Transcript Chapter 4

Chapter 4
Forces in one Dimension
Force-is a push or pull exerted on an
object
•
•
•
Can cause objects to speed up
Can cause objects to slow down
Can cause objects to change direction
FORCE is a vector quantity; It has both
magnitude and direction
A force can change the speed and direction of an
object, therefore a force changes an object’s ……..
VELOCITY
A change in an object’s velocity is ……..
ACCELERATION
Therefore a force causes an acceleration
Force is measured in Newtons N
it is equal to the amount of net force
required to accelerate a mass of one
kilogram at a rate of one meter per
second squared; kg m/s2
Types of forces
• Contact Force- an object from the
external world touches the other object
(SYSTEM) being studied
• Field Forces- forces exerted without
contact to the system; gravity and magnetism
• Agents- the cause of the force
When analyzing how a force affects motion of
an object it is Important to identify the object
(the system) and all the forces acting on it.
Book sitting on a table
System= Book
F table on the
book
Physics
F earth on
book
Forces acting on the bookexternal world
F earth on book
F table on the book
Book sitting on a table
Physics
Motion diagram
1. Draw a diagram of the
situation.
2. Circle the system
3. Identify all areas where
the system touches the
external world- These are
the contact forces
4. Identify all the field
forces acting on the
system
Free Body Diagram- similar to
the particle model for motion.
1. Represent the object (system)
with a dot
2. Represent each force with an
arrow that points in the direction
the force is applied
3. Try to make each arrow
proportional to the magnitude of
the force. If unsure of the
magnitude make your best
estimate
4. All force arrows should point
away from the dot even if they
are a push
Book on table
F table on the book
F earth on book
How would you describe
this motion diagram?
Book is moving to the
right
Physics
Identify the system
The book
Identify the forces.
Force of table
Force of gravity
Push or pull on the book
Friction
Combining Forces
Suppose you push on a table and exert 100 N of force;
you would create an acceleration.
If someone else joined you and exerted the same force
the acceleration would be twice as much and the
resultant force vector would be 200 N
Suppose the other person would push from
the other side with a force of 100 N?
The resultant force would be zero, and therefore no
acceleration would be created and the table would
not move
Suppose one person pushed with a force of 100 N and
the other pushed with a force of 50 N in the opposite
direction
This would result in a net force of 50 N
in the direction of the greater force.
Sir Isaac Newton (1642-1727),
mathematician and physicist, one of the
foremost scientific intellects of all time.
Developed Laws explaining motion, force
and gravity. Also is credited with the
development of Calculus. Actually wrote
more on religion and philosophy than
science and math.
Newton’s First Law of Motion- An object at
rest tends to remain at rest an object in motion tends to remain
in motion in a straight line at a constant speed, if the net force
on an the object is zero.
Inertia- tendency of an object to resist change;
Newton’s first law is sometimes referred to as the
Law of Intertia
Common Forces
Force
Symbol Definition
Direction
Friction
Ff
Contact force that opposes sliding Parallel to surface and
between 2 surfaces
opposite the direction
of sliding
Normal
FN
Contact force exerted by a surface Perpendicular to and
on an object
away from the surface
Spring
Fsp
Push or pull a spring exerts on an
object
Opposite the
displacement of object
at end of spring
Tension
FT
The force exerted by a taut rope
or cable attached to an object
Away from object and
parallel to rope
Thrust
Fthrust
General term used to describe
forces that move objects such as
rockets, planes, cars etc.
In the same direction
as the acceleration
Weight
Fg
A field force caused by the pull of
gravity
Down toward center of
Earth
Newton’s 2nd Law of Motion
What net force is required to accelerate a car
𝐹𝑛𝑒𝑡 = 𝑚𝑎
at a rate of 2 m/s if the car has a mass of
2
3,000 kg?
