Transcript By Newton`s second law

Chapter 3-1
Newton’s Second Law
3.1
Force, Mass, and Acceleration
Newton’s first law of motion: the motion
of an object changes only if an unbalanced
force acts on the object
Coming up…
Newton’s second law of motion: describes
how the forces exerted on an object, its mass,
and its acceleration are related.
Newton’s Second Law
3.1
Force and Acceleration
Q: Which has a greater
force?
1.) throwing a ball
gently
OR
2.) throwing a ball
really hard?
WHY?
Newton’s Second Law
3.1
Force and Acceleration
A: The hard-thrown
ball: it has a greater
change in velocity,
and the change
occurs over a
shorter period of
time…
Newton’s Second Law
3.1
Force and Acceleration
Remember: acceleration is the change in
velocity divided by the time it takes for the
change to occur.
So, a hard-thrown ball ALSO has a greater
acceleration than a gently thrown ball
(because it has a greater velocity over a
shorter period of time)
Newton’s Second Law
3.1
Mass and Acceleration
Q: If you throw a softball
and a baseball as hard
as you can, why don’t
they have the same
speed?
A: because of their
masses
Newton’s Second Law
3.1
Mass and Acceleration
Q: If it took the same amount of time to
throw both balls, which would have
less acceleration?
A: the softball because the acceleration of
an object depends on its mass as well as
the force exerted on it.
*Force, mass, and acceleration are
related.
Notice…
Newton’s Second Law
3.1
Newton’s Second Law
Newton’s second law of motion: the
acceleration of an object is in the same
direction as the net force on the object, and it
can be calculated from the following
equation:
Newton’s Second Law
3.1
Calculating Net Force with the Second
Law
Or, more simply,…
F = force (units = Newtons)
m = mass (units = kilograms)
a = acceleration (units = m/s)
Practice Problems
1. You’re helping your friend move. You choose a 30 kg
box and push it down a moving ramp at an
acceleration of 2 m/s/s. With what force did you push
it?
A: F = ma
F = (30)(2)
F = 60 N
2. A ball is thrown and accelerates at a rate of 15 m/s/s.
The ball has a mass of .1 kg. What is the force?
A: F = ma
F = (.1)(15)
F = 1.5 N
You can also solve for variables OTHER THAN force…
3. A force of 50 N is applied to a box. The box has a
mass of 10 kg. What is the acceleration?
A: F = ma
50 = 10a
10 10
a = 5 m/s/s
Finally…
Newton’s Second Law
3.1
Suppose you give a skateboard a push with
your hand…
According to Newton’s first law of motion,
if the net force acting on a moving object is
zero, it will continue to move in a straight
line with constant speed.
Does the skateboard keep moving with constant
speed after it leaves your hand? Why or why
not?
Newton’s Second Law
3.1
Remember: when an object slows down, it is
still accelerating (speeding up, slowing down,
or changing direction)
By Newton’s second law, if the skateboard is
accelerating, there must be a net force acting
on it… which force is it?
Newton’s Second Law
3.1
Friction
Friction: the force that opposes the sliding
motion of two surfaces that are touching each
other.
The amount of friction between two surfaces
depends on two factors:
1. the kinds of surfaces
2. the force pressing the surfaces together
Newton’s Second Law
3.1
What causes friction?
1. a “smooth” surface is not really smooth… it
has microscopic “bumps” on it
2. if two surfaces are in contact, welding, or
sticking, occurs where the bumps touch each
other
3. these microwelds (bumps sticking) are the
source of friction
Newton’s Second Law
3.1
Sticking Together
The larger the force pushing the two surfaces
together, the stronger these microwelds (or
the “sticking”) will be, because more of the
surface bumps will come into contact.
To move one
surface over the
other, a force
must be applied
to break the
microwelds.
Newton’s Second Law
3.1
Suppose you have filled a cardboard box with
books and want to move it.
It’s too heavy to lift,
so you start pushing
on it, but it doesn’t
budge.
If the box doesn’t
move, then it has
zero acceleration.
Newton’s Second Law
3.1
Newton’s second law says that if the
acceleration is zero, then the net force on the
box is zero.
Therefore: another force that cancels your
push must be acting on the box…
Newton’s Second Law
3.1
Static Friction
That force is the friction due to the microwelds
that have formed between the bottom of the
box and the floor.
Static friction: the
frictional force
that prevents two
surfaces from
sliding past each
other.
Newton’s Second Law
3.1
You ask a friend to help you move the box…
Pushing together, the
box moves. Together
you and your friend
have exerted enough
force to break the
microwelds between
the floor and the
bottom of the box.
Newton’s Second Law
3.1
Sliding Friction
If you stop pushing, the box quickly comes to
a stop.
This is because as the box slides across the
floor, another forcesliding
frictionopposes the motion of the box.
