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Newton’s Laws of Motion
Observation #1 An object at rest remains at rest, unless
something makes it move.
Observation #2 A object in motion continues in motion with
constant velocity, unless something makes
it change its velocity.
Constant velocity = constant speed in the
same direction.
Observation #3 An object will not change its velocity unless a
net external force acts on it.
Combining Observations 1 & 2
An object left alone will not change it’s velocity. Something must cause a change in velocity.
A force is something that causes an acceleration or change in velocity
Change in speed
Change in direction
By definition is a push or a pull
Force SI unit of force is the Newton (N)
1 N = 0.225 lb
1 lb. = 4.448 N
A Force is a Vector
It has a magnitude, measured in N or lbs.
It acts in a particular direction.
Can exist during physical contact (tension,
friction, applied force) = Contact Force
Can exist with NO physical contact, called field
forces(gravitational, electric)= Noncontact Force
Newton’s First Law An object in motion remains in motion in a straight line
and at a constant speed (velocity) or an object at rest
remains at rest, unless acted upon by an external
(unbalanced) force.
TWO conditions and one constraint.
Condition #1 – The object CAN move but must be at a CONSTANT SPEED
Condition #2 – The object is at REST
Constraint – As long as the forces are BALANCED. If all the
forces are balanced the SUM of all the forces is ZERO.
The bottom line: There is NO ACCELERATION in this case AND the
object must be at EQILIBRIUM ( All the forces cancel out).
00 Faccel
Inertia
Another way to say Newton’s First Law is to
say the Law of Inertia
Inertia is the tendency of objects to resist
changes in motion.
The amount of inertia an object has is
determined by its mass.
Quantity of matter, also called MASS.
Italian for “LAZY”.
Unit for MASS = kilogram.
Inertial Reference Frame
Newton’s Law require measurements to be
made in a reference frame that is not
accelerating to be valid. (moving at constant
velocity)
This excludes situations where the rotation of
the Earth is noticeable.
Large air currents and ocean currents.
Long range missiles.
Newton’s First Law – Inertia Examples
Types of Forces
Contact Forces- result from physical contact
between two objects.
Field Forces- (Noncontact) force that can exist
between two objects even in the absence of
physical contact. (Action-at-a-Distance Force)
Common Types of Forces:
Gravitational Force
Normal Force
Frictional Force
Tension Force
Common Forces
Force of gravity
(Fg) pulls straight
down.
Friction (Ff) occurs
between two objects
that can slide against
each other.
It opposes motion.
Common Forces
Normal force (FN) is the
support force from a
surface.
It is called “normal”
because it is always
perpendicular to the
surface.
Tension (FT) is the force in
a rope or string.
The tension is the same
in every part of a rope.
Determining the Force of Gravity
The magnitude of the force of gravity on
something is called the weight.
Is how MASS is effected by gravity
Weight = mass x gravity
g = 9.81 N/kg
NOTE: MASS and WEIGHT are NOT the same thing. MASS never changes.
mgW
What is the weight of an 85.3-kg person on earth? What is the weight of same person on Mars (g=3.2 m/s2)?
NW
NWmgW
MARS 96.272)2.3)(3.85(
94.835)8.9)(3.85(
Equilibrium Model
A system moving at a constant speed (velocity)
or at rest MUST be at “EQUILIBRIUM”. Fnet = 0
According to Newton’s First Law, objects in
equilibrium have a net external force equals 0. ,
Δv = 0 , ∑ F = 0
TIPS for solving problems:
• Draw a free body diagram
• Resolve anything into COMPONENTS
• Write equations of equilibrium
• Solve for unknowns
Determining Net External Force
The net external force is the sum of all the
forces acting on the object.
Since forces are vectors, we must use
vector addition to find the sum, or resultant.
Free-body diagrams are useful for
determining the net force acting on an
object.
Free-Body Diagram
Free-body diagrams consider just one object and the forces that act on it.
To draw a free body diagram
Draw a dot to represent the object.
Draw and label vector arrows representing all the forces acting on the object.
All the vectors should be shown as acting at a single point.
A pictorial representation of forces complete with labels.
W1,Fg1 or m1g
•Weight(mg) – Always
drawn from the center,
straight down
•Force Normal(FN) – A
surface force always drawn
perpendicular to a surface.
