Transcript Newton`s Laws of Motion

Newton’s
Laws of Motion
I. Law of Inertia
II. F=ma
III. Action-Reaction
Mass vs. Weight
• MASS
• How much and what
material an object is
made of (what types
of atoms and how
many of them)
• Measured in grams or
kilograms (kg)
• Is constant for an
object independent
of location
• WEIGHT
• Force of gravity
acting on a mass
• Measured in Newtons
or Pounds
Fg=mag
• Force on 1 kg is 9.8
Newtons or 2.2 lbs
• 1N = 1kg· m/s2
Newton’s Laws of Motion
• 1st Law – An object at rest will stay at rest, and an
object in motion will stay in motion at constant velocity,
unless acted upon by an unbalanced force.
• 2nd Law – Force equals mass times acceleration.
• 3rd Law – For every action there is an equal and
opposite reaction.
Forces
• A force is a push or a pull
• A force can cause
– a stationary object to move
– a moving object to stop
– an object to accelerate (change speed or direction)
• Net force
– the combination of all the forces acting on an object.
– changes an object’s state of motion.
• Balanced Force
– Net force is 0, object at rest
– Or constant velocity
• Unbalanced
– Net force is not 0, Object moves
– Or accelerates
1st Law of Motion
(Law of Inertia)
An object at rest will stay at
rest, and an object in motion
will stay in motion at constant
velocity, unless acted upon by
an unbalanced force.
INERTIA
the tendency of an object
to resist any change in its motion
Inertia is a property of matter and does not
depend on the position or location of the object. But it does depend on:
MASS
a quantitative measure of inertia
FORCE
“a push or pull”
1st Law
• Once airborne,
unless acted on
by an
unbalanced
force (gravity
and air – fluid
friction), it
would never
stop!
1st Law
• Unless acted
upon by an
unbalanced
force, this golf
ball would sit
on the tee
forever.
Why then, do we observe
every day objects in motion
slowing down and becoming
motionless seemingly without
an outside force?
Objects on earth, unlike the
frictionless space the moon
travels through, are under
the influence of friction.
What is this unbalanced force that acts on an object in motion?
• There are four main types of friction:
•
•
•
•
Sliding friction: ice skating
Rolling friction: bowling
Fluid friction (air or liquid): air or water resistance
Static friction: initial friction when moving an object
Slide a book
across a table and
watch it slide to a rest
position. The book
comes to a rest
because of the
presence of a force that force being the
force of friction which brings the book
to a rest position.
• In the absence of a force of friction, the book
would continue in motion with the same speed
and direction - forever! (Or at least to the end
of the table top.)
Newtons’s 1st Law and You
Don’t let this be you. Wear seat belts.
Because of inertia, objects (including you) resist changes
in their motion. When the car going 80 km/hour is stopped
by the brick wall, your body keeps moving at 80 m/hour.
2nd Law
2nd Law
The net force of an
object is equal to the
product of its mass and
acceleration, or F=ma.
2nd Law (F = m x a)
• How much force is needed to accelerate a 1400
kilogram car 2 meters per second/per second?
• Write the formula
• F=mxa
• Fill in given numbers and units
• F = 1400 kg x 2 meters per second/second
• Solve for the unknown
• 2800 kg-meters/second/second or
2800 N
Newton’s 2nd Law proves that different masses
accelerate to the earth at the same rate, but with
different forces.
• We know that objects
with different masses
accelerate to the
ground at the same
rate.
• However, because of
the 2nd Law we know
that they don’t hit the
ground with the same
force.
F = ma
F = ma
98 N = 10 kg x 9.8
m/s/s
9.8 N = 1 kg x 9.8
m/s/s
Example 2
• How much force must a 30,000kg jet plane develop to
achieve an acceleration of 1.5m/s2? (neglecting air
friction)
• Fnet=ma
• Fnet=(30,000 kg) (1.5 m/s2)= 45,000 N
• Fapp = Fnet
Check Your Understanding
• 1. What acceleration will result when a 12 N net force
applied to a 3 kg object? A 6 kg object?
• 2. A net force of 16 N causes a mass to accelerate at a
rate of 5 m/s2. Determine the mass.
• 3. How much force is needed to accelerate a 66 kg skier
1 m/sec/sec?
