© 2001-2005 Shannon W. Helzer. All Rights Reserved. Unit 5 Graphical Vector Addition and Newton’s...

© 2001-2005 Shannon W. Helzer. All Rights Reserved.

Unit 5Graphical Vector Addition

and Newton’s Law


Vectors

Vectors are physical quantities that not only have a magnitude (size) but also that have a direction in which they act.

For instance, we have already used the velocity triangle. Velocity is the speed of a body in a given direction. Another vector quantity commonly used is displacement which is a

distance traveled in a specific direction. Yet another vector used in our every day lives is the force vector made

up of a push or a pull in a given direction. In the next slide we will exam the nature of the displacement vector.

5-1


Vectors vs Scalars Suppose the three friends below drive their four wheelers a distance of 100.0 m. Will they end up in the same place? Why or why not. No, 100.0 m is a scalar and does not specify a specific direction. Now suppose they drive 175.0 m due East. Will they end up in the same place? Why or why not. Yes, 175.0 m East is a vector and specifies a specific direction.

5-2


Identical Vectors

If any two vectors have the same magnitudes and directions, then they are identical vectors.

Here vectors B and D are identical even though they are in different places.

B

Protractor

D

Protractor

5-3


Adding Vectors Graphically

C = A + BA

B

C

Vectors are always added “head to tail.”

Always measure the angle from the +x axis.

What are the two parts of a vector?

Given vectors A and B, find vector C.

[email protected]

[email protected]

?C

Protractor

Protractor

Protractor

5-4


Hand Glider Trip

5-5


Graphical Vector Addition – Hand Glider

On the first part of a hand glider flight, a pilot flies her glider 300.0 m due East (A = 300 m @ 0).

Afterwards, she turns North West and flies 450.0 m (B = 450 m @ 135 ).

Finally, she turns due South and flies 250.0 m (C = 250 m @ 270)

What is her displacement (D) from her takeoff point?

D = A + B + C

5-6


Graphical Vector Addition - Robots

Three Physics track robots pull on a book as shown.

They pull with the following forces: 7.0 N @ 45, 8.0 N @ 180, and 5.0 N @ 270 .

Find the net force applied to this most valuable book.

5-7


Graphical Vector Addition - Robots

Three Physics track robots pull on a book as shown.

They pull with the following forces: 7.0 N @ 45, 8.0 N @ 180, and 5.0 N @ 270 .

Find the net force applied to this most valuable book.

5-8


Force and Interactions Force – a “push or pull”

Contact Force – you physically pushing (touching) on a wall

Long-range Force – like magnets or like Weight (gravity)

Force – a vector quantity. Has what two parts?

SI Unit – the Newton abbreviated as “N”

Superposition of Forces – forces combine according to vector addition

5-9

1F

PullR

2F

1F

2F

R

Push

21 FFR


An object remains at rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force.

Here, the skateboard/log combination is at rest until acted on by the force imposed by the rocket.

Newton’s First Law of Motion – At Rest

5-10


Newton’s First Law of Motion – In Motion For an object in motion, the object will continue in a straight line until

acted on by some “outside” force. Consider the space shuttle turning while in space flight. What produces

the forces?

5-11


Newton’s First Law of Motion – In Motion For an object in motion, the object will continue in a straight line until

acted on by some “outside” force. Consider the space shuttle when landing. What produces the forces?

5-12


Newton’s Second Law of Motion

Relationship between the acceleration of a body and the force that produced the acceleration.

Newton’s Second Law – If there is a non-zero net force on a body, then it will accelerate.

In equation form the relationship can be expressed in two ways as follows:

m

Fa

amF

5-13


Newton’s Second Law – Non-Equilibrium Situation

The net result of a Non-Equilibrium situation is that the body, upon which the net force acts, will begin to accelerate.

amFFFF

...321

1F

1F

2F

amFF

1

amFFF

21

5-14


Newton’s Third Law Newton’s Third Law - If body A exerts a force on body B (action),

then body B exerts a force on body A (the reaction). These two forces have the same magnitude but are opposite in direction.

