Chapter 5

Newton’s Laws of Motion

What determines acceleration on objects?

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Units of Chapter 5

• Force and Mass

• Newton’s First Law of Motion

• Newton’s Second Law of Motion

• Newton’s Third Law of Motion

• The Vector Nature of Forces

• Normal Force, Tension,

• Free body diagram, Problem solving skills

• Weight, Apparent weight 2

5-1 Force and Mass

Force: push or pull

Force is a vector – it has magnitude and

direction

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5-1 Force and Mass

Mass is the measure of

how hard it is to

change an object’s

velocity.

Mass can also be

thought of as a

measure of the quantity

of matter in an object.

The more matter one

object has, the harder it

is to change its

velocity. 4

5-2 Newton’s First Law of Motion

If you stop pushing an object, does it stop

moving?

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Only if there is friction! In the absence of any net

external force, an object will keep moving at a

constant speed in a straight line, or remain at rest.

This is also known as the Law of Inertia.

If the net force on an object is zero, it’s velocity is

constant (a=0). INERTIA (need safety belt)

Attention: If there is friction, Air resistance… net

force is not zero.)

In order to change the velocity of an object ,

magnitude or direction , a net force is required.

Example: Object on desk.

Net force =_____

5-2 Newton’s First Law of Motion

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Objects want to keep doing what they are already

doing.

For example:

in space…

Movie Unstoppable

Your dog knows…

5-3 Newton’s Second Law of Motion

If net force is not zero, velocity will not be constant.

a≠0

Object’s acceleration will be in the same directions

as the net force.

Acceleration direction is not the velocity direction.

Acceleration direction determines velocity change.

Fnet = ma

Acceleration is proportional to net force.

The more net force, the larger the acceleration. 7

5-3 Newton’s Second Law of Motion

Fnet = ma

Acceleration is inversely proportional to mass:

Same Force, less mass object gets bigger a.

Same Force, more mass object gets smaller a.

More mass, more inertia, harder to change v, less a

Less mass, less inertia, easier to change v, more a

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5-3 Newton’s Second Law of Motion

An object may have several forces acting on it;

the acceleration is due to the net force:

(5-1)

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SI unit for forces: Newton, (N)

F= m a; 1 Newton of net force gives 1 kg mass

1m/s2 acceleration.

1 N = 1 kg * m/s2

Attention: when you solve problem, if you first

convert every value to standard SI unit.

(m, s, m/s, m/s2 , N, ….) you can plug the numbers

and automatically get SI unit in your answer.

In order to give object of mass m a downward

acceleration of g=9.8 m/s2, how much force is

needed?

Gravity force = m g 10

Weight

The weight of an object on the Earth’s surface is

the gravitational force exerted on it by the Earth.

, also known as Gravity, G

G=mg

1 kg mass weights 9.8 Newton on earth.

9.8 Newton gravity force gives 1kg mass an

acceleration of 9.8m/s211

5-3 Newton’s Second Law of Motion

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5-4 Newton’s Third Law of Motion

Forces always come in pairs.

If object A exerts a force “F” on object B (action)

then object B must exert a force “negative F” on

object A (reaction).

Action and reaction forces are always

equal in size and opposite in directions.

Action /Reaction pair examples:

I push you, I feel your resistant.

These two forces are always equal and opposite(Will you push a nail tip or blade with large force?

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The 3rd law of Newton’s law is about two objects !

Not one object!

No, because the reaction resistant force from the blade

is as big as the push you give to it)

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Newton’s 3rd law applications:

1.

2. Throw heavy object forward. You feel recoil backward.

3. Swim, push water back, so that you can move

forward (water’s reaction force on you is forward)

4. Walk/run, you need to press down and back, so that

floor’s reaction force is upward and forward.

(That’s why on ice and sand it’s so hard to walk or drive)

5, Water hose sneak around….

6, Air balloon flies upward, while gas in it was squeezed

downward. (demo)

7, Your gravity, you 100 kg earth act 980 N gravity

force on you downward.

You act 980 N, gravity force on Earth upward.

5-4 Newton’s Third Law of Motion

Some action-reaction pairs:

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These two forces are not action and reaction pair:

I push you on left side.

He push you on your right side.

On one object bearing two forces.

These two forces are not action and reaction.

They can be equal or not. Nobody guarantee these

two forces to be equal.

I push you and you resist me, these two forces are

action and reaction pair. Newton’s 3rd law guarantee

these two forces to be equal in side and opposite in

directions.

These is very useful for calculations.

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These two forces are two forces acting on one object.

These two forces can be equal or not.

Free-body diagrams:

A free-body diagram shows every force acting on

an object.-Use a dot to represent the object of interest.

-Use one arrow with correct length and direction

to represent each force.

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Exercise for yourself: Forces add as vectors.

A hockey puck is acted on

by one or more forces, as

shown in Figure 5-19.

Rank the four cases, A, B,

C, and D, in order of the

magnitude of the puck's

acceleration, starting with

the smallest. Indicate ties

with an equal sign. (Use

only the symbols < and =,

for example A < B=C.) A < D < B < C

5-5 The Vector Nature of Forces: Forces in

Two Dimensions

The easiest way to handle forces in two

dimensions is to treat each dimension

separately, as we did for kinematics.

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The normal force is

the force exerted by

a surface on an

object.

Very often it is a

supporting force.

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5-7 Special forces, Normal Forces

5-7 Special forces, Normal Forces

Normal force is the force from a surface. Label N.