𝐹𝑛𝑒𝑡
𝑎=
𝑚
𝐹𝑛𝑒𝑡
𝑚=
𝑎
Fnet=(3000kg)(2 m/s2)
= 6000 N
What is the acceleration of softball if it has a
mass of 0.5 kg and hits the catcher's
glove with a force of 25 N? a= 25 N/ .5 kg
= 50 m/s2
What is the mass of a falling rock if it produces
a force of 147 N? m= 147 N/ 9.8m/s2
= 15 kg
Weight and Apparent Weight
Weight- a measure of the force of gravity on an object;
we measure weight in pounds or kilograms, but really it is
a force
Fg=ma
Fg= m(9.8
2
m/s )
Weight changes when g varies, on or near the surface of
the earth g is constant. Therefore if you step on a
bathroom scale the scale provides the only upward force
and therefore records you weight.
Fscale
Fg
Apparent weight- is the force an object exerts as
a result of all the forces acting on it, giving the
object an acceleration
Suppose you are standing on a scale in an
elevator and the elevator accelerates upward.
Would the scale read more , less or equal to
when the elevator is standing still?
The scale will read more because the upward
force is added to the upward force of the scale
Fscale
Felevator
Fgravity
Suppose the elevator cable broke. What would the
scale read?
The scale would read less and if the person was in free
fall it would read zero because both you and the scale
would be acceleration at the same rate (-9.8 m/s2)
Weightlessness- there is no contact force pushing up
on the object and would have an apparent weight of
zero.
Drag Force and Terminal Velocity
Drag Force- force exerted by a fluid (liquid or gas) on the
object on the object moving through the fluid; drag force is
opposite the motion of the object
• Properties of the fluid
 Viscosity, temperature
• Properties of the object moving through the fluid
 Size, shape and mass
• Motion of the object- as speed increases so does the
magnitude of the drag force. Because the faster it moves
the more molecules it is coming into contact with.
If a tennis ball is dropped it starts with an initial
velocity of 0 m/s and therefore the drag force is
also zero. As the ball falls the velocity increases as
does the drag force. Eventually the drag force
upwards is going to equal the force of gravity
downward and the ball will stop accelerating and
will continue to fall at a constant velocity.
Terminal velocity- the constant velocity that
is reached when the drag force is equal to the force
of gravity.
Newton's Third Law
Newton's Third Law is often stated:
For every action there is an equal
and opposite reaction.
For every action there is an equal and
opposite reaction.
• People associate "action" and "reaction" with "first an action,
then a reaction" - as in, first Suzie smacks Johnnie (action)
then Johnny says "Mommy! Suzie hit me!" (reaction). That is
NOT what is going on here! The action and reaction forces
exist at the same time.
• "action...reaction" means that forces always occur in pairs.
(Forces are interactions between objects, like conversations
are interactions between people.)
• The two forces involved are called the "action force" and the
"reaction force."
If A pushes B, then B pushes A
A pushes B
B pushes A
action force
reaction force
Both of these forces are occurring
at the same time, They are
interacting
http://www.batesville.k12.in.us/physics/phyne
t/mechanics/newton3/ActionReaction.html
“For every action there is an
equal and opposite reaction.”
“equal" means two things:
• Both forces are exactly the same size. They are equal in
magnitude.
• Both forces exist at exactly the same time. They both
start at exactly the same instant, and they both stop at
exactly the same instant. They are equal in time.
“For every action there is an
equal and opposite reaction.”
"opposite" means
• that the two forces always act in opposite
directions - exactly 180o apart.
Why Don't Action & Reaction
Forces Cancel?
"If A pushes B, then B pushes A with an equal and
opposite force. If these forces are equal and opposite,
they cancel, producing a net force of zero. This means
that neither object can accelerate, which means that
Newton's Laws predict that nothing can ever move.“`
We know this statement has to be untrue because
we know that things do move? WHY IS IT UNTRUE?
Farmer Brown hitches Old Dobbin to his wagon one day, then says, "OK, Old Dobbin,
let's go!"
Old Dobbin turns to Farmer Brown and says, "Do you remember back in high school,
when we took Physics together?
"Yes, I do. We were lab partners in that class, and we had a lot of fun." says Farmer
Brown.
"Ah, yes! Those were the good old days, all right!", says Old Dobbin, "You do remember
Newton's Three Laws, of course, which tell how all objects move?“
"Yes, I do! I remember that Newton's Laws of Motion are the cornerstone of
mechanics. Now, let's get this wagon moving!"
