Download Forces and Motion

Forces and the Laws of
Motion
Changes in Motion
Force is a push or a pull exerted on an object
Force causes a change in velocity
A force acting on a mass causes an acceleration
change in velocity
If 1 kg of mass is accelerated by 1 m/s2 then 1
Newton (N) of force is needed
Some forces act when two objects are in contact. These
are contact forces
Some forces act from a distance (the objects are not in
contact). These are Field Forces
Newton’s First Law of Motion
Inertia – The tendency of an object to maintain its
present state of motion
Mass – Measure of matter in an object
Galileo conducted experiments and concluded that if no
friction is present, an object in motion will remain in
motion at constant velocity forever
Inertia, Mass and Motion
Inertia is a
property of mass.
The more mass
an object has the
greater its
inertia.
Big Mass, big
inertia
Small
mass,
small
inertia
Newton’s 1st Law of Motion
“Law of Inertia”
An object will remain at rest or in motion in a straight line
at constant velocity (not accelerating) unless an
UNBALANCED FORCE acts on the object.
At Rest
In Motion
Unless an
unbalanced
force acts on the
object
Because of Inertia, the car stops (force of the wall)
but the driver keeps on moving! Seat belt anyone?
Gravity, Mass and Weight
The weight of an object is the force that is applied to an
object by gravity
FWeight = m x g
Since g has been measured to be the same for all objects,
neglecting air resistance, the greater the mass of an
object the greater the objects weight
A scale measures the amount
of support force needed to
balance the downward force
of gravity
Your weight (or anything’s
weight), is the product of
your mass times the
acceleration of gravity at your
location
FWeight = m x gAt That Location
Special Applications of Newton’s Laws
Weight and Friction
Weight – The force between too bodies, usually between
a large mass and a much smaller mass
Weight is not an inherent property of an object (like
mass or inertia) but is location dependent
The farther an object is from the center of the mass, the
less the objects weight
The acceleration of gravity by a body is the same for all
objects
What keeps the arrow moving after it is released
from the bow?
Early scientist thought that an “invisible force”
called impetus pushed the arrow as it moved
through the air.
Force Diagrams  Free Body Diagram
A force diagram shows all
of the forces acting on an
object using force vectors
First, analyze the
problem
Second, draw a simple diagram
of the object
Third, put a point in the
middle of the diagram
and draw the first
vector in the direction it
is acting
Draw the gravitational force
pointing directly toward the
center of the earth
Determine the upward or
normal force acting on the
object
The last force for this
problem is the frictional
force between the tires and
the road
Net or Unbalanced Force – The force that remains when
all of the force vectors are added
Adding all of the forces on the car equals 0 (No net
force)
Now there is a net force since Fresistance is less than Fforward
Finding the Net or Unbalanced Force
1. Draw a force free body diagram and identify all of the
forces acting on the object
2. Determine an appropriate coordinate system and
sketch the force vectors using that coordinate system
3. Find the x and y components of the vectors
4. Find the net force acting in the x and y direction
5. Determine the net force (magnitude and direction)
6. If the net force is 0 the object is in equilibrium.
Newton’s Second and Third Laws
Force, Mass and Acceleration
Newton’s Second Law – The net force acting on an object
equals the mass of the object times the objects
acceleration.
F=mxa
Force is a vector. The vector property of direction is in
the direction of the acceleration. Mass is a scalar and
changes the magnitude of the force.
Solving Newton’s Second Law for acceleration gives:
a = F/m
The acceleration of an object is directly proportional to
the net force on an object and inversely proportional to
the mass of the object
Net Force causes acceleration
What TOTAL mass is being accelerated? The weight of the hanging mass
is accelerating the total mass of the system.
Adding a mass on the cart
increases the mass of the system.
Did the force increase? How will it
affect the acceleration.
