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Academic PhysicsAcademic Physics

Forces UnitForces Unit

Table of ContentsTable of Contents

Introduction to Forces

Atwood’s MachineNewton’s Laws

Friction

Dynamics

Free Body Diagrams

Net Force

Complex Force Probs

Inclined Planes

Mass and Weight

Introduction to ForcesIntroduction to Forces A force is a push or pull, an agent that A force is a push or pull, an agent that

can affect the state motion of an can affect the state motion of an object.object.

Force is measured in Newtons Force is measured in Newtons (symbol N)(symbol N)

Forces can be created from direct Forces can be created from direct contact or be remote.contact or be remote.

There are also special forces that There are also special forces that occur within atoms.occur within atoms.

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Introduction to Forces 2Introduction to Forces 2

These forces These forces involve pushing involve pushing and pulling objects and pulling objects directly or through directly or through some object(s).some object(s).

Examples include:Examples include: Direct TouchDirect Touch Using strings, Using strings,

chains, or ropes.chains, or ropes. BuoyancyBuoyancy

These Forces do These Forces do not require direct not require direct contact.contact.

Examples include:Examples include: GravitationGravitation Electrostatic Electrostatic

ForcesForces Magnetic ForcesMagnetic Forces

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Direct Contact Forces

Remote Forces

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Introduction to Forces 3Introduction to Forces 3 There are also some special There are also some special

additional forces that exist in additional forces that exist in physics. These include:physics. These include: Strong Nuclear Force: Force that allows Strong Nuclear Force: Force that allows

atomic nuclei to stay in tact.atomic nuclei to stay in tact. Weak Nuclear Force: Force that is Weak Nuclear Force: Force that is

involved in radioactive nuclear decay.involved in radioactive nuclear decay.

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Introduction to Forces 4Introduction to Forces 4 Kinematics is the study of motion Kinematics is the study of motion

involving how objects move, involving how objects move, including the following quantities.including the following quantities. Position, Distance, DisplacementPosition, Distance, Displacement Speed, VelocitySpeed, Velocity AccelerationAcceleration

Dynamics is the study of relating Dynamics is the study of relating forces to kinematics, involving why forces to kinematics, involving why objects move.objects move.

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Mass and WeightMass and Weight Mass is a measure of the amount of matter in Mass is a measure of the amount of matter in

an object, a measurement that is constant. an object, a measurement that is constant. The unit for mass is the kilogram (kg)The unit for mass is the kilogram (kg)

Weight is the force on an object due to Weight is the force on an object due to presence of gravity, a variable quantity presence of gravity, a variable quantity dependent upon location. The unit for weight dependent upon location. The unit for weight is the Newton (N)is the Newton (N)

As always the acceleration due to gravity is As always the acceleration due to gravity is The equation involving weight is shown The equation involving weight is shown

below.below.


Mass and Weight 2Mass and Weight 2 Below are 3 sample calculations Below are 3 sample calculations

involving weight.involving weight. Calculate the weight of a 15kg lawn Calculate the weight of a 15kg lawn

mower.mower.

Calculate the mass of a frog weighing 4N.Calculate the mass of a frog weighing 4N.

Calculate the gravity on Mars if a 4.0kg Calculate the gravity on Mars if a 4.0kg object weighs 15.2Nobject weighs 15.2N


W mg 215 9.8 ms

W kg 147W N

0.41m kg2

4

9.8 ms

Nm

Wm

g

Wg

m

15.2

4

Ng

kg 23.8 m

sg

Newton’s Laws of MotionNewton’s Laws of Motion Sir Isaac Newton was a Sir Isaac Newton was a

British scientist that did British scientist that did extensive research and extensive research and devised theories involving devised theories involving forces and mechanics.forces and mechanics.

Newton devised 3 laws Newton devised 3 laws that describe that describe relationships between relationships between forces and motion.forces and motion.

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Sir Isaac Newton

(1643-1727)

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Newton’s Laws of Motion Newton’s Laws of Motion 22 Newton’s first law is known as the Law Newton’s first law is known as the Law

of Inertia. It is stated as follows:of Inertia. It is stated as follows:

Every object continues in its state of Every object continues in its state of motion, being at rest or at a constant motion, being at rest or at a constant velocity in a straight line, unless acted velocity in a straight line, unless acted upon by an outside forceupon by an outside force

In short, objects only experience In short, objects only experience acceleration unless a force is involved.acceleration unless a force is involved.