"Do you remember how Newton's Third Law says that every action force has an equal
and opposite reaction force?", says Old Dobbin, ignoring Farmer Brown's impatience.
"Yes, I do." says Farmer Brown, sensing trouble.
"Newton's Third Law says that if I pull on the wagon, the wagon exerts an equal and
opposite force on me. Don't you agree?", asks Old Dobbin.
"Yes... but..."
"If these two forces are equal and opposite, they will cancel, so that the net force is
zero, right?", argues Dobbin.
"Well, I suppose so," stammers Farmer Brown.
"The net force is always the important thing. If the net force is zero, then Newton's
Second Law (and Newton's First Law, too) says that the acceleration of the wagon must
be zero."
"Yes, I remember Newton's Second Law very well, Old Dobbin.", says Farmer Brown,
hopefully. "This physics discussion is certainly interesting, but let's get going!"
"But that's the point!", objects Old Dobbin, "If the wagon's pull is always equal and
opposite of my pull, then the net force will always be zero, so the wagon can never move!
Since it is at rest, it must always remain at rest! Get over here and unhitch me, since I
have just proven that Newton's Laws say that it is impossible for a horse to pull a wagon!"
At this point, Farmer Brown throws up his hands in dismay and turns to you. "Please help
me!" he says, "I really should have paid more attention in physics class! I know that
Newton's Laws are correct, and I know that horses really can pull wagons. There has to be
an error in Old Dobbin's argument, but what is it? How can I convince Old Dobbin that if
he pulls on the wagon, it will move?"
Fold dobbin
Fwagon
Fnet=0 if net force is zero there is no acceleration and
therefore no movement
Only the forces that act on an object can cancel. Forces that act
on different objects don't cancel
The yellow arrow labeled "wagon" is a force exerted by the wagon on
the horse. The blue arrow labeled "horse" is a force exerted by the
horse on the ground.
The two forces colored yellow in the diagram are a Newton's Third
Law force pair - "horse pulls wagon" and "wagon pulls horse". They
are equal in magnitude and opposite in direction.
The two forces colored blue in the diagram are a Newton's Third Law
force pair - "horse pushes ground" and "ground pushes horse". They
are also equal in magnitude and opposite in direction.
Why does the wagon accelerate?
Newton's 2nd Law says that an object accelerates if there is a net (unbalanced)
force on it. Looking at the wagon in the diagram above, you can see that there is
just one force exerted on the wagon - the force that the horse exerts on it. The
wagon accelerates because the horse pulls on it!
If the ground pushes harder on the
horse than the wagon pulls, there
is a net force in the forward
direction, and the horse
accelerates forward.
If the wagon pulls harder on the
horse than the ground pushes,
there is a net force in the backward
direction, and the horse
accelerates backward. (This
wouldn't happen on level ground,
but it could happen on a hill...)
HOMEWORK
The Question:
"When a rifle shoots a bullet, Newton's Third Law says that the force
that the rifle exerts on the bullet is exactly the same size as the force
that the bullet exerts on the rifle - yet the bullet gets a much greater
acceleration than the rifle. How can this be?"
Tension- the force exerted by a string, rope, chain etc.
FT
Fg
If the bucket is hanging, the
bucket is in equilibrium and
therefore the tension on the rope
is equal to the weight
(gravitational pull downward) of
the bucket. When talking about
tension we will always assume
that the rope is massless.
Therefore the tension on a rope
is equal to the weight of all
objects hanging below it
Tug-of-war
Suppose each side of this tug of war are exerting
500 N of force. What is the tension on the rope?
Fright on left= 500 N= FA on rope
Fleft on right= 500 N= FB on rope
A 50.0 kg bucket is being lifted by a rope. The rope
will not break if the tension is 525 N or less. The
bucket started at rest and after being lifted for 3.0
m it is moving at 3.0 m/s. If the acceleration is
constant is the rope in danger of breaking?
Fnet=FT + (-Fg)
FT=Fnet+ Fg
= ma + mg
= m(a + g)
𝑣𝑓 2 = 𝑣𝑖 2 + 2ad