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Chapter 4
Newton’s Laws of Motion
Sir Isaac Newton
Philosophiae Naturalis Principia Mathematica (1687)
Opticks (1704)
"Nature and nature's laws lay hid in night;
God said 'Let Newton be' and all was light."
Newton’s Three Laws
Inertia:
“Every body continues in its state of rest, or of uniform
motion in a straight line, unless it is compelled to change
that state by a force impressed on it.”
Force, Mass, Acceleration (F=ma):
“The change in motion is proportional to the motive force
impressed; and is made in the direction of the right line
in which that force is impressed.”
“Action = Reaction”:
“To every action there is always opposed an equal reaction;
or, the mutual actions of two bodies are always equal,
and directed to contrary parts.”
Newton’s Law Summary
1. Velocity is zero or constant when net force is zero.
2. F=ma
3. Action = Reaction (in opposite direction)
Net Force
Net force (or total force) is the sum of all the
forces applied to an object.
FA
FB
FC
For example, if there are
three people, A, B and C
pushing the crazy kid.
The net force on him is:
r
r
r
Fnet  FA  FB  FC
First Law and Net Force
The First Law deals with cases when there is
no net force.
r
r
r
r
Fnet  FA  FB  FC  0
FA
FB
FC
“Every body continues in
its state of rest, or of
uniform motion in a straight
line, unless it is compelled
to change that state by a
force impressed on it.”
Puck on ice
Ice has very little friction (so no net force), so the inertia
keeps the puck moving once it is set in motion.
Mass or Inertia
 Inertia is the tendency of an object to
remain at rest or in motion with constant
speed along a straight line.
 Mass (m) is the quantitative measure of
inertia. Mass is the property of an object
that measures how hard it is to change its
motion.
 Units: kg
Mass vs. Weight
 Mass is an intrinsic property of an object.
A rock has same mass whether it is on the moon
or on Earth.
Mass does not change
 Weight is the force exerted on an object by
gravity: W=mg
This is different depending upon the strength of
the gravitational force.
You weigh less on the Moon than on Earth.
Example
What is the weight of a man of mass 70kg on Earth?
W  mg  (70kg)(9.8m / s )  686N
2
Weight is measured in N.
(Pound: 1lb = 4.448N)
We sometimes use the symbols W or Fgravity to denote weight.
Same mass, different weight
Newton’s 1st Law
There are many forces act on the plane, including
weight (gravity), drag (air resistance), the thrust of
the engine, and the lift of the wings. At some point
the velocity of the plane is constant. At this time,
the total (or net) force on the plane:
lift
1. is pointing upward
2. is pointing downward
3. is pointing forward
4. is pointing backward
correct
5. is zero
drag
thrust
weight
r
r
r
r
Fnet  Fdrag  Fweight  Fthrust  Flift  ???
Newton’s 1st Law
Newton's first law states that if no net force
acts on an object, then the velocity of the
object remains constant. Since the velocity
is constant, the total force on the plane
must be zero, according to Newton's first
lift
law.
r
r
r
r
Fdrag  Fweight  Fthrust  Flift  0
drag
thrust
weight
Newton’s Second Law
Unit: N (Newton)
F = ma
Deals with the effect of a non-zero net force.
Non-zero net force causes acceleration.
r
r
r
r
Fnet  FA  FB  FC  0
FA
FB
FC
Some Math
r
In vector notation:
r
F  ma
What does the vector symbol mean?
F  Fx iˆ  Fy ĵ  Fz k̂,
r
a  ax iˆ  ay ĵ  az k̂
 Fx iˆ  Fy ĵ  Fz k̂  max iˆ  may ĵ  maz k̂
 Fx  max

  Fy  may
 F  ma
z
 z
F = ma applies to each
component independently.
F means NET FORCE!!!
The F in F = ma is the net force on the object.
If you are careful, you may write instead:
Fnet = ma
Always remember to find the net force first!
r
r
r
r
Fnet  FA  FB  FC  ma
FA
FB
FC
Simple Examples: Find a
F = 200N
m = 10kg
F 200N
F  ma  a  
 20m / s 2
m 10kg
F = 200N
m = 10kg
F = 150N
F 200N  150N
a 
 5m / s 2
m
10kg
Find the magnitude of a
First write the forces as vectors :
r
F1  5cos20 oiˆ  5sin 20 o ˆj  4.70iˆ  1.71 ˆj
r
F  8cos60 oiˆ  8sin 60 o ˆj  4.00iˆ  6.93 ˆj
2