Sliding friction: the force that opposes the
motion of two surfaces sliding past each
other.
Newton’s Second Law
3.1
As a wheel rolls over a surface, the wheel
digs into the surface, causing both the wheel
and the surface to be deformed.
Newton’s Second Law
3.1
Rolling Friction
Static friction acts over the deformed area
where the wheel and surface are in contact,
producing a frictional force called rolling
friction.
Rolling friction: the frictional force between
a rolling object and the surface on which it
rolls
So, the three types of friction are:
1. static friction
2. sliding friction
3. rolling friction
Newton’s Second Law
3.1
Air Resistance
1. When an object falls toward Earth, it is
pulled downward by the force of gravity.
2. BUT… a friction-like force called air
resistance opposes the motion of objects
that move through the air.
3. Air resistance causes objects to fall with
different accelerations and different speeds.
Q: Why does the elephant hit
the ground first? Does it
have a greater acceleration?
A: No… it’s the same… the
acceleration of gravity (9.8
m/s/s). BUT air resistance
DOES depend on the size
and shape of an object. The
elephant also has a faster
terminal velocity.
Newton’s Second Law
3.1
Air Resistance
4. Air resistance acts in the opposite direction
to the motion of an object through air.
5. If the object is falling downward, air
resistance acts upward on the object.
6. The size of the air resistance force also
depends on the size, shape, and speed of an
object.
Newton’s Second Law
3.1
Air Resistance
• The amount of air resistance on an object
depends on the speed, size, and shape of
the object.
• Air resistance, not
the object’s mass, is
why feathers, leaves,
and pieces of paper
fall more slowly
than pennies, acorns,
and apples.
Newton’s Second Law
3.1
Terminal Velocity
Newton’s Second Law
3.1
Terminal Velocity
terminal velocity: the highest speed a
falling object will reach.
depends on the:
1. size
2. shape
3. mass
of a falling object
Section Check
3.1
Question 1
Newton’s second law of motion states that
_________ of an object is in the same
direction as the net force on the object.
A.
B.
C.
D.
acceleration
momentum
speed
velocity
Section Check
3.1
Answer
The answer is A. Acceleration can be calculated
by dividing the net force in newtons by the mass
in kilograms.
Section Check
3.1
Question 2
The unit of force is __________.
A.
B.
C.
D.
joule
lux
newton
watt
Section Check
3.1
Answer
The answer is C. One newton = 1 kg · m/s2
Section Check
3.1
Question 3
What causes friction?
Answer
Friction results from the sticking together
(microwelds) of two surfaces that are in contact.
End 3-1
Start 3-2
Gravity
3.2
What is gravity?
Gravity: an attractive force between any two
objects that depends on the masses of the
objects and the distance between them.
Gravity
3.2
Earth’s Gravitational Acceleration
1. free fall: when all forces except gravity
acting on a falling object can be ignored
(objects appear to be weightless)
2. Close to Earth’s surface, the acceleration of
2
a falling object in free fall is about 9.8 m/s .
3. This acceleration is given the symbol g
and is sometimes called the acceleration of
2
gravity…and again, it’s 9.8 m/s
Gravity
3.2
Earth’s Gravitational Acceleration
By Newton’s second law of motion, the
force of Earth’s gravity on a falling object is:
Force = the object’s mass X the acceleration
of gravity on Earth (F = ma or, in this case,
F = mg).
Gravity
3.2
Weight
Weight: the gravitational force exerted on an
object; it changes if gravity changes
Because the weight of an object on Earth is
equal to the force of Earth’s gravity on the
object, weight can be calculated from this
equation:
Weight (N) = mass (kg) x acceleration of gravity (m/s/s)
OR
W = mg
Gravity
3.2
Weight and Mass
1. Weight and mass are not the same. Weight
can change… mass doesn’t.
2. Weight is a force and mass is a measure of
the amount of matter an object contains.
3. Weight and mass are related. Weight
increases as mass increases.
Examples of Weight Problems:
1. A boy “weighs” 150 lbs. when he steps on a
scale. How many Newtons does he weigh?
A: 150 lbs. = 68 kg
2.2
W = mg (a = g = acceleration of gravity)
W = (68)(9.8)
W = 666.4 N
2. Now calculate your weight in Newtons.
Remember to first convert your “weight” in
pounds to kilograms.
Ex: 130 lbs. = 59 kg
2.2
W = mg
W = (59)(9.8)
W = 578.2 N
Gravity
3.2
Weight and Mass
The table shows how various weights on
Earth would be different on the Moon and
some of the planets.
Gravity
3.2
Projectile Motion
projectiles: follow a curved path due to the
Earth’s gravity
Examples:
1.) a thrown ball
2.) a bullet shot from a gun
3.) a thrown dart
4.) an archer’s arrow
*all aim above target*
Gravity
3.2
What is happening to the rolling (or thrown)
ball?
