Transcript Phy 201: General Physics I Lecture Notes

Phy 201: General Physics I
Chapter 4: Forces & Newton’s Laws of Motion
Lecture Notes
Newton’s 1st Law
Every object continues in its state of rest, or of motion unless
compelled to change that state by forces impressed upon it.
• Also known