# Chapter 4 Newton's Laws

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```					Chapter 4: Newton's Laws
Forces
 We are now concerned with the causes of motion (dynamics)

   Force ( F or F ): an action exerted on an object which may
change its state of rest or motion.
 Examples:
o Push
o Pull
o Air resistance
o Friction
Two types of forces:
1.   Contact Force: results from physical contact between
two or more objects; physical.

2.   Field Force: results from no physical contact; objects
don’t touch.
   Less is known about field forces
   Magnetism, force fields, etc. are examples.
The Four Fundamental Forces of Nature

 The four natural forces are all field forces
 They are not fully understood (special
relativity, quantum mechanics, string
theory….scientists are still working on
these!)
The Four Fundamental Forces of Nature

1)       Nuclear Force (or the
Strong Force): holds the
subatomic particles
together.
     Acts as atomic glue within
an atom:

(shouldn’t those positive
charges be fighting to get
away from one another?)
The Four Fundamental Forces of Nature

2) The Weak Force: repelling force that causes radioactive
decay; dissolves the Nuclear Force.

3) Electromagnetic Force (EM): Positive and negative
charge interactions; North and South pole interactions.
 Can be attractive or repulsive

4) Gravitational Force: Gravity; anything that has mass has
an attractive force.
Strength
Can we rank the four forces in terms of strength?
Strongest
1. Nuclear
2. EM                 Range
3. Weak               Can we rank the four forces in terms of range?
4. Gravity
Weakest                                   Longest Range
1. Gravity
2. Weak
3. EM
4. Nuclear
Shortest Range
THE LAW OF UNIVERSAL
GRAVITATION

m1                                 m2

r

m1m2
F 2
r
•The gravitational force is proportional to the masses of the objects.
•The force is inversely proportional to the distance between them,
squared.
m1m2
F G 2
r

11
G  6.67 x10         N  m / kg
2        2
4 units
3 units
2 units
1 unit

Let’s look at the inverse-square
nature for the force of gravity.
Gravity is the most dominant, far-reaching force in

nature.

Yet it is the weakest!

Gravity is caused by MASS….yet there is more

gravity than mass to explain it….
THE MASS
Every object possesses inertia.
Inertia is the tendency of a body at rest to remain at
rest, and of a body in motion to continue in motion
or
Inertia is the sluggishness of an object to changes in its state of
motion.
Mass - a measure of the inertia of an object
Inertia is what causes the injury in a car accident:

If a body is travelling at 50 mph and it hits a wall, the body tries to
continue moving at 50 mph! The seatbelt, dashboard, windshield, etc
will work against this forward motion.
Mini Lab – Inertia of a coin and the spinning egg

Perform the mini-labs, then sketch and write an
Homework: You’re the Attorney….
You are an attorney defending a
bus driver on a personal injury
case. The plaintiff claims that she
was sitting in the back of a moving
bus when the driver suddenly
applied the brakes, causing a
suitcase from the front of the bus
to fly back and hit her. She is suing
the driver and the bus company
for pain and suffering. How would
Recap: Inertia
 Inertia is Newton’s First Law of Motion:

“An object at rest stays at
rest, and an object in
motion stays in motion
unless acted upon by an
outside force.”
Recap: Force

In general force is the agency of change.
In mechanics forces cause accelerations.
It is a vector.
It is an action exerted on a system.
Newton’s Second Law of Motion
 The Second Law of Motion states that the
acceleration of an object is proportional to
the force, and is inversely proportional to its
mass.

Huh?
F             a
The total of all forces that act on                 m
an object is the net force.
(Only the net force is shown in
the figures on this slide.)                F        m        a

F            m            a
This symbol means
The acceleration of an object is directly proportional to
proportional to the net force.                        
a F
Consider the same net
F
m       a
force applied to different
m
mass objects.
F           a
m

m

m
The acceleration is          F
m
a
inversely proportional to
the mass of the object.
a 1
m
So in other words….

∑F = ma
“Sigma” – means the
sum of, or total
Force       Mass         Acceleration

SI Units: F = ma = (kg) (m/s2)

So the unit of force is kg m/s2 which equals a newton (N).

1 N = 1 kg m/s2
THE STANDARD KILOGRAM

The standard kilogram is an object whose mass is defined to be one
kilogram.
Abbreviation is kg.
There is an English unit of mass. The slug.
A slug weighs 32.2 lb.
THE NET EXTERNAL FORCE

The net force (∑F) is the total of all of the forces acting. Sometimes
it’s just one force, and sometimes there are many.

You must add them all up to find the net force.

Direction is important! They are all vectors, after all….
THE NET FORCE

Have you ever played Tug-of-War?

You have to find out who is winning, and by how much, before you
can solve problems with the equation F = ma.
If 65-kg Ramiro pulls to the left with 250 N of force, and 50-kg Maria pulls to
the right with 200 N of force, what is the net force? What is the acceleration
of the loser?