Newton’s Third Law - for every action force there is an equal, but opposite, reaction force.

Example - you sitting on your seat. Your weight (a force) is pressing down on your seat. The seat is pushing back up on your butt. As a result of these two equal but opposite actions, you do not fall through the seat and to the ground.

Action-Reaction Force Pair – the forces involved in Newton’s Third Law

5-15


Newton’s Third Law - Example Consider a book resting on a table. Why doesn’t the book fall through the table?

gmW

NW

gmN

The weight, W, and the normal force, N,

comprise an action-reaction pair. The normal force is the force which opposes

the weight of the book. It always acts perpendicular to the surface

upon which the body rests. They balance each other; therefore, the book

does not fall through the table.

5-16


Newton’s Laws – A Review Newton’s First Law - An object remains at rest, or in uniform motion in a

straight line, unless it is compelled to change by an externally imposed force.

Newton’s first law describes an Equilibrium Situation. An Equilibrium Situation is one in which the acceleration of a body is

equal to zero. Newton’s Second Law – If there is a non-zero net force on a body, then it

will accelerate. Newton’s Second Law describes a Non-equilibrium Situation. A Non-equilibrium Situation is one in which the acceleration of a body is

not equal to zero.

Newton’s Third Law - for every action force there is an equal, but opposite, reaction force.

5-17


Net Force – Equilibrium at Rest What is the downward force on the crate pictured? Weight (W) – a force resulting from the gravitational acceleration acting

upon a body. What is the upward force acting on the crate? The Normal Force (N) – the upward force exerted on a body by the surface

upon which it rest. Always acts perpendicular to the surface. Net Force – What is the net force acting on the crate? Remember

Newton’s third law.

The forces are equal and opposite. Will this crate accelerate in the vertical direction? Why or why not?

5-18gmW

gmN

0 WNFNET


What forces are acting on the train while it is moving in a straight line at a constant speed?

Engine Force (FE) – Force applied to propel the train along the tracks.

Opposition Force (Fo) – friction between the tracks, wind resistance, etc. that attempts to slow the train down.

What is the acceleration of the train? Negative, Zero, or Positive. Is this an equilibrium or non-equilibrium situation?

Net Force – Equilibrium in Motion

EF

OF

5-19


Net Force – Non-Equilibrium Describe what happens in the animation below. What forces were acting on the train? Engine Force (FE) – Force applied to propel the train along the tracks.

Opposition Force (Fo) – friction between the tracks, wind resistance, etc. that attempts to slow the train down.

Which force was larger? What is the acceleration of the train? Negative, Zero, or Positive. Is this an equilibrium or non-equilibrium situation?

5-20

EF

OF


Net Force – Non-Equilibrium Describe what happens in the animation below. What forces were acting on the train? Opposition Force (Fo) – friction between the tracks, wind resistance, etc.

that attempts to slow the train down. What is the acceleration of the train? Negative, Zero, or Positive. Is this an equilibrium or non-equilibrium situation?

OF

5-21


Equilibrium or Non-equilibrium

When the helicopter is on the ground, what state is it in?

Why isn’t it accelerating? In order to get it accelerating,

what would we need? What state is it in when it is

hovering in place? In order to get it to accelerate,

what would we need?

5-22


Example 1 A 3.5 kg block being pushed across a floor experiences an acceleration of

4.0 m/s2.

a. What is the net force acting on the block?

b. If F1 is 16 N, then what is the magnitude of the force of friction, F2,

opposing F1?

1F

2F

amFFF

21

5-23


Example 2 A 5.0 kg block being acted upon by three horizontal forces as shown

below.

When F1 acts alone on the block, it produces an acceleration of 1.8 m/s2 to the right. Likewise, F3 produces an acceleration of 1.1 m/s2 to the right.