m  2kg

Then find the net force vector :
r
r r
Fnet  F1  F2  8.70iˆ  5.22 ˆj
Apply the second law :
r
r
Fnet  8.70iˆ  5.22 ˆj  ma
r 1
 a  (8.70iˆ  5.22 ˆj )  (4.35iˆ  2.61 ˆj )m /s2
2
Now we can find the magnitude :
r
a  4.35 2  2.612  5.07m /s2
r 
r r
You can also use v  v0  at to figure out the velocity.
When the net force is zero
r
r
r
r
r r
If Fnet  0, using F  ma, we have a  0.
r
r
r r
On the other hand, if a  0, we have Fnet  0.
Zero Net Force on a Lamp
T : Tension
W : Weight ( Fgravity  mg)
T  W  0N  T  W
When Fnet is non-zero
When Fnet ≠ 0, since F=ma, we have a≠0.
No net force, no acceleration.
Net force leads to acceleration.
If an object is accelerating, there must be a
non-zero net force.
Example
The mass of m = 2kg is accelerating
upward at 4m/s2. Find the tension.
Fnet  T  mg
but Fnet  ma  T  mg  ma
T  ma  mg  m(a  g)
 (2kg)(4  9.8)m / s 2  27.6N
mg
Example
The mass of m = 2kg is accelerating
downward at 4m/s2. Find the tension.
a  4m / s
2
mg  T  ma
T  m(g  a)  (2kg)(9.8  4)m / s 2  11.6N
T-mg or mg-T ?
In non-vector notation, we usually assume the
variable a represents the magnitude of the
acceleration, and is therefore positive whether it
is up or down. In other words, unless stated
otherwise, we will not use the up/positive,
down/negative convention.
With this new convention, whenever you have
opposing forces, the forces pointing in the
same direction as a comes first, minus the
forces in the opposite direction as a.
T-mg or mg-T ?
T  mg  ma
mg  T  ma
Another way to remember, if a > 0, you want:
(big number) - (small number) = ma
or
(same direction) - (opposite direction) = ma
Two forces
F1 = 200N
a
m = 10kg
F2 = 350N
It is obvious that a is going to point toward the left:
350N  200N  ma
350N  200N
a
 15m / s 2 : Accelerate toward the left
10kg
Newton’s Third Law
 For every force, there is an equal and
opposite force
every “action” has a “back-reaction”
these are precisely equal and precisely
opposite
Newton’s Third Law
You cannot push without being pushed back just as
hard
In tug-of-war, each side experiences the same force (opposite
direction)
When you push on a brick wall, it pushes back on you!
Force Pairs Illustrated
Force on box
by person
Force on floor by box
Force on person
by box
Force on box
by floor
Force on person Force on floor
by person
by floor
Not shown are the forces of gravity and the associated floor forces
Don’t all forces then cancel?
How does anything ever move (accelerate) if
every force has an opposing pair?
Action and reaction force act on different
objects.
Force on box
by person
Net Force
on box
Force on box
by floor
Exercise: Action/Reaction
 Suppose a tennis ball (m= 0.1 kg) moving at a velocity v = 40
m/sec collides head-on with a truck (M = 500 kg) which is
moving with velocity V = 10 m/sec.
 During the collision, the tennis ball exerts a force on the
truck which is smaller than the force which the truck exerts
on the tennis ball.
TRUE or FALSE ?
 The tennis ball will suffer a larger acceleration during the
collision than will the truck.
TRUE or FALSE ?
 Suppose the tennis ball bounces away from the truck after
the collision. How fast is the truck moving after the
collision?
< 10 m/sec
= 10 m/sec
> 10 m/sec ?
Exercise: Action/Reaction solution
 During the collision, the tennis ball exerts a force on the
truck which is smaller than the force which the truck exerts
on the tennis ball.
TRUE or FALSE ?
Equal and opposite forces!
The tennis ball will suffer a larger acceleration during the
collision than will the truck.
TRUE or FALSE ?
Acceleration = Force / mass
 Suppose the tennis ball bounces away from the truck after
the collision. How fast is the truck moving after the
collision?
< 10 m/sec
= 10 m/sec
> 10 m/sec ?
Force from the ball causes deceleration.
Normal Force
Force from a solid surface (e.g. wall, ground)
providing support for an object.
“Normal” means “perpendicular”, Normal
Force is always perpendicular to the solid
surface.
Notations:
FN, Fn, N or n
Example of Normal Force
Suppose the elevator is not accelerating.
m=70kg, what does the scale read?
A scale actually measure the normal force,
NOT mg!!!
The forces must cancel each other:
FN  mg  686N
This is a special case,
in general FN  mg!!!
Example of Normal Force 2
Suppose the elevator is accelerating up.
m=70kg, a=5m/s2
FN  mg  ma
 FN  m(g  a)  1036N
Note that FN  mg!!!
In general, the normal force
is what a scale measures.
Example of Normal Force 3
Suppose the elevator is accelerating down.
m=70kg, a=5m/s2
mg  FN  ma
 FN  m(g  a)  336N
Note that FN  mg!!!
Make sure you see the difference
in these 3 cases!
Be careful with the normal force
Fn
Fy
mg

Fn  Fy  mg

 Fn  mg  Fy
m  1.5kg
 Fn  mg  F sin   9.7N

Note that mg  14.7N


Fn  mg in general! !!
What is Fn now?
Fn
mg Fy
m  1.5kg
 Fn  mg  F sin   21.8N

 
Fn  mg  Fy
Note that mg  14.7N


Fn  mg in general! !!