kg Poloma hands a 13 kg box to a 61 kg Stephanie, who stands on a platform. Stephanie, who stands on a platform. What is the normal force exerted by the What is the normal force exerted by the platform on Stephanie?platform on Stephanie?

FFNN = F = Fg(Steph)g(Steph) + F + Fg(box)g(box)

FFNN = (m = (m(Steph)(Steph)+ m+ m(box)(box))g)g

FFNN = (13kg+ 61kg)9.8m/s = (13kg+ 61kg)9.8m/s22

FFNN = 725 kgm/s = 725 kgm/s2 2 or 725 Nor 725 N

FN

Fg(Steph)

Fg(box)

2. Scales (Elevator Problems)2. Scales (Elevator Problems)

a. a. weight on scale is from the weight on scale is from the normal forcenormal force of the scale pushing of the scale pushing back up on the object which is back up on the object which is pushing down due to gravitypushing down due to gravity

b. with elevator at rest, a = 0 and b. with elevator at rest, a = 0 and FFnetnet = 0 = 0

scaleweight

normal force

Fnet = 0 = FN - W

FN = W

Scales reading is true weight of object

c. elevator moving up so “a” is c. elevator moving up so “a” is positive and the positive and the FFnetnet =m =m aa

weight

normal force

Fnet = m a = FN - W

FN = m a + W

Scales reads an

apparent weight – not

true weight but net force

acting on object.

d. elevator moving down, “a” is d. elevator moving down, “a” is negative and the Fnegative and the Fnetnet = -ma = -ma

weight

normal force

Fnet = -ma = FN - W

FN = - m a + W

Practice ProblemPractice ProblemYour mass is 75.0 kg, and you are standing on a Your mass is 75.0 kg, and you are standing on a bathroom scale in an elevator. Starting from rest, the bathroom scale in an elevator. Starting from rest, the elevator accelerates upward at 2.00 m/selevator accelerates upward at 2.00 m/s2 2 for 2.00 s for 2.00 s and then continues at a constant speed. Is the scale and then continues at a constant speed. Is the scale reading during acceleration greater than, equal to, or reading during acceleration greater than, equal to, or less than the scale reading when the elevator is at less than the scale reading when the elevator is at rest?rest?

W = mg = 75kg(9.8m/sW = mg = 75kg(9.8m/s2) = 735N, ) = 735N,

at rest Fat rest Fnetnet = 0 so F = 0 so FNN= W or F= W or FN N = F= Fscalescale = 735N = 735N

But during upward acceleration………But during upward acceleration………

FFnetnet = ma = F = ma = FN N - W or F- W or FN N = ma+W= 75kg(2m/s= ma+W= 75kg(2m/s22)+(735N))+(735N)

So FSo FN N = F= Fscalescale= 885N (It reads greater during upward = 885N (It reads greater during upward acceleration!)acceleration!)

Newton’s Third LawNewton’s Third Law

All forces come in pairs and the All forces come in pairs and the forces in a pair act on different forces in a pair act on different objects and are equal in strength objects and are equal in strength and opposite in directionand opposite in direction

Interaction ForcesInteraction Forces

Action - Reaction

If you hit a tennis ball with a racquet, the force on the ball due to the racquet is the same as the force on the racquet due to the ball, except in the opposite direction.

If you drop an apple, the Earth pulls on the apple just as hard as the apple pulls on the Earth.

If you fire a rifle, the bullet pushes the rifle backwards just as hard as the rifle pushes the bullet forwards.

“For every action there’s an equal but opposite reaction.”

Practice ProblemPractice Problem

When a softball with a mass of 0.18 kg When a softball with a mass of 0.18 kg is dropped, its acceleration toward is dropped, its acceleration toward Earth is equal to Earth is equal to g, g, the acceleration due the acceleration due to gravity. What is the force on Earth to gravity. What is the force on Earth due to the ball, and what is Earth’s due to the ball, and what is Earth’s resulting acceleration? Earth’s mass is resulting acceleration? Earth’s mass is 6.0 x 106.0 x 102424 kg. kg.

FFballball = ma = .18kg(9.8m/s = ma = .18kg(9.8m/s22) = 1.76N) = 1.76N

FFballball = F = FEarth Earth (Action-Reaction Pair)(Action-Reaction Pair)

FFEarthEarth = 1.76N = ma; = 1.76N = ma; a = 1.76N/ma = 1.76N/mEarthEarth

a = 1.76N/6.0 x 10a = 1.76N/6.0 x 102424 kg = 2.94 x 10 kg = 2.94 x 10-25 -25 m/sm/s22

Fg(Earth)

Fball

Earth / AppleHow could the forces on the tennis ball, apple, and bullet, be the same as on the racquet, Earth, and rifle? The 3rd Law says they must be, the effects are different because of the 2nd Law!

Earth

apple

3.92 N

3.92 N

0.40 kg

5.98 1024 kg

A 0.40 kg apple weighs 3.92 N (W = mg). The apple’s weight is Earth’s force on it. The apple pulls back just as hard. So, the same force acts on both bodies. Since their masses are different, so are their accelerations (2nd Law). The Earth’s mass is so big, it’s acceleration is negligible.

Earth / Apple (cont.)

a = mm a

Apple’s big acceleration

Apple’s little mass Earth’s little

acceleration

Earth’s big mass

The products are the same, since the forces are the same.

Lost in Space

Suppose an International Space Station astronaut is on a spacewalk when her tether snaps. Drifting away from the safety of the station, what might she do to make it back?

Fhand on bowling ball is the force that the hand exerts upward on the bowling ball.

Fbowling ball on hand is the force that Earth exerts downward on the bowling ball.

Fbowling ball on Earth is the force that the bowling ball exerts upward on Earth.

Fhand on bowling ball and Fbowling ball on hand; FEarth on bowling ball and Fbowling ball on Earth. are interaction pairs because they are of equal magnitude and opposite direction and act on different objects.

Fbowling ball on hand acts only on the hand, Fbowling ball on Earth acts only on Earth, and Fhand on bowling ball and FEarth on bowling ball act only on the bowling ball.

The movement of the ball is due to unbalanced forces on it, not the balanced force of interaction pairs that act on each object.

SwimmingDue to the 3rd Law, when you swim you push the water (blue), and it pushes you back just as hard (red) in the forward direction. The water around your body also produces a drag force (green) on you, pushing you in the backward direction. If the green and red cancel out, you don’t accelerate (2nd Law) and maintain a constant velocity.

Note: The blue vector is a force on the water, not the on swimmer! Only the green and red vectors act on the swimmer.

Demolition Derby

When two cars of different size collide, the forces on each are the SAME (but in opposite directions). However, the same force on a smaller car means a bigger acceleration!