• 4. What is the force on a 1000 kg elevator that is falling
freely at 9.8 m/sec/sec?
Check Your Understanding
•
1. What acceleration will result when a 12 N net force applied to a 3 kg object?
12 N = 3 kg x 4 m/s/s
•
2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass.
16 N = 3.2 kg x 5 m/s/s
•
3. How much force is needed to accelerate a 66 kg skier 1 m/sec/sec?
66 kg-m/sec/sec or 66 N
•
4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?
•
9800 kg-m/sec/sec or 9800 N
Example 3
• If a 1400 kg car goes from 0 to 60 mph (27
m/s) in 5 seconds, how much force is applied
to achieve this?
Example 4
• If I throw a 0.145 kg baseball at 20 m/s
baseball and my ‘windup distance’ is 0.6
meters, how much force am I applying?
Example 5
• A 2.2 kg book is slid across a table. If Fnet = 2.6
N what is the book’s acceleration?
• Fnet=ma
• 2.6 N = (2.2kg) a
• a = 1.18 m/s2
Example 6
• If you drop a 20 kg object what is its
acceleration? What is its weight?
• acceleration = 9.8 m/s2
• Weight = force
• Fg=ma
• Fg= (20 kg) (9.8 m/s2)
• Q: If a jet cruises with a constant velocity and the thrust
from its engines is constant 80,000 N. What is the
acceleration of the jet?
• A: Zero acceleration because the velocity does not change.
• Q: What is the force of air resistance acting on the jet?
• A: 80,000 N in the opposite direction of the jet’s motion
3rd Law
•For every action, there is an
equal and opposite
reaction.
3rd Law
According to Newton,
whenever objects A
and B interact with
each other, they exert
forces upon each
other. When you sit in
your chair, your body
exerts a downward
force on the chair and
the chair exerts an
upward force on your
body.
3rd Law
There are two forces
resulting from this
interaction - a force
on the chair and a
force on your body.
These two forces are
called action and
reaction forces.
Newton’s 3rd Law in Nature
• Consider the propulsion of a
fish through the water. A fish
uses its fins to push water
backwards. In turn, the
water reacts by pushing the
fish forwards, propelling the
fish through the water.
• The size of the force on the
water equals the size of the
force on the fish; the
direction of the force on the
water (backwards) is
opposite the direction of the
force on the fish (forwards).
3rd Law
Flying gracefully
through the air, birds
depend on Newton’s
third law of motion. As
the birds push down on
the air with their wings,
the air pushes their
wings up and gives
them lift.
3rd Law
• Consider the motion
of a car on the way to
school. A car is
equipped with wheels
which spin backwards.
As the wheels spin
backwards, they grip
the road and push the
road backwards.
Other examples of Newton’s Third Law
• The baseball forces
the bat to the left (an
action); the bat forces
the ball to the right
(the reaction).
3rd Law
The reaction of a rocket is
an application of the third
law of motion. Various
fuels are burned in the
engine, producing hot
gases.
The hot gases push against
the inside tube of the rocket
and escape out the bottom
of the tube. As the gases
move downward, the rocket
moves in the opposite
direction.
Types of Forces
• Applied Force – Fapp
• An applied force is a force that is applied to an object by a person or
another object. If a person is pushing a desk across the room, then
there is an applied force acting upon the object. The applied force is
the force exerted on the desk by the person.
• Gravity Force (also known as Weight) = Fgrav
• The force of gravity is the force with which the earth, moon, or
other massively large object attracts another object towards itself.
By definition, this is the weight of the object. All objects upon earth
experience a force of gravity that is directed "downward" towards
the center of the earth. The force of gravity on earth is always equal
to the weight of the object as found by the equation:Fgrav = m * g
• where g = 9.8 N/kg (on Earth) and m = mass (in kg)
Types of Forces
• Normal Force = Fnorm
• The normal force is the support force
exerted upon an object that is in contact
with another stable object. For example, if a
book is resting upon a surface, then the
surface is exerting an upward force upon the
book in order to support the weight of the
book. On occasions, a normal force is
exerted horizontally between two objects
that are in contact with each other. For
instance, if a person leans against a wall, the
wall pushes horizontally on the person.
