Transcript Newton’s Second Law of Motion – Force & Acceleration

Newton’s Second Law of Motion
– Force & Acceleration
Chin-Sung Lin
Newton & His Second Law
Review – Newton’s First Law
Usually called the law of inertia
Every object continues in a state of rest,
or of motion in a straight line at constant
speed, unless it is compelled to change
that state by an unbalanced force
exerted upon it
Implies the second law of motion
Unbalanced Force
Unbalanced force means the net force ≠ 0
F
What will the unbalanced force result in?
Newton’s Second Law
Newton’s second law – Force & Acceleration
The acceleration produced by a net force
on an object is directly proportional to
the magnitude of the net force, is in the
same direction as the net force, and is
inversely proportional to the mass of the
object
Net Force = 0
Zero net force means zero acceleration
No acceleration is the evidence of zero net
force
Zero acceleration means
state of rest or
state of constant velocity
Force Causes Acceleration
Acceleration ~ Net force
(Direct Proportion)
a
a ~ Fnet
F
Mass Resists Acceleration
Acceleration ~ 1/mass
(Inverse Proportion)
a ~ 1/m
a
m
Force Causes Acceleration
Acceleration ~ Net force
a ~ Fnet
Acceleration ~ 1/mass
a ~ 1/m
a = Fnet /m
or
Fnet = m a
F=ma
Example: How much Force?
?
Example: What’s the Acceleration?
Example: What’s the mass?
m=?
a = 100 m/s2
F = 1000000 N
Weight is Gravitational Force
Fnet = m a
Fg = m g
or
W=mg
Weight, mass and Acceleration
Weight, mass and Acceleration
Weight on Earth & Moon?
Same Mass
Mass on Earth & Moon?
Same Weight
Friction Force
Friction acts on materials that are in
contact with each other, and is always
acts in direction to oppose motion
When There is No Friction
Coefficient of Friction (m)
Friction mainly due to the irregularities in
the two surfaces
The irregularities between surfaces of
different materials are described by the
coefficients of friction (m)
Friction mainly determined by the surface
and the weight of the object
Friction Force (Ff)
Friction force (Ff) can be categorized into
two different types: Static and Kinetic
Ff
Maximum Static Friction
Kinetic Friction
F
Maximum Static
Friction
Coefficient of Friction (m)
Static Friction Force
As long as an object does not move, the friction
force (Ff) must be equal in size and opposite in
direction to the applied force (F)
Ff = F
The static frictional force can have any value
from zero up to a max. value (maximum static
friction force)
Ff
Maximum Static Friction
F
Maximum Static Friction Force
Maximum static friction force is directly
proportional to the normal force and the
coefficient of static friction (ms).
Ff = FN  ms
Ff
Maximum Static Friction
F
Example: Static Friction Force
If a block is not moving, what’s the friction
force?
50 kg
20 N
Example: Static Friction Force
If the coefficient of static friction between a
block and the ground is 0.2, (a) what’s the
maximum static friction force? (b) Will the
block move? (c) What’s the friction force?
50 kg
80 N
Example: Static Friction Force
If a wooden block is resting on a wooden
floor, (a) How much force is required to make
the block move? (b) Will the block move? (c)
What’s the friction force while moving?
50 kg
100 N
Kinetic Friction Force
If the applied force exceeds the maximum static
friction force, the object will slide in the
direction of the applied force, and the friction
force reduces to a constant value called kinetic
friction force
The value of the kinetic friction is independent
of the speed of the object Ff
Kinetic Friction
F
Kinetic Friction Force
Kinetic friction force is directly proportional
to the normal force and the coefficient of
static friction (ms).
Ff = FN  mk
Ff
Kinetic Friction
F
Example: Kinetic Friction Force
If a block is moving at constant velocity,
what’s the friction force?
50 kg
20 N
Example: Kinetic Friction Force
If a block is moving and coefficient of kinetic
friction between the block and the ground is
0.1, (a) what’s the friction force? (b) What’s
the acceleration of the block?
50 kg
80 N
Example: Kinetic Friction Force
If a wooden block is sliding on a wooden floor,
(a) what’s the friction force? (b) What’s the
acceleration of the block?
20 kg
100 N
Example: Kinetic Friction Force
If a 40-kg block is pushed by a force of 100 N
and accelerates at 2 m/s2, (a) what’s the
friction force? (b) What’s the coefficient of
kinetic friction between the block and the
ground?
40 kg
100 N
Example: Kinetic Friction Force
If a 40-kg block is sliding down an incline
plane of 30o at constant speed, (a) what’s the
friction force while sliding? (b) What’s the
coefficient of kinetic friction between the
block and the ground?
Application – Anti-Lock Brake
Air Resistance
R
Fg
Free Falling & Air Resistance
When there is air resistance (R), the
acceleration of a free falling object reduced.
The acceleration of a falling object is:
a = Fnet/m = (Fg – R)/m = (mg – R)/m = g – R/m
Air Resistance & Terminal Speed
When the air resistance on an object equals
the weight of the object, the net force is
zero and no further acceleration occurs.
Acceleration terminates: the object has
reached its terminal speed or terminal
velocity.
a = 0 m/s2 = g – R/m
g = R/m
R = mg
Reduce the Terminal Speed
Force vs. Pressure
Pressure
Pressure (P):
The amount of force per unit of area
Pressure = Force / Area of application
or
P = F/A
Unit:
Newtons per square meter, or pascals (Pa).
Example: Pressure
200 kg
Which one has larger pressure?
5 kg
200 kg
5 kg
.2m x .2m x .2m
2m x 2m x 2m
Summary
 Newton’s second law - Fnet = m a
 Force causes acceleration & mass resists acceleration
 Weight is gravitational force - Fg = m g
 Acceleration of different masses on Earth
 Mass and weight on Earth and moon
 Friction force and coefficient of friction (m)
 Static friction force and kinetic friction force
Summary
 Friction force Ff = m FN
 Air resistance and terminal speed
 Pressure vs. force