Transcript Newton`s Second Law

Newton’s Laws of Motion
Sir Isaac Newton described the
relationship between motion and
force in 3 laws
Newton’s First Law- aka:the law of inertia
• An object at rest remains at rest and an object in
motion maintains its velocity unless it
experiences an unbalanced force.
• An object at rest tends to stay at rest
• An object in motion tends to stay in motion at the
same velocity
• This is known as inertia
• Inertia: tendency to resist change until an outside
force acts upon the object
– Example: When in a car and the car stops, your
body continues forward. Seat belts are used to
counter this effect.
• Inertia is related to an object’s mass
• Mass is actually a measure of inertia
– An object with a small mass has less inertia
– An object with a greater mass has more inertia
• Which object would be easier to change the
motion of?
Inertia
• Why you slide into
your friend on the
Music Express Ride
• Why you can’t stop
instantaneously
when driving a car
• We use seat belts
and air bags to help our bodies
slow down when inertia keeps
them going
Safety!
• Seat belts and car seats provide protection.
• Because of inertia, you slide toward the side of a
car when the driver makes a sharp turn.
• When the car you are riding in comes to a stop,
your seat belt and the friction between you and
the seat stop your forward motion.
• On earth objects in motion appear to slow
down on their own, however an outside force
is acting on them. This outside force is usually
friction.
• In space, where there is
no friction and object
in motion will continue
to stay in motion and
just keep going unless
something acts upon it.
Newton’s Second Law
• Newton’s first law depends upon the net force
being zero or balanced
• Newton’s second law depends upon the net
force being unbalanced
• Newton’s Second Law: The unbalanced force
acting on an object equals the object’s mass
times the acceleration
• Force = mass x acceleration
• F = ma
F = ma
F = ma
• The force needed will increase when the mass
increases F = ma
A)
B)
• F and m are directly proportional
• Which requires more force?
F = ma
• The force needed will increase when the
acceleration increases F = ma
A)
B)
• F and a are directly proportional
• Which requires more force?
F = ma
• If force is constant, then the higher the
mass the lower the acceleration F = ma
• m and a are inversely proportional
Force is measured in Newtons
• 1 Newton = 1 kg x 1 m/s2
• The pound (lb) is sometimes used as a unit of
force.
• 1 N = 0.225 lbs
or 1 lb = 4.448 N
• Example: a baseball accelerates downward at
9.8 m/s2. If the gravitational force is the only
force acting on the baseball and is 1.4 N, what
is the baseball’s mass?
Newton’s Second Law
Zookeepers lift a stretcher that holds a sedated lion.
The total mass of the lion and stretcher is 175 kg,
and the lion’s upward acceleration is 0.657 m/s2.
What is the unbalanced force necessary to produce
this acceleration of the lion and the stretcher?
1. List the given and unknown values.
Given:
mass, m = 175 kg
acceleration, a = 0.657 m/s2
Unknown: force, F = ? N
Newton’s Second Law, cont.
2. Write the equation for Newton’s second law.
force = mass  acceleration
F = ma
3. Insert the known values into the equation,
and solve.
F = 175 kg  0.657 m/s2
F = 115 kg  m/s2 = 115 N
Gravity
• Law of gravitational force: objects in the universe
attract each other through gravitational forces.
• The force of gravity is increased if one or both of
the object’s masses increase
• The gravitational pull between two heavy objects
is greater then the gravitational pull between two
light objects
• The farther apart (the greater the distance)
between two objects, the less the gravitational
pull.
GRAVITY
• Sir Isaac Newton (1642–1727) generalized his
observations on gravity in a law now known as
the law of universal gravitation.
Universal Gravitation Equation
F = G m1 m2
d
m1 and m2 are the masses of the two objects
d is the distance between the two objects
G is a constant G = 6.673 x 10-11 N m2/kg2
Huh…What do you need to know?