Consider some realistic situations in Consider some realistic situations in which forces and acceleration are which forces and acceleration are paired.paired.


Newton’s Laws of Motion Newton’s Laws of Motion 33 Newton’s Second Law deals with the Newton’s Second Law deals with the

relationship between force, mass, and relationship between force, mass, and acceleration. It is stated as follows:acceleration. It is stated as follows:

The acceleration of an object is The acceleration of an object is directly proportional to net force, directly proportional to net force, inversely proportional to mass, and in inversely proportional to mass, and in the same direction as the net force.the same direction as the net force.

It also can be written in equation It also can be written in equation form, which is shown below.form, which is shown below.

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F ma

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Newtons Laws of Motion Newtons Laws of Motion 44 Here are 2 sample calculations Here are 2 sample calculations

involving Newton’s 2involving Newton’s 2ndnd Law. Law. How much force is required to How much force is required to

accelerate a 0.2kg hockey puck with an accelerate a 0.2kg hockey puck with an acceleration of ?acceleration of ?

What is the acceleration on the puck if What is the acceleration on the puck if the force is 10N?the force is 10N?

F ma 20.2 20 ms

F kg 4F N

220 ms

Fa

m

10

0.2

Na

kg 250 m

sa

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Newton’s Laws of Motion Newton’s Laws of Motion 55 Newton’s third law deals with the effects Newton’s third law deals with the effects

of forces on multiple objects during an of forces on multiple objects during an interaction. It is written as follows:interaction. It is written as follows:

Every action has an equal and opposite Every action has an equal and opposite reaction.reaction.

Each force is paired with another forceEach force is paired with another force Consider several examples:Consider several examples:

A Hammer and NailA Hammer and Nail A Cannon Firing a Cannonball.A Cannon Firing a Cannonball.


Free Body DiagramsFree Body Diagrams Free Body Diagrams (FBD’s) Free Body Diagrams (FBD’s)

show all the forces acting on a show all the forces acting on a single object.single object. The object is represented by a The object is represented by a

dot.dot. Forces are represented by Forces are represented by

labeledlabeled arrows. arrows. Only forces are shown on the Only forces are shown on the

diagram, not other values such diagram, not other values such as mass, acceleration, and as mass, acceleration, and velocity.velocity.

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W

N

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Free Body Diagrams 2Free Body Diagrams 2 There are several special forces involved in There are several special forces involved in

FBD’s, which are listed below.FBD’s, which are listed below. Weight (W): Force due to presence of gravityWeight (W): Force due to presence of gravity Normal Force : Supporting force of surfaces; Normal Force : Supporting force of surfaces;

always perpendicular to surface.always perpendicular to surface. Tension (T): Force found in strings and chains.Tension (T): Force found in strings and chains. Buoyancy (B): Supporting force of floatation.Buoyancy (B): Supporting force of floatation. Friction (FFriction (Fff): The force acting against motion.): The force acting against motion. Air Resistance (FAir Resistance (Fairair): Oppositional force of air on ): Oppositional force of air on

moving objectsmoving objects

N


Free Body Diagrams 3Free Body Diagrams 3 Here are some sample FBD’s of objects.Here are some sample FBD’s of objects. Please note: the diagrams are superimposed over Please note: the diagrams are superimposed over

the pictures. You are never required to draw a the pictures. You are never required to draw a picture, only the FBD.picture, only the FBD.


Falling Rock

Boy Pulling Wagon

Sled On Hill

W

N��

W W

N��

fFfF

airFappF

Net ForceNet Force Net force is the vector sum of Net force is the vector sum of

all forces acting on an object.all forces acting on an object. If , then an object will not If , then an object will not

accelerate. The situation is called accelerate. The situation is called equilibrium.equilibrium.

If , then an object will If , then an object will accelerate. This situation is called accelerate. This situation is called nonequilibrium.nonequilibrium.