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Direction: Always perpendicular

& away from surface.

Size : depend on press of object.

How much you press, how much

It supports.

The normal force

may be equal to,

greater than, or less

than the weight.

When you pull on a string or rope, it becomes

taut. We say that there is tension in the string.

Special forces, Tension, Lable T

Direction: Always along rope,

always pointing away from

Object.

Size :

Tension inside

massless rope

in all location

has the

same size.

6-2 Strings and Springs

The tension in a real rope will vary along its

length, due to the weight of the rope.

Here, we will assume that

all ropes, strings, wires,

etc. are massless unless

otherwise stated.

Tension inside massless

rope in all location

has the same size.

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** problem solving strategy and steps

This is the most important slides for this semester.

1, Identify and isolate the object of interest, a dot.

2, Identify all forces on the object acted by

other objects. Label them using arrows of correct

length and direction

3, Pick x – y axis. ( based on acceleration

direction for convenience)

4, Break up all forces into x-y components

5, Set equations:

Add all force components in x directions = max

Add all force components in y directions = may

Fnet x= m ax , Fnet y= m ay (x & y are independent )

6, Solve for any two unknowns, from the above two

equations. (If know a, can solve force. If know forces

can find a. Again Math skills here. )

6-3 Translational Equilibrium

When an object is in translational equilibrium,

(Not moving or moving at constant velocity.)

the net force on it is zero:

This allows the calculation of unknown forces.

Add all force components in x directions = 0

Add all force components in y directions = 0

The traffic light problem.

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Example 1An object of mass m being dragged

with force F at angle q. (know m, F, q)

Find Normal force N, and acceleration.

1- object m, use a dot

2- label all forces on it mg, N, F

3- pick axes

4- components. F both x & y direction.

x direction: Fx component: Positive

y direction: Fy component: Positive

Fx= +Fcosq Fy = +Fsinq

5- Total F=ma for both x & y directions

+ or -?

Fnet x : Fcos θ =m ax,

Fnet y : N+Fsinθ-mg =may= 0

6- solve ax :

solve N :

ax =Fcos θ / m

N = mg - Fsinθ

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Example 2Incline plane. No friction.

We know m and angle q,

Find acceleration, and N.

1, object: dot

2, forces: mg, N, anything else?

3, pick x-y axes cleverly. (Along motion direction,

So that we know for sure ay=0)

4, force components: weight along incline: mgsinq

weight perpendicular to incline: mgcosq

It’s very important to do the drawing yourself.

5, Total F=ma; x direction : mgsinq =max

y direction: N-mgcosq=0

6, solve equations: ax=gsinq; N=mgcosq; Check for special angles. If q=0, a=0, N=mg; If q=90, a=g, N=0,

Make sense. Large q, Larger sinq, Larger a, smaller q, Less N

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5-6 Apparent Weight

Apparent weight: Your perception of your weight is

based on the contact forces between your body

and your surroundings. It’s N or T…

If you are accelerating

your surroundings , your

apparent weight may be

more or less than your

actual weight.

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If Accelerating downward,

Define downward to be positive direction:

mg-N=may ; so N= mg- may

N<mg, you still has same mg, but no enough support.

That’s what frightens you badly in those terror rides.

Apparent weight =N <mg,

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If acceleration is downward,

Mass unchanged. Gravity unchanged.

But Normal force is less. Apparent weight is less.This is what frightens you in the theme park rides.

Even in complete dark, you can tell N<mg, feel downward a

In an elevator, that is accelerating upward:

N>mg , N - mg = m|ay|; N= mg + m|ay|) > mg

Mass unchanged, gravity unchanged,

But apparent weight is more!Look at the poor girl.

T= mg + m|ay|, when a is upward

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If no elevator, try quickly stand up or squat on scale.

Acceleration is not equal to 0 (Try it at home)

This is how Wii fit detect your motion (acceleration)

by measuring the Normal forces between it and you.

________________________________________Question, in an elevator, going down at constant velocity

N > = < mg???? a=????

Answer: a= 0; N = mg

Q: Constant velocity elevator going up ?

Apparent weight, N= ??

Before next class, at least Read Chapter 6-1 friction,

Summary of Chapter 5• Force: a push or pull

• Mass: measures the difficulty in accelerating an

object

• Newton’s first law: if the net force on an object

is zero, it stay at rest or keep constant velocity.

•Newton’s second law: for one object

• Free-body diagram: a sketch showing all the

forces on an object. Remember to decompose in

x and y directions.

•Solve F=ma in both x and y direction separately

Add all forces in x directions = max

Add all forces in y directions = may

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Summary of Chapter 5

• Newton’s third law: If object 1 exerts a force

F on object 2, then object 2 exerts a force –F

on object 1.

• Contact forces: an action-reaction pair of

forces produced by two objects in physical

contact

• Forces are vectors

• Newton’s second laws can be applied to x

and y each components of the forces

separately

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Summary of Chapter 5

• Weight: gravitational force exerted by the Earth on

an object, Always DOWNWARD.

•On the surface of the Earth, W = mg

• Apparent weight: force felt from contact with a floor

or scale. It’s determined by both mg and acceleration

• Normal force: Always perpendicular to the surface.

(away from the surface)

• Normal force is determined by the amount of

“pressing” again the surface. It may be equal to,

lesser than, or greater than the object’s weight.

• Tension force in a string is always ALONG the string.

It is equal everywhere if the string has no mass. 34