• Force of gravity is directly proportional to the
masses of the objects
– Masses go up, force of gravity goes up
• Force of gravity is inversely proportional to the
distance between the objects
– Distance goes up, force of gravity goes down
• No matter how big or small an object is, it will
exert a gravitational force. We just don’t notice it
for small objects.
• You have a gravitational attraction for all objects
around you, but since the earth is so large, the pull
of gravity towards the earth is greater and the only
force you feel
• An apple hanging from a tree;
– There is a gravitational attraction between the apple
and the tree
– There is a gravitational attraction between the apple
and the earth
– When the apple stem breaks, the apple falls to the
ground because the force of gravity is greater between
the apple and the earth than the apple and the tree.
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Free-Fall Acceleration
As an object falls to the earth, the distance
between the object and the earth decreases,
thus increasing the gravitational pull.
As two objects move farther apart, the force
of gravity between them decreases.
When gravity is the only force acting on an
object, the object is said to be in free fall.
Free-fall acceleration due to gravity is
abbreviated by “g” and is approx equal to 9.8
m/s2 at the earth’s surface.
• In the absence of air resistance (fluid friction), all
object near the earth’s surface accelerate at the
same rate.
• ALL objects exhibit the SAME free-fall
acceleration (g).
• But how can this be if the objects do not have the
same mass….how can a heavy object not
accelerate faster?
• Well….A heavier object has greater gravitational
pull, but a heavier object is more difficult to
accelerate. The extra mass compensates for the
additional gravitational force, thus allowing freefall acceleration (g) to remain the same.
Weight
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F
F
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Weight is dependant upon gravity, mass is not.
Weight: the force on an object due to gravity
Weight = mass x free-fall acceleration
w = mg
Since weight is a force, we measure weight in newtons (N) a
newton = kg x m/s2
A small apple weighs approx 1N
A 1.0 kg book has a weight of 9.8 N
=
mx a
= Weight = 1 kg x 9.8 m/s2 = 9.8 kg x 9.8 m/s2 = 9.8 N
Less gravity in space gives apparent weightlessness, because
weight changes but mass does not.
– An object can not be weightless! It can be close because of
increased distance between object, so a very low gravitational pull
would result.
Mass to Weight
Weight is gravity acting on the object’s mass.
On Earth 9.8 m/s2
W = ma
weight = mass x acceleration due to gravity
9.8 N = 1 kg x 9.8 m = 9.8 kg x m

(that’s a newton)
s2
s2
Therefore 1 kg = 9.8 N
Weight loss plan?
How much does a 50. kg student weigh on
Earth?
50. kg| 9.8 N = 490 N
| kg
How much does she weigh on the moon, with
1/6 gravity? 9.8/6 =1.6
50. kg| 1.6 N = 80 N
| kg
Air resistance
• When air resistance balances the force of gravity
(weight), the object’s velocity will be constant.
• This is because the two forces are equal but
opposite.
• Terminal velocity: the maximum velocity that can
be reached when the force of gravity and the force
of air resistance are equal.
• When a skydiver opens his parachute, the air
resistance increases greater, thus slowing them
down
• A skydiver is not in free fall. This is a
misnomer.
• Free-fall only occurs when the only force
acting upon an object is gravity.
• So free-fall can only occur when there is no air
resistance, in other words…it can only occur in
when there is no air…..in a vacuum.
• Because there is no air in space, free-fall can
occur in space.
• Astronauts float in space because they are in
free-fall, not because they are “weightless”!
Orbiting
• An object is said to be orbiting when it is
travelling in a circular path around another
object
• Gravity pulls a space shuttle towards earth
causing free-fall
• The shuttle is also moving forward at a
constant speed
• When these two actions combine, orbiting
occurs
Orbiting
Orbiting
Orbiting
Orbiting objects are in
free fall.
The moon stays in
orbit around Earth
because Earth’s
gravitational force
provides a pull on the
moon.
Two motions combine
to cause orbiting.
Projectile Motion
• Projectile motion: when two forces combine
to form a resultant motion
– Orbiting is an example of projectile motion.