When all three forces are acting on the block, it experiences an acceleration of 2.3 m/s2

a. What is the magnitude and direction of force F2 acting on the block?

1F

2F

amFFFF

321

3F

5-24


What can help? A Large 4X4 is stuck on a sheet of ice. What could the driver do to drive

her truck on the ice? How about a set of tire spikes? What interaction occurs between the spikes and the ice?

5-25


Frictional Forces Whenever two bodies interact by direct contact of their surfaces, we call the

interaction forces “contact forces.”

Can you name one contact force we have already discussed?

The Normal Force.

Name another contact Force?

Friction Force.

Frictional forces results from the intermolecular (electrical) forces.

As one body slides across another, these forces continually form and break.

5-26


Frictional Forces

There are two kinds of friction forces: Kinetic and Static Forces.

Kinetic Frictional Forces – the kind of friction that acts when a body slides over a surface. Better thought of as “sliding” friction.

The coefficient of kinetic friction is denoted as k. k is a proportionality constant.

5-27


Frictional Forces

If the body is at rest and you try to push it across the floor with an ever increasing force, then initially the box will not move because the frictional force between the body and the floor exerts an equal, but opposite, force against the body.

This force is known as the static friction force.

5-28


Static Friction v. Kinetic Friction Static friction exist when an object wants to move but is held in

place by the force of friction. This force of friction is greater than the component of the weight

acting down the plane. If we continue to rotate the plane, the component of the weight

acting down the plane will eventually become larger than the normal force.

When this happens, the object will begin to slide changing from static friction to kinetic friction.

Force of Friction v. Time

-7

-6

-5

-4

-3

-2

-1

0

1

0 2 4 6 8 10

Time (s)

Fri

ctio

n (

N)


Presence of Frictional Forces

In the presence of friction, which ball do you think would go the farthest? Why?

5-29


Absence of Frictional Forces

In the absence of friction where would a ball originally positioned as shown stop?

Why?

5-30


Newton’s Laws Applications

What type of friction acts on the piano as it slides down the ramp?

5-31



What type of friction acts on the piano as it rests on the ramp?

Draw the Free Body Diagram for the piano.

The Normal force is always ______________ to the surface.

5-32


Newton’s Laws Applications – Free Body Diagrams

Two tractors pull on a crate as shown. How many forces are acting on the crate? If the crate started from rest, then which way did it accelerate? Draw the FBD for the crate. What type of a situation is depicted below?

DigDug

5-33


Setting the Standard When we do problems involving

kinematics, it is important that we stick to a standard when imputing data into the know-want table.

This standard enables us to take into account the vector nature of acceleration, velocity, displacement, etc.

Here is a diagram we will use in order to help us correctly input data into the table.

This standard is based upon the Cartesian Coordinate system.

If a body travels West, then what sign would you give its velocity?

If a body travels at an angle of 90 degrees, then what sign would you give its velocity?

3-3


Forces on a Car – Free Body Diagrams What is the name of the force exerted by the car onto the road? The weight. What force opposes the weight of the car? The normal force acting perpendicularly to the surface of the road. The normal force is always perpendicularalways perpendicular to the surface. Draw the FBD for the car.

N

W

5-34



The recoil caused by a cannon firing a cannonball demonstrates which of Newton’s Laws?

Draw the FBD for the cannon as the gun powder explodes.

5-35


Net Force – Non-Equilibrium Describe what happens in the animation below. Now, draw the FBD.

5-36



Watch the two shots below.

Which one demonstrates Newton’s first law?

Which one demonstrates Newton’s second law?

5-37


Newton’s Laws Applications Use Newton’s Laws to describe what happened… To the hatchet as it was thrown. As it flies towards the log. When it hits the log. What about the log itself?

5-39


Setting the Standard - Torque a

2m

1m


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© 2001-2005 Shannon W. Helzer. All Rights Reserved. Unit 5 Graphical Vector Addition and Newton’s...

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