F1 = -250 N (because left is negative on the x-axis)
F2 = +200 N
∑F = F1 + F2 = -250 N + 200 N = -50 N or 50 N to the left

Since F = ma,    a = F/m = (-50 N) / (50 kg) = - 1.0 m/s2 or 1.0 m/s2 to the left.

Sorry Maria!
Free Body Diagrams
 FBDs are drawn to isolate forces acting on a system
 FBDs are required and graded on the AP Test

1) Create a dot for the object of interest
2) Draw force vector arrows originating
from the object of interest
3) Label the forces with subscripts

 When done with the FBD, you may draw additional
diagrams showing components and net forces.
FBD Example
 A crate is being pulled to the right 50 N by a rope. The force
of gravity has an effect of 100 N (its weight) and the ground
supports it with the same amount of upward force. Friction on
the ground also provides 25 N of force opposing direction of
motion. Draw a free body diagram showing all forces.
Fsup

Ffric            Fr

Fgrav

The free body diagram is done!
The next diagram: Component Diagram
 With the initial FBD complete, you can start filling in values
and components:
The labeled diagram allows us to easily solve
Fsup = 100 N           for the net force:

∑Fx = Fr + Ffric = 50N + (-25N) = 25N

Ffric = 25 N              Fr = 50 N   ∑Fy = Fsup + Fgrav = 100N + (-100N) = 0N

∑F = √(Fx2 + Fy2) = 25 N
Fgrav = 100 N
A net force
diagram would
∑F = 25 N
be as follows:
∑F = 25 N

 If the crate had a mass of 10 kg, how quickly
would it accelerate across the ground?

 F = ma → a = F/m = 25N/10 kg = 2.5 m/s2
Practice!
 Draw an FBD, a component diagram, and find the
net force of each system:
1. An elevator’s cable provides a 1000 N force
upward while the force of gravity (its weight)
pulls down 600N.
2. A car is being towed by a 2000 N force at an
angle of 15° from the horizontal. Friction is
providing a 400 N force against the motion of
the car along the horizontal.
3. A motor moves a boat through water with a 600
N force. The water provides 150 N of resistance.
A strong wind blows in the direction of the
boat’s motion with a force of 50 N.
4. Two students pull on a stubborn donkey as
shown. How hard is the donkey pulling back?
The Elevator
Connected objects
 A 200 kg beam is connected by a cable to a 300 kg beam
below it. The two are raised with an acceleration of 0.50
m/s2 by another cable attached to the 200 kg beam. Ignoring
the masses of the cables, find the tension in each.
Atwood’s Machine Problems
If m1 is less than m2, solve for the acceleration of the
system and for T (the tension in the string).

Draw two FBD’s for the system:
Combined objects in two dimensions (no friction) :
Find the acceleration and tension.
THE FRICTION FORCE
It is a force acting on an object that opposes the sliding
of that object on a surface.

The friction force is parallel to the surface and opposite
to the direction of motion.

When an applied force exceeds the maximum static
friction force (Fs), an object will begin to slide.

When an object is already sliding, kinetic friction (Fk)is
present.
THE COEFFICIENT OF KINETIC
FRICTION
For surfaces in contact that are sliding, the coefficient of
kinetic friction is the ratio of the friction force to the
normal force.

friction force Fk
k                
normal force n
THE COEFFICIENT OF STATIC
FRICTION
For surfaces on the verge of sliding the coefficient of
static friction is the ratio of the maximum static
friction force to the normal force.

max imum static friction force Fs max
s                                
normal force              n
FRICTION
Friction opposes the motion between surfaces in contact
with one another.
When there is a tendency for movement between two
surfaces and yet there is no motion, the friction is static
friction.
Static friction has an upper limit.
When there is motion between the two surfaces, the friction
is kinetic (sliding) friction.
FFA
FA
FA  FA
A                    F
F
F

On the verge of slipping
Sliding

Maximum Static Friction

Friction, F

Kinetic (sliding) Friction
Applied Force, FA
A student pulls a rope attached to a 10.0 kg pumpkin and
tries to move it across a field. If k between the pumpkin
and the ground is 0.250, what is the force of friction?
A witch tries to get her broom stick off
the ground for a midnight flight. If the
broom stick provides 200 N of force
and the coefficient of friction is 0.15,
what is her acceleration? The witch
and her broom have a mass of 45 kg.
You can keep a 3 kg book from dropping by pushing it
horizontally against a wall. Draw force diagrams,and
identify all the forces involved. How do they combine to
result in a zero net force? Will the force you must supply to
hold the book up be different for different types of walls?
A hockey puck is given an initial speed of 20.0 m/s on a frozen pond and slides
120 meters before it stops. Find the coefficient of kinetic friction of the ice and
puck.
How much force is necessary to

5m
pull the block up the ramp at
constant velocity?

12 m
Examine the pulley system on the front counter. If the cart has 4.0 kg
of mass and the weight-hanger has 0.050 kg of mass, what is the
acceleration? Assume the counter is frictionless.
4.0 kg

0.050 kg

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