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PHY166 Fall 2005
4 – Newton´s laws
Aristotle (384-322 b.c.)
12 century -> Latin
Dominating views
„Forces cause objects
to move;
No force – no velocity“
Aristotle disregarded
friction forces
Galilei (+2000 years)
Questioned Aristotles
„Forces cause objects
to accelerate;
No force – velocity
constant“
v = v0 + at
x = x0 + v0t + 12 at 2
Newton (1642-1727)
1687 – The mathematical Principles
of Natural Philosophy (Principia)
Newton´s laws: Foundation
of modern Physics
Relativistic
mechanics
v ~ c=3 ·108 m/s
Newton
mechanics
Quantum
Mechanics
m ~ me ~ 10-30 kg
♦ Newton´s first law:
Objects that are not subject to action of forces are moving with zero or constant velocity
(follows from the second law; has historical significance – disproves Aristotle)
♦ Newton´s second law: F = ma
F – force; m – mass;
Unit of force:
kg m/s2 = N(ewton)
a – acceleration
Allows to compute acceleration from force etc.
Consequences: (i) First law for F=0;
(ii) Statics for a=0, i.e., F =0 (important applications in engineering)
Force F is the sum of all forces acting on the object:
F = ∑ Fi = F1 + F2 + F3 + ...
1
i
Addition of vectors
2
(Tail-to-tip)
3
Sum
2
Mass m is the measure of inertia of the object
♦ Newton´s third law: F12 = −F21
Helps to identify forces in systems of
interacting bodies
Two objects pressed against each other
1
F12
Example: Measuring weight
with a spring scale
mg
F12
F21
2
2
F12
1
F21
Two objects connected by flexible thread
1
2
2
F21 – read by scale!
F21 = −F12= mg
mg+ F12 = 0
F12 = − mg
In this way the weight W=mg
is measured
In isolated systems
the sum of all (internal) forces is zero;
Only external forces
can accelerate the system as the whole
Examples:
• rocket
• car,
• smart mule
• Baron Münchhausen
3
Friction
• Sliding friction -> static friction
• Rolling friction
• Viscous friction
FN
F
Sliding friction
Surfaces are
rough
Ffr
 µFN , v ≠ 0
F fr = 
µ s FN , v = 0
mg
µs>µ
Ffr
Ffr
µ s FN
µFN
v≠0
v=0
v
F
4
Rolling friction
FN
a
v
mg
Viscous friction
Ffr
v
Air or liquid
Ffr=−αv
5
Inclines
y
FN
Ffr
v
θ
x
mg
For a moving block
FN + ( mg ) y = FN − mg cos θ = 0
F fr , x + (mg ) x = − µFN + mg sin θ = ma
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Problems:
♦ Two blocks joined by thread
a-?
F12
1
m1
F21
2
F
m2
F12 - ? (tension of the thread)
♦ Apparent weight in elevator
N-?
a
z
N
Scale
mg
7
♦ Pulley
F
1. If a=0, F - ? (Statics)
2. If F given, a - ?
F
F
z
a
Load
2F
8
y
♦ Pulling a boat
Known: F, α
x
River
f
Find: pushing force f, net force
α
F
Pole (push)
Rope (pull)
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