•Tension(T or FT) – force in
ropes and always drawn
AWAY from object.
•Friction(Ff)- Always drawn
opposing the motion. m2g
T
T
FN
Ff
Free Body Diagrams
mg
FN Ff
Free Body Diagrams
Fa
A 10-kg box is being pulled across the table to
the right at a constant speed with a force of 50N.
a) Calculate the Force of Friction
a) Calculate the Force Normal
mg
FN
Fa Ff
NFF fa 50
NFmg n 98)8.9)(10(
Example
Suppose the same box is now pulled at an angle
of 30 degrees above the horizontal.
a) Calculate the Force of Friction
b) Calculate the Force Normal
mg
FN Fa
Ff 30
NFF
NFF
axf
aax
3.43
3.4330cos50cos
Fax
Fay
NF
FmgF
mgFF
mgF
N
ayN
ayN
N
73
30sin50)8.9)(10(
!
Example
"The acceleration of an object is directly proportional
to the NET FORCE AND inversely proportional to the
mass."
ma
Fa NET
1
Acceleration is directly proportional to the NET
Force.
DIRECTLY = They do the same thing. If the force
increases, the acceleration increases. If the force
decreases, the acceleration decreases.
Acceleration is inversely proportional to the mass.
INVERSELY = They do the opposite.
If the mass decreases, the acceleration will
increase. If the mass increases, the acceleration
will decrease.
Newton’s Second Law )(amF
Newton’s 2nd Law
N.S.L. works based on these
direct and inverse
relationships. As 2 of the
variable change, ONE of them
must remain constant.
If the force is constant, the
acceleration and mass change
as shown above.
F(net)=ma
2F=m(2a)
3F=m(3a)
If we add a second dog pulling with
100N just like the first dog, we
could pull the sled with twice the
acceleration, provided the mass of
the sled was constant.
Putting it all Together
NETFa m
a1
0
Force Total
NET
NET
NETNET
F
FF
maFm
Fa
10 N 3 N
Magnitude of FNET=
Direction =
Acceleration =
7 N
RIGHT
10 kg
0.70 m/s2
1. Draw a free body diagram
2. Break vectors into components if needed
3. Find the NET force by adding and subtracting
forces that are on the same axis as the
acceleration.
4. Set net force equal to “ma” this is called
writing an EQUATION OF MOTION.
NOTE: To avoid negative numbers, always
subtract the smaller forces from the larger one.
Newton’s 2nd Law Tips
Example An elevator with a mass of 2000 kg rises with an
acceleration of 1.0 m/s2. What is the tension in the
supporting cable?
mg
T
T
T
mgmaT
mamgT
maFNET
)8.9)(2000()1)(2000(
Equation of Motion
21,600 N
Example A 50 N applied force drags an 8.16 kg log to the right
across a horizontal surface. What is the acceleration of the log if the force of friction is 40.0 N?
50 N 40 N
mg
Fn a
a
a
a
maFF
maF
fa
NET
16.810
16.84050
1.23 m/s2
Example A sled is being accelerated to the right at a rate of 1.5
m/s2 by a rope at a 33 degree angle above the + x . Calculate the Frictional Force if the mass of the sled is 66 kg and the tension in the rope is 150 N.
mg
FN
Ff
Tcos
Tsin
f
f
f
f
NET
F
F
FmaT
maFT
maF
)5.1)(66(33cos150
cos
cos
26.8 N
Newton’s Third Law “For every action there is an EQUAL and
OPPOSITE reaction.
This law focuses on action/reaction pairs
(forces)
They NEVER cancel out
All you do is SWITCH the wording!
•PERSON on WALL
•WALL on PERSON
Newton’s Third Law This figure shows the force during a
collision between a truck and a train.
You can clearly see the forces are
EQUAL and OPPOSITE. To help you
understand the law better, look at
this situation from the point of view
of Newton’s Second Law.
TrainTrainTruckTruck
TrainTruck
aMAm
FF
There is a balance between the mass and acceleration.
One object usually has a LARGE MASS and a SMALL
ACCELERATION, while the other has a SMALL MASS
(comparatively) and a LARGE ACCELERATION.