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NetF

0NetF

0NetF

0a 0NetF

Forces Unbalanced

NonequilibriumEquilibrium

0a 0NetF

Forces Balanced


Net Force 2Net Force 2 Net Force can be found by performing Net Force can be found by performing

graphical or analytical vector addition.graphical or analytical vector addition. If the forces are along the same If the forces are along the same

directional line, they can be simply added directional line, they can be simply added or subtracted (Right +, Left -).or subtracted (Right +, Left -).

An sample net force calculation is shown An sample net force calculation is shown below.below. For the given FBD of a tug of war, find FFor the given FBD of a tug of war, find FNetNet..


54LF N45RF N

Net R LF F F

45 54NetF N N

9NetF N

DynamicsDynamics Dynamics basically involves Dynamics basically involves

combining force problems with combining force problems with kinematics problems. In a given kinematics problems. In a given situation with forces, Newton’s 2nd situation with forces, Newton’s 2nd Law serves as a “bridge” between Law serves as a “bridge” between forces and motion.forces and motion.

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Forces F = ma Kinematics


FrictionFriction Friction occurs between two surfaces in Friction occurs between two surfaces in

contact, always opposing motion (180° contact, always opposing motion (180° opposite)opposite)

Static friction occurs between surfaces at Static friction occurs between surfaces at relative rest between each other.relative rest between each other.

Sliding friction (also known as kinetic Sliding friction (also known as kinetic friction) occurs between surfaces in friction) occurs between surfaces in relative motion with each other.relative motion with each other.

For any two given surfaces in contact, the For any two given surfaces in contact, the static friction will be greater than the static friction will be greater than the sliding friction.sliding friction.

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Friction 2Friction 2 Friction can be quantified using a Friction can be quantified using a

coefficient coefficient (a Greek letter “mu”) (a Greek letter “mu”) An equation using the coefficient is An equation using the coefficient is

shown here.shown here.

The coefficient depends on the two The coefficient depends on the two surface types involved. It is also unitless.surface types involved. It is also unitless.

The equation shows that frictional force The equation shows that frictional force also depends on the normal force .also depends on the normal force .

fF N

N


Friction 3Friction 3 A sample friction problem is shown below.A sample friction problem is shown below.

The coefficient of friction between 2 wood surfaces is The coefficient of friction between 2 wood surfaces is 0.4. A wood block (m = 1.3kg) is pushed across this flat 0.4. A wood block (m = 1.3kg) is pushed across this flat surface with a force of 21N. surface with a force of 21N.

a) Draw an FBD for the problem. a) Draw an FBD for the problem.

b) What is the weight of the block?b) What is the weight of the block?

c) What is the normal force acting on the block?c) What is the normal force acting on the block?

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W

fF appF

N��

W mg 21.3 9.8 ms

W kg 12.74W N

*On a flat surface, the normal force is equal to the weight.12.74N N��

Friction 4Friction 4 The sample friction problem is continued below.The sample friction problem is continued below.

The coefficient of friction between 2 wood surfaces is The coefficient of friction between 2 wood surfaces is 0.4. A wood block (m = 1.3kg) is pushed across this flat 0.4. A wood block (m = 1.3kg) is pushed across this flat surface with a force of 21N. surface with a force of 21N.

d) What is the force of friction acting on the block?d) What is the force of friction acting on the block?

e) What is the net force acting on the block?e) What is the net force acting on the block?

f) What is the acceleration of the block?f) What is the acceleration of the block?

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fF N��

0.4 12.74fF N 5.096fF N

W

fF

N��

Net app fF F F 21 5.096NetF N N 15.904NetF N

NetFF ma a

m

15.904

1.3NetF N

am kg

212.23 ms

a

appF

Friction 4Friction 4 There are other oppositional forces that There are other oppositional forces that

behave similarly to friction.behave similarly to friction. Air resistance opposes motion of objects Air resistance opposes motion of objects

through air. through air. Consider the “wind” felt by riding in a car.Consider the “wind” felt by riding in a car. Terminal velocity is the velocity at which a Terminal velocity is the velocity at which a

falling object will reach equilibrium and fall falling object will reach equilibrium and fall at a constant velocity. This is dependent at a constant velocity. This is dependent upon the shape, size, and density of the upon the shape, size, and density of the object.object.


Friction 5Friction 5 The picture below shows a falling The picture below shows a falling

object during different stages of its object during different stages of its fall.fall.


