Download Fourth Week

Summary for last week:
Newton’s 2nd Law + 1st Law
•
!
Fresultant =
"
!
Fi
! !
!
!
= F1 + F2 + ...+ FN = ma Object
all forces acting on object
due to other objects
if we measure acceleration in an inertial coordinate system
!
Newton’s Third Law
• If object A exerts a force F AonB on object B, there is an
equal and opposite force
F BonA = - F AonB that B exerts on A.
• Both forces have exactly same magnitude, regardless of
motion (acceleration) of either object.
• The two forces act on different bodies and in opposite
direction. They are called a “Action-Reaction Pair”.
=> F Action = - F Reaction
Examples I
• Gravitational downwards Force - mg on object of mass m
<=> equally strong upwards Force + mg on Earth
• Person pulling with force F on object <=> object pulls
with force -F on person
• Person pushing object forward <=> object pushes back on
person with equal force
• Weight of object - mg pushing down on support <=>
support pushing object up with normal force + mg .
• Rocket “pushing out gas” - gas pushing rocket forward.
Examples II: Tension
• Rope, Chain etc.:
Imagine “cut” at some point
“upper” half exerts force on “lower” half
“lower” half exerts force on “upper” half
Equal : Action-Reaction Pair F U = -F L
=> Tension T = |F U | = |F L | at that point
• Force acting at end point = Tension at that point T 1
mg
T2
Important Points:
•
For Newton’s Second Law, use only forces acting on object to
calculate ΣF = m a , not reaction forces on other objects.
•
No object can exert a net force on itself (Münchhausen trick):
Force of one part on another exactly balanced by Reaction Force =>
total sum = zero.
Nothing can experience a force without exerting a force
HOWEVER: Effect of (reaction) force on one object may be a lot
smaller than the effect of the (equal-sized) action force on the other
object (cannon recoil…)
Action+Reaction pair = INTERACTION
(most fundamental; all forces are due to interactions)
•
•
•
How can we tell that a force is acting
(and how strong it is)?
•
Operational definition based on Newton’s Second Law.
•
By looking at its effects:
– the object (mass point) is accelerating
– a solid is stretched or bent (spring [balance], rope, …)
•
From our knowledge of Force Laws:
– an object of mass m will experience a force
F y = - mg pointing downwards on the surface of Earth
– A rope which is pulled with force of strength |F| at one end will exert force of same
strength at its other end (in the direction of the rope) if it doesn’t accelerate and its
weight is negligible (Newton’s 3rd Law).
– General gravitational force law (later in semester), electromagnetism (even later in
semester)…
Web of Forces and Masses
• Use Newton’s 2nd and 3rd law to create relationships
between known forces and masses and unknown ones:
• Masses:
Standard in Paris
Force Laws: Gravitation
Known Forces: Springs
Compare accelerations (3rd Law, 2nd Law)
Balance forces (Superposition)
Unknown mass
• New Forces
–
–
–
–
Measure a, m (2nd Law)
Balance with known force (spring, pulley + weight,…)
Observe reaction (3rd Law)
Develop Force Law, apply to new situations
Scalars and vectors
• Scalars are observables which can be expressed with a
simple number (and appropriate units). Examples: Time,
mass, temperature,...
• Vectors are observables which have both a magnitude (a
number with units) and a direction. Examples:
Displacement, velocity, force, acceleration…
• It is very important to distinguish these! two entities: use
different notation (A for scalar, A or A for vector), and
clearly indicate size and direction for a vector result.
a
!
Example: Displacement
• Size: actual distance from Point A to Point B (don’t forget
units)
• Direction: Describe which way to go.
• Note: Vectors which have different sizes, different units, or
different directions are different. BUT: starting point does
not matter:
Specifying a vector
1.) By giving its length (size, magnitude, absolute value with units) and its direction.
Examples: “1100 m exactly northeast from here” or “0.17
m at an angle of 45o above the x-axis, in the x-y plane”.
2.) You can represent vectors by drawing arrows. The length
of the arrow represents the size of the vector (e.g., 2 cm
represent 2 N) and the direction of the arrow is in the
direction of the vector.
Seb
See
Vectors can be added to (or subtracted
from) each other.
1.) Geometrically: See examples. Use either “tail to head”
method or “parallelogram” method
2.) Mathematically (a bit too advanced for our purpose)
Example: Equilibrium - car at rest
• Equilibrium: All forces acting on an object add up to zero
(vectorially).
• The object will either be (stay) at rest or will move with
constant velocity.
• Example: Car sitting still on an inclined plane (or moving
down with constant velocity)
F Friction
F Normal
F Weight
x
α
y
Example: Car accelerating down ramp
• Net force: All forces acting on an object add up to a net
force along the ramp (vectorially).
• The object will accelerate down the ramp.
F Friction
F Normal
x
F Weight
α
y
Equilibrium - Sailboat
Wind Force
Drag
Normal Force
on Keel