Newton’s 3rd Law Examples
Action: HAMMER HITS NAIL
Reaction: NAIL HITS HAMMER
Action: Earth pulls on YOU
Reaction: YOU pull on the earth
Newton’s Law of Gravitation
What causes YOU to be pulled down? THE
EARTH….or more specifically…the EARTH’S
MASS. Anything that has MASS has a gravitational
pull towards it.
MmFgWhat the proportionality above is
saying is that for there to be a
FORCE DUE TO GRAVITY on
something there must be at least 2
masses involved, where one is
larger than the other.
Newton’s Law of Gravitation
As you move AWAY from the
earth, your DISTANCE increases
and your FORCE DUE TO
GRAVITY decrease. This is a
special INVERSE relationship
called an Inverse-Square.
2
1
rFg
The “r” stands for SEPARATION
DISTANCE and is the distance between
the CENTERS OF MASS of the 2 objects.
We us the symbol “r” as it symbolizes the
radius. Gravitation is closely related to
circular motion as you will discover later.
N.L.o.G – Putting it all Together
2
21
2
211
2
21
1067.6
Constant nalGravitatio UniversalG
alityproportion ofconstant
r
mmGF
kgNmxG
G
r
mmF
g
g
earth eLEAVING th areyou when thisUse
earth on the areyou when thisUse
2
21
r
mmGF
mgF
g
g
Try this!
earth eLEAVING th areyou when thisUse
earth on the areyou when thisUse
2
21
r
mmGF
mgF
g
g
mxr
kgxM
r
MGg
r
MmGmg
6
24
2
2
1037.6 Earth theof radius
1097.5Earth theof Mass
Let’s set the 2 equations equal to each other since they BOTH
represent your weight or force due to gravity
SOLVE FOR g!
2
26
2411
/81.9)1037.6(
)1097.5)(1067.6(sm
x
xxg
Which has more force?
When the boxer hits the bag, which has more
force, the boxer on the bag or the bag on the
boxer?
Newton’s Third Law
If an object, A, pulls or pushes on an object,
B, then B also pulls or pushes on A. The
force on each object has the same
magnitude, but the forces are oppositely
directed.
Action-Reaction Pairs
Action-Reaction Pairs
A pair of forces
between two objects
is called an action-
reaction pair.
Newton’s Laws Simplified
Force is required to cause an acceleration.
Force = mass x acceleration
All forces come in pairs.
Constant Force Model vs. Equilibrium
Model
Equilibrium
∑F = 0.
Object will be at rest or
move with constant
velocity.
Position vs. time graph-
Constant Force
∑ F = constant.
Object will accelerate in
the direction of the net
force.
Position vs. time graph-
Normal Force Normal Force (FN) if one component of a
force that a surface exerts on an object with
which it is in contact, perpendicular to the
surface
Block on table, block’s weight pushes down on
table, the table pushes back up on block
Follows Newton’s 3rd Law, for every action
there is an opposite reaction
Size of FN indicates how hard two object press
against each other
If object is resting on horizontal surface and no
other forces act, then FN = W
Tension Force
Force often applied by means of cables or
ropes that are used to pull an object (FT)
Tension is often defined as the tendency of a
rope or a cable to be pulled apart
FT of a rope that is pulling an object is the
same size as the force being applied to
the object being pulled
Assume rope is massless, tension can be
transmitted undiminished through rope unless
stated otherwise (then tension would be different
along different areas of the rope)
Frictional Forces
Frictional forces
oppose the applied
force.
They act in the
opposite direction of
the motion
Two Types of Friction
Static
Kinetic
F Applied F Friction
Static Friction
Static friction (Fs) is the frictional force that acts on a static (nonmoving) object.
When an object is not moving, the frictional force will equal the applied force but be in the opposite direction.
Fs= - Fapplied
F Applied FS
Static Friction
There is a maximum amount of static friction, Fs,max .
Once the applied force exceeds Fs,max the object breaks free and begins moving.
F Applied FS
Kinetic Friction
Kinetic friction is the
frictional force on a
moving object.
The force of kinetic
friction is less than
the maximum static
friction.
The net force on a
moving object is
equal to Fapplied - Fk
F Applied FK
Force of Friction
The Force of Friction
is directly related to
the Normal Force.