– When a curved path forms when an object is
thrown, launched, or projected
• Projectile motion combines vertical force and
horizontal force. These forces are independent of
each other and do not affect each other, but
when they combine, they form an arc or curved
path.
• Horizontal force: comes from the projecting
object. You are responsible for the horizontal
force when throwing a ball.
• Vertical force: comes from gravity
• Because object always accelerate downward,
your aim should be above the target when firing
an arrow
How does something go into orbit?
• Newton's Cannon
• A “thought” experiment
– Not too slow…drops back to earth
– Not too fast…escapes earth
– Just right…horizontal force balances with vertical
gravity to maintain orbit
• The thought experiment becomes real with
satellites and space stations and planets and
moons and…
ACCELERATION, GRAVITY, AND VELOCITY FORMULAS
Use algebra to rearrange for the desired quantity.
a = vf - vi v = velocity (final velocity-initial velocity)
t
t = time a= acceleration (due to gravity 9.8 m/s2 )
Use this if the problem involves acceleration…change in velocity.
You may be asked to calculate velocity. If the object is dropped
its initial velocity=0 and you will calculate for final velocity.
_______________________________________________
d = at2
a = acceleration (due to gravity 9.8 m/s2 )
2
t = time
d = distance
Use this if you are asked to calculate how far a dropped object
travels in a certain amount of time.
_________________________________________________
v = d
d= distance
v= velocity
t= time
t
Use this for average velocity, not acceleration. It does not
account for changes in velocity (acceleration)
Newton’s Third Law
• For every action force, there is an equal and
opposite reaction force
• When you kick a soccer ball, you are exerting
force on the ball, but the ball is also exerting
an equal but opposite force on your foot.
• Action force: the force exerted ON the ball BY
your foot
• Reaction force: the force exerted ON your foot
BY the ball
• When you sit on a chair, you are exerting an
action force by pushing on the chair and the chair
is exerting a reaction force on you, by pushing
upward to keep you supported.
• Force always exists in pairs.
• These forces are always equal but opposite.
• However, they do not cancel each other out
because they are acting on different objects
• The force from your foot is equal to the force
from the ball when you kick it, but the force from
the ball on your foot is not as effective because it
is coming from an object with small mass and
acting on an object with greater mass
Momentum
• The product of the mass and velocity of an
object
• Momentum = mass x velocity
• p = mv
• When a car and a truck are traveling at the
same velocity, and both brake at the same
time with the same brake force, the truck
takes longer to stop than the car because of its
increased mass
• A bowling ball has greater momentum than a
kickball even though they are approximately the
same size and could be travelling at the same
velocity. The bowling ball has a greater mass!
• The speed also affects momentum: a fast moving
train has more momentum than a slow moving
train even though they are the same mass
• If an object is not moving its momentum is zero
• Like velocity, momentum has direction. It is in
the same direction as the velocity
• When you catch a baseball, if you extend the time as
your are changing the ball’s momentum, then you can
reduce the sting on your hand by reducing the force
exerted on your hand by the ball.
• Momentum is conserved in collisions. It can be
transferred from one object to another, but the same
amount of momentum is constant.
• When two cars hit head on, if they get stuck together,
they will move together in the direction of the car with
the greater momentum.
• When two cars hit head on, if they bounce off of each
other, the momentum is still conserved.
• When playing billiards: the cue ball hits another ball and
transfers its momentum to the ball. The other ball is
moved forward by the action force from the cue ball.
The cue ball stops due to the reaction force from the
other ball
Momentum
Calculate the momentum of a 6.00 kg bowling
ball moving at 10.0 m/s down the alley toward
the pins.
1. List the given and unknown values.
Given:
mass, m = 6.00 kg
velocity, v = 10.0 m/s down the alley
Unknown: momentum, p = ? kg • m/s (and
direction)
2. Write the equation for momentum.
momentum = mass x velocity
p = mv
3. Insert the known values into the equation,
and solve.
p = mv = 6.00 kg  10.0 m/s
p = 60.0 kg • m/s down the alley
Conservation of Momentum