Normal Force and Gravity
• Gravity always pulls straight down
• Normal force (FN) is perpendicular to surface and equal
and opposite to component of gravitational force (Fg)
FN
Fg
• This may lead to an unbalanced ‘sliding’ force that is
the component of the gravitational force
Types of Forces
• Friction Force = Ffrict
• The friction force is the force exerted by a surface as an object
moves across it or makes an effort to move across it.
• There are four types of friction force – sliding, static friction,
rolling, and fluid (through gases or liquids) friction.
• Thought it is not always the case, the friction force often
opposes the motion of an object. For example, if a book slides
across the surface of a desk, then the desk exerts a friction force
in the opposite direction of its motion. Friction results from the
two surfaces being pressed together closely, causing
intermolecular attractive forces between molecules of different
surfaces. As such, friction depends upon the nature of the two
surfaces and upon the degree to which they are pressed
together. The maximum amount of friction force that a surface
can exert upon an object can be calculated using the formula
below:
• Ffrict = µ • Fnorm
Friction
• The force of friction (Ff):
1. Is always opposite to the direction of motion or
impending motion
2. Usually has a smaller value if the object moving
than if it is stationary

(static friction > kinetic friction);
3. Depends on the nature of the pair of surfaces
involved (the value of μ);
Friction
• The force of friction (cont’d):
4. Is proportional to the force pressing the surfaces
together (the normal force);
≤μ

static friction: Ff

kinetic friction: Ff =μk FN
s
FN
5. Is usually independent of the contact area and
speed.
Example
• If a 1 kg mass sits on a flat surface with a
coefficient of static friction of 0.5, what is the
force of friction (Ff) if:
• A horizontal force of 1 N is applied?
• A horizontal force of 10 N is applied?
• A horizontal force of 100 N is applied?
Types of Forces
• Air Resistance Force = Fair
• The air resistance is a special type of frictional force that acts
upon objects as they travel through the air. The force of air
resistance is often observed to oppose the motion of an object.
This force will frequently be neglected due to its negligible
magnitude (and due to the fact that it is mathematically difficult
to predict its value). It is most noticeable for objects that travel
at high speeds (e.g., a skydiver or a downhill skier) or for objects
with large surface areas. Air resistance
• Tension Force = Ftens
• The tension force is the force that is transmitted through a
string, rope, cable or wire when it is pulled tight by forces acting
from opposite ends. The tension force is directed along the
length of the wire and pulls equally on the objects on the
opposite ends of the wire.
Free Body Diagrams
• Free-body diagrams are diagrams used to show the
relative magnitude and direction of all forces acting
upon an object in a given situation. A free-body diagram
is a special example of the vector diagrams that were
discussed.
• The size of the arrow in a free-body diagram reflects
the magnitude of the force. The direction of the arrow
shows the direction that the force is acting. Each force
arrow in the diagram is labeled to indicate the exact
type of force. It is generally customary in a free-body
diagram to represent the object by a box and to draw
the force arrow from the center of the box outward in
the direction that the force is acting. An example of a
free-body diagram is shown at the right.
Free Body Diagrams
• The only rule for drawing free-body diagrams is
to depict all the forces that exist for that object
in the given situation. Thus, to construct freebody diagrams, it is extremely important to
know the various types of forces. If given a
description of a physical situation, begin by
using your understanding of the force types to
identify which forces are present. Then
determine the direction in which each force is
acting. Finally, draw a box and add arrows for
each existing force in the appropriate direction;
label each force arrow according to its type.
Free Body Diagram
The net force acting on an object is the
vector sum of all the forces acting on it.
Examples:
9N
8N
8N
8N
3N
4N
?
7N
12 N
6N
5N
If an object is remaining at rest, it
is incorrect to assume that there
are no forces acting on the object.
We can only conclude that the
net force on the object is zero.
4N
4N
7 N
Equations for this unit:
• Previous equations we might need:
•
•
•
•
vf = vi + at (or a = ∆v/t, to rearrange it)
∆x = vi + ½at2
∆x = ½ (vi + vf)t
vf2=vi2+2a∆x
• New equations:
•
•
•
•
F=ma
Ff=µFN
Ff=µkFN
Ff≤µsFN