Transcript Forces

Forces and
Newton’s Laws of Motion
Chapter 4
Inertia
All objects naturally tend to continue moving
in the same direction at the same speed.
All objects resist changing their velocity.
(velocity is speed and direction)
Resistance to changing velocity is inertia.
The amount of inertia is the mass.
Mass is measured in kilograms (kg).
Forces
External forces can change an object's velocity.
Total external force is called net force F.
Net force F determines how quickly and in
what direction the velocity changes.
When net force F is zero, the velocity remains
unchanged. If the object is moving, it keeps
moving in a straight line.
Newton's first law
When net force F  0 , the velocity stays
the same. (same speed and same direction)
The reverse is also true.
When the velocity stays the same,
the net force F  0 .
Newton's first law is also called the law of inertia
because an object's inertia keeps it moving in the
same direction at the same speed if the net force
is zero.
Inertial reference frame
An inertial reference frame is a coordinate
system in which Newton’s law of inertia is
valid.
Inertial frames have a constant velocity.
All accelerating reference frames are noninertial because Newton’s law of inertia is not
valid in accelerated coordinate systems.
Non-inertial frame: A car when speeding up,
slowing down, or turning a corner.
Net force F
The net force F is the vector sum of all
external forces acting on a single object.
F  F1  F2  F3 
Individual Forces
Net Force
F
4N
10 N
6N
The SI unit of force is the newton (N).
Net force F
Individual Forces
F1
Net Force
F
3N
F2
37
4N
F  F1  F2
F
F2
4N
F1
3N
5N
Newton's second law
An object's acceleration vector is equal to the
net force F acting on the object divided by
the object's mass.

a


F
m
Acceleration direction is same direction as
net force F .
Newton's second law
Use x and y components when you need
more than + and - to specify directions.
F

ma


or

Fx  max

Fy  may
SI unit of force

a


F
F  ma
m
newton N is the SI unit for force
 m  kg  m
N =  kg   2   2
s
s 
Force diagram (also known as free-body diagram)
ALWAYS draw a force diagram with a force
vector for each individual, external force
acting on a single object.
mass 1850 kg
F  275N  395N  560N  110N
Net force F is in the +x direction.
Example: What is the car's acceleration?
Net force is +110 N and car's mass is 1850 kg
F +110 N
m

a

 0.059
m
1850 kg
The “+” sign indicates the +x direction.
s
2
Newton's third law
Two objects always exert equal and opposite
forces on each other.
Forces always occur in pairs.
Each object experiences the force equally,
but the forces are in opposite directions.
Example: You are pushing down on the chair
with some force and the chair is pushing on
you with the same amount of force but in the
opposite direction (up).
Example
Astronaut pushes with 36 N on a spacecraft.
What are their accelerations?
11,000 kg
92 kg
The two objects exert 36 N of force on each other.
a spacecraft 
F
mspacecraft

36 N
m
 0.0033 2
11,000 kg
s
aastronaut 
F
mastronaut

36 N
m
 0.39 2
92 kg
s
Example
Find the tension in the trailer drawbar and the force D that propels the truck forward.
Ignore the forces of friction and air resistance.
Unbalanced horizontal force
Unbalanced horizontal forces
FN
FN
Fg
Fg
Equal and opposite forces
on different objects
Forces
There are two general types of forces in nature,
fundamental and non-fundamental.
Fundamental
Non-fundamental
gravity
electromagnetism
weak nuclear
strong nuclear
push
pull
support
friction
tension
...
Universal law of gravity
Every two objects in the universe attract
each other with the gravity force.
centerline
Equal attracting forces in exactly opposite directions.
(Newton's 3rd law: equal and opposite forces on two objects)
magnitude
universal gravity constant
m1m2
F G 2
r
G  6.673 1011
N m2
kg 2
Weight is the gravity force on an object
 ME 
MEm
Fg  G
 m  G 2   mg
2
RE
 RE 
Fg  mg
where
ME
N
m
g  G 2  9.8  9.8 2
r
kg
s
Example: a 5 kg mass "weighs" 49 N