The weight of the mass is
the force that accelerates
the system
Newton’s Second Law and Falling Objects
Neglecting air resistance, all objects fall at the same rate
of acceleration, g
F/m = g = F/m
The greater the mass, the greater force needed to
accelerate the object. So the ratio of F/m is g
Newton’s Third Law of Motion
F
F
Newton’s Third Law of Motion – Forces always
act in pairs. For every force there is an equal and
opposite force
F
F
a
a
a=
F/M
a = F/
m
The cannon applies a force to the cannon ball, and the
cannon ball applies an equal but opposite force to the
cannon
Gravity, Force and Newton’s Third Law
The earth exerts a force on
the apple that causes the
apple to accelerate down. But
the apple also exerts an equal
but opposite force on the
earth, causing the earth to
accelerate up!
Since the earth’s mass is MUCH greater than the mass of
the apple, the acceleration of the earth up is VERY small
-FApple on Earth = FEarth on Apple
Application of Newton’s Laws & Free Body Diagram
The force of gravity
(FWeight) always acts
toward the center of the
earth and is constant for
that object
FNormal
The force of the
surface (FNormal)
always acts
PERPENDICULAR
to the surface
q = 0O
FWeight
When the angle of the incline is 0O FW = FN
y
FW is the weight of the
wagon and is toward the
center of the earth
FN is the force of the incline that
supports the wagon and DOES
NOT equal FW
FW
This is the parallel component
down the incline F=
q is not 0O
This component is FPerpindiuclar (F ) and is equal in
magnitude but opposite direction of FN
x
A Closer Look At The Forces on an Incline
q for the vectors is
the same as q for
the incline
FW
F is the adjacent component of
FW
F= is the opposite component of
FW
The Static and Kinetic Forces of Friction and
Free Body Diagram
Fn
Fn
Fa
Fa
Fg
In figure a, there
is no frictional
force because
there is no force
trying to set the
jug in motion
Fn
Fg
In figure b, a
force is being
applied, but not
enough to set
the jug in
motion
Fg
In figure c the
applied force is
greater than the
maximum
frictional force
so the jug
accelerates
Fn
Fa
Fg
Friction acts to oppose the applied force. The
frictional force increases until it reaches a
maximum. The frictional force BEFORE the jug
moves is called the Static Force of Friction FS,
the force that is opposing the motion.
Fn
Fk= Fa
Fk
FS
Fg
After the jug is in motion, the force needed to maintain
constant motion is the Kinetic Force of Friction FK For
most surfaces FS > FK
FS
The nature of friction is due to the irregularities of the
surfaces in contact. Friction is really a microscopic
effect
The frictional force equals the applied force
until the maximum frictional force between
the surfaces is reached. At that point the
object begins to move. For most surfaces,
the applied force to maintain constant
motion is less than needed to begin the
motion
A graph of the applied force vs. frictional force. The
peak in the graph represents the maximum static
frictional force and the horizontal line is the kinetic force
that maintains constant motion
Calculating the Frictional Force
The frictional force is determined by the Normal force of
the surface on the object and the type of surfaces that
are in contact
Ff = mFN
and
m = Ff / FN
Where m (mu) is the coefficient of static (mS) or kinetic
(mK) friction. Since m is a ratio of two forces, it lacks a
unit
Objects in Equilibrium
When the FNet on an object is 0, it is in Equilibrium
Objects in Equilibrium are not accelerating
Objects in Equilibrium may or may not be moving
If M1 and M2 have the same
mass, then the system is in
equilibrium
M2 > M 1
If M1 and M2 do not have the
same mass, then the system
is not in equilibrium and the
masses will accelerate
y
SF = FNet
FW is the weight of the
wagon and is toward the
center of the earth
FN is the force of the incline that
supports the wagon and DOES
NOT equal FW
The Frictional Force,
Ff is acting on the
wagon and is
opposite the motion
FW
Now there is a force acting
DOWN the incline that is
PARALLEL to the surface of
the incline F=
q is not 0O
This component is FPerpinduclar (F ) and is equal in
magnitude but opposite direction of FN
x
Pulling a Wagon Up an Incline  Free Body Diagram
Fn is the normal
upward force from
the incline.
FApplied is up
the incline
Ff is acting down
the incline
because the
motion is now up
the incline
SF = FNet
FW is the gravity
acting on the wagon’s
mass.