1. Gravity exerts an unbalanced force on the
ball, changing the direction of its path
from only forward to forward and
downward.
2. The result of these 2 motions: the ball
appears to travel in a curved path
Gravity
3.2
Centripetal Force
Centripetal force: the net force exerted toward the
center of a curved path
Anything that moves in a circle is doing so because a
centripetal force is accelerating it toward the
center.
Gravity
3.2
Example #1: a car rounds a curve on a
highway… the centripetal force is the
frictional force, or the traction, between
the tires and the road surface.
Example #2: people on many amusement
park rides (gravitron, yo-yo, etc.)
Gravity
3.2
Example #3: Earth’s gravity exerts a
centripetal force on the Moon that keeps it
moving in a nearly circular orbit.
Gravity
3.2
Example #4: an object tied to a string whirling
around your head…the string exerts a
centripetal force on the object that keeps it
moving in a circular path
Section Check
3.2
Question 1
Gravity is an attractive force between any
two objects and depends on __________.
Answer
Gravity is an attractive force between any two
objects and depends on the masses of the objects
and the distance between them.
End 3-2
Start 3-3
The Third Law of Motion
3.3
Newton’s Third Law
Newton’s Third Law of Motion: for every
action force, there is an equal and opposite
reaction force
Example #1:
Jumping on a trampoline… you apply
downward force as the trampoline exerts an
equal upward force on you
Example #2:
a male skater pulling upward on a female
skater as she pulls downward on him
Example #3:
kickback occurs when a gun is fired
Example #4:
Jet or rocket propulsion due to compressed
gas release
The rocket exerts a force on
gas molecules, pushing them
backwards. The gas
molecules exert a force on
the rocket, pushing it
forward.
What is happening here?
The Third Law of Motion
3.3
Action and Reaction Forces Don’t
Cancel
1. According to Newton’s Third Law, action
and reaction forces act on different objects.
2. Therefore, even though the forces are equal,
they are not balanced because they act on
different objects.
The Third Law of Motion
3.3
Example: a swimmer “acts” on the water
and the “reaction” of the water pushes the
swimmer forward
Thus, a net force,
or unbalanced
force, acts on the
swimmer so a
change in his or her
motion occurs.
The Third Law of Motion
3.3
Momentum
1. A moving object has a property called
momentum that is related to how much
force is needed to change its motion.
2. momentum (kg m/s) = mass (kg) x
velocity (m/s)
p = mv
p = momentum (kg m/s)
m = mass (kg)
v = velocity (m/s)
Note: momentum (units = kg m/s) has a
direction because velocity has a direction
The Third Law of Motion
3.3
Law of Conservation of Momentum
1. The momentum of an object doesn’t
change unless its mass, velocity, or both
change.
2. Momentum, however, can be transferred
from one object to another.
3. The law of conservation of momentum:
states that if a group of objects exerts forces
only on each other, their total momentum
doesn’t change.
The Third Law of Motion
3.3
When Objects Collide
The results of a collision depend on the
momentum of each object.
When the first puck
hits the second puck
from behind, it gives
the second puck
momentum in the
same direction.
The Third Law of Motion
3.3
When Objects Collide
If the pucks are speeding toward each other
with the same speed, the total momentum is
zero.
Practice Problems:
1. What is the momentum of a car with a mass
of 1300 kg traveling at a velocity of 28 m/s?
Answer: p=mv
p=(1300)(28)
p=36,400 kg m/s
2. A baseball thrown by a pitcher has a
momentum of 6.0 kg m/s. If the baseball’s
mass is .15 kg, what is the baseball’s
velocity?
Answer: p=mv
6.0=(.15)v
v=40 m/s
3. What is the mass of a person walking with a
velocity of 0.8 m/s if their momentum is 52.0
kg m/s.
Answer: p=mv
52=0.8m
m=65 kg
Section Check
3.3
Question 1
According to Newton’s third law of motion,
what happens when one object exerts a force
on a second object?
Answer
According to Newton’s law, the second object
exerts a force on the first that is equal in
strength and opposite in direction.
Section Check
3.3
Question 2
The momentum of an object is the product
of its __________ and __________.
A.
B.
C.
D.
mass, acceleration
mass, velocity
mass, weight
net force, velocity
Section Check
3.3
Answer
The correct answer is B. An object’s momentum
is the product of its mass and velocity, and is
given the symbol p.
Section Check
3.3
Question 3
When two objects collide, what happens to
their momentum?
Section Check
3.3
Answer
According to the law of conservation of
momentum, if the objects in a collision exert
forces only on each other, their total momentum
doesn’t change, even when momentum is
transferred from one object to another.
End 3-3