Release Some Time After Release

Terminal Velocity

Release

Terminal Velocity

Mid Fall

W W

airF

W

airF

Speed

Drop

Atwood’s MachineAtwood’s Machine A machine called an A machine called an

Atwood’s Machine involves Atwood’s Machine involves two masses connected by a two masses connected by a string and hung from a string and hung from a pulley.pulley.

These machines serve as These machines serve as great devices for developing great devices for developing an understanding of force an understanding of force and acceleration concepts.and acceleration concepts.

Atwood’s Machine AppletAtwood’s Machine Applet


Atwood’s Machine 2Atwood’s Machine 2 In order to solve Atwood’s machine In order to solve Atwood’s machine

problems, a FBD must be drawn for problems, a FBD must be drawn for each mass. each mass.

Next, the net force equations must be Next, the net force equations must be set up for each mass (Align with set up for each mass (Align with direction of motion as the positive direction of motion as the positive direction).direction).


Mass 1 Mass 2

1W

T T

2W

2 1NetF W T T W

2 1NetF W W

Atwood’s Machine 3Atwood’s Machine 3 Calculate the acceleration using Calculate the acceleration using

Newton’s 2Newton’s 2ndnd Law. Law.

The equation can also be modified into:The equation can also be modified into:

This is a generalized equation for any This is a generalized equation for any Atwoods machine.Atwoods machine.


1 2

NetFa

m m

2 1

1 2

m g m ga

m m

2 1

1 2

g m ma

m m

*Total mass must be used.

Atwood’s Machine Atwood’s Machine A sample Atwood’s machine problem is A sample Atwood’s machine problem is

shown below.shown below.


Complex Force ProblemsComplex Force Problems These problems involve multiple These problems involve multiple

objects, each with their own forces objects, each with their own forces involved.involved.

A FBD must be drawn for each A FBD must be drawn for each object.object.


Block Hanging Mass

Inclined PlanesInclined Planes Inclined planes are slopes in which the effects Inclined planes are slopes in which the effects

of gravity affect the movement of objects.of gravity affect the movement of objects. The pitch of the slope is gauged by an angle The pitch of the slope is gauged by an angle

formed at the base called formed at the base called .. The weight of an object on the incline is The weight of an object on the incline is

directed straight down.directed straight down. However, the normal force is not directed However, the normal force is not directed

upward, but perpendicular to the incline.upward, but perpendicular to the incline.


N��

W

Does this look like an equilibrium situation to you?

Inclined Planes 2Inclined Planes 2 The component of an object’s weight that is parallel to the The component of an object’s weight that is parallel to the

incline will tend to accelerate the object.incline will tend to accelerate the object. This can be calculated by recognizing the presence of This can be calculated by recognizing the presence of

some similar right triangles in relation to the forces some similar right triangles in relation to the forces present.present.

The component of the weight perpendicular to the plane The component of the weight perpendicular to the plane is also important, especially in its relation to the normal is also important, especially in its relation to the normal force.force.

The following relationships can be found from the diagram.The following relationships can be found from the diagram.


N��

W

||W

W

||W

W

|| sinW W

cosW W W N

��

||W

W

Inclined Planes 3Inclined Planes 3 A sample incline problem is shown A sample incline problem is shown

below.below.


SummarySummary Forces are included in almost every aspect of our lives.Forces are included in almost every aspect of our lives. Newton’s Laws help us to understand how forces relate Newton’s Laws help us to understand how forces relate

to the motion of objects (Kinematics and Dynamics).to the motion of objects (Kinematics and Dynamics). FBD’s illustrate the layout of forces for a given situation.FBD’s illustrate the layout of forces for a given situation. The net force is used to determine acceleration of an The net force is used to determine acceleration of an

object.object. Equilibrium and nonequilibrium situations are essential Equilibrium and nonequilibrium situations are essential

to understand, as they relate to situations in reality.to understand, as they relate to situations in reality. Friction is a realistic force that can be quantified and is Friction is a realistic force that can be quantified and is

dependent upon surface type and normal force.dependent upon surface type and normal force. Special situations, such as the Atwood’s machine and Special situations, such as the Atwood’s machine and

inclines, provide interesting examples from which to inclines, provide interesting examples from which to better understand force concepts.better understand force concepts.

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