Mostly due to the
fact that BOTH
are surface
forces
Nkkf
Nssf
Nf
FF
FF
FF
friction oft coefficien
alityproportion ofconstant
Note: Friction ONLY depends on the MATERIALS
sliding against each other, NOT on surface area.
The coefficient of
friction is a unit less
constant that is
specific to the
material type and
usually less than
one.
Friction & Newton’s 1st Law If the coefficient of kinetic friction between a 35-kg crate
and the floor is 0.30, what horizontal force is required to
move the crate to the right at a constant speed across the
floor?
mg
Fn
Fa
Ff
(0.30)(35)(9.8)
a f f k N
a k N
N
a k
a
a
F F F F
F F
F mg
F mg
F
F
102.9 N
Friction & Newton’s 2nd Law Suppose the same 35 kg crate was not moving at a
constant speed, but rather accelerating at 0.70 m/s/s.
Calculate the applied force. The coefficient of kinetic
friction is still 0.30.
mg
Fn
Fa
Ff
(35)(0.70) (0.30)(35)(9.8)
NET
a f
a k N
a k
a k
a
a
F ma
F F ma
F F ma
F mg ma
F ma mg
F
F
127.4 N
Inclines
cosmg
sinmg
mg
FN Ff
Tips
•Rotate Axis
•Break weight into components
•Write equations of motion or
equilibrium
•Solve
Friction & Inclines A person pushes a 30-kg shopping cart up a 10 degree
incline with a force of 85 N. Calculate the coefficient of friction if the cart is pushed at a constant speed.
cosmg
mg
Fn Fa
Ff
sinmg
sin
sin cos
cos sin
sin cos
sin
cos
85 (30)(9.8)(sin10)
(30)(9.8)(cos10)
a f f k N
a k N N
a k
a k
ak
k
F F mg F F
F F mg F mg
F mg mg
F mg mg
F mg
mg
0.117
Example
A 5-kg block sits on a 30 degree incline. It is attached to string that is thread over a pulley mounted at the top of the incline. A 7.5-kg block hangs from the string.
a) Calculate the tension in the string if the acceleration of the system is 1.2 m/s/s
b) Calculate the coefficient of kinetic friction.
m1
m1g
m2g
FN T
T Ff
30
30
m2gcos30
m2gsin30
1 1
2 2
2
( sin )
cos
NET
f
N
F ma
m g T m a
T F m g m a
F m g
Example Cont.
1 1
1 1
(7.5)(9.8) (7.5)(1.2)
NETF ma
m g T m a
m g m a T
T
T
64.5 N
2 2
2 2
2 2
2 2
2 22
2 2
2
( sin )
sin
sin
sin
sincos
sin
cos
64.5 (5)(1.2) (5)(9.8)(sin 30)
(5)(9.8)(cos30)
f
f
k N
k N
k N
N
k
k
k
T F m g m a
T F m g m a
T F m g m a
T m a m g F
T m a m gF m g
F
T m a m g
m g
0.80 N
Coefficient of Friction Example
A 24 kg crate, initially at rest, requires a 75 N
force to set it in motion. Once moving, a
force of 53 N is needed to keep it moving with
constant velocity.
Find the coefficient of static friction and the
coefficient of kinetic friction.
Coefficient of Friction Example
n
s
sF
F max,
mgF
mgF
F
n
n
Y
0
0
N 75
0-N 75
0
,
,
MaxS
MAXS
X
F
F
F
Fn
75 N FS,Max
F gravity=mg
32.0
)m/s kg)(9.81 24(
N 75N 752
S
smg
Coefficient of Friction Example
23.0
)m/s kg)(9.81 (24
N 35
0
N 53
2
k
kk
n
n
k
n
kk
mg
F
mgF
mgF
F
F
F
Fn
75 N Fk
F gravity=mg
Air Resistance
The force of air resistance (FR) is a form of friction.
FR depends on velocity.
FR
Fg
Terminal Speed
At some speed, the air resistance will be equal in magnitude to the force of gravity. (FR = -Fg).
Once an object reaches that speed, it will no longer accelerate. It will continue to fall at a constant speed.
FR
Fg