N
Fg  mg   5kg   9.8   49 N
kg 

Fg
Fg
Contact forces
Support
FN
Perpendicular to the contact surfaces
Friction
f
Tangent to the contact surfaces
Sliding friction (kinetic) f k
Non-sliding (static) f s
Normal means perpendicular so the support force is
often called the normal force.
Examples: Forces on the block
F  ma  0
15 N block
F  FN  Fhand  Fg
15 N
F   FN  11 N  15 N  0
FN  26 N
F  ma  0
F  FN  Frope  Fg
F   FN  11 N  15 N  0
FN  4 N
15 N
Apparent weight
Apparent weight is the reading of the scale.
It is equal to the support force the scale exerts on the
person and the person exerts on the scale.
forces on
the person
F  ma   FN (by scale )  Fg
Static friction
Static means the two surfaces are
not sliding across each another.
Friction force direction
opposes the impending
relative motion between two
objects.
Static friction magnitude is just
enough to prevent motion.
0  f static  f
MAX
static
 s FN
0  s  1
static friction coefficient
Kinetic friction
Kinetic friction opposes sliding motion
f k   k FN
0  k  1
kinetic friction coefficient
Friction forces do not depend on contact area.
Friction depends on contact force FN .
Example: Find sliding distance
Kinetic friction force causes the sled to slow down.
a
F  ma  Fg  FN  f k
0°
k  0.05
f k  FN k
ma180  Fg   90  FN 90  f k 180
Fx   40kg  ax   f k   FN k
force
diagram
get the directions
analyze the x and y components

N
Fy   40kg  0    Fg  FN    40kg   9.8   FN
kg 

0  392 N  FN  FN  392 N  f k   392 N  0.05   19.6 N
m
 40kg  ax  19.6 N  ax  0.49 2  x  32.65m
s
Tension force
Flexible things like
rope, string, cables
exert tension forces.
Force direction is
always tangent to the
rope, etc.
Tension force has
the same magnitude
at each end.
Tension force
Pulleys change the direction of
a tension force, but not the
magnitude of the force.
man
FN
Ftension
force of the
rope on the
block
Ftension
Fg
Fg
Newton's third law tells us that
the rope exerts the same
amount of force on the man as
the man exerts on the rope.
force of the
man on the
rope
To simplify things, physics ropes and cables are usually massless and pulleys are
usually frictionless. The rope has no weight that needs to be considered.
Equilibrium
Equilibrium mean balanced.
For equilibrium the forces are balanced and the
net force F  0 .

Velocity magnitude & direction stay the same.
F  0
or

F
Fx  0
y
0
Equilibrium Reasoning Strategy
Select an object to analyze.
Draw a force diagram showing only the forces
acting on the object, but not forces that the object
exerts on other things.
Choose a set of x and y axes.
Set up balanced force equations
The sum of the x force components add up to zero.
The sum of the y force components add up to zero.
Solve for any unknown quantities.
Example
find F
Object is the
pulley, but first find
the tension in the
rope
Ftension
2.2 kg
First, select the block as the object.
If the block stays at rest, then the forces
acting on it are balanced. Therefore,
the tension and gravity forces are
balanced. ( Second law: F  0 )
m

Fg  mg   2.2kg   9.8 2   21.56 N
s 

Second, select the pulley as the object
0
0
21.56 N
180
If the pulley stays at rest, then the forces on the
pulley are balanced. (Second law: F  0 )
F  F  T1  T2  0
F  F 180  21.56 N 35  21.56 N   35  0
F  F 180  21.56 N 35  21.56 N   35  0
F  35.32 N
Fx=F cos θ
Fy=F sin θ
-F
0
F180
17.66 N
12.37 N
21.56N35
17.66 N
-12.37 N
21.56N 35
0
0
F  0
Example
Engine weighs 3150 N
100
10
90
F  T1100  T2  10  3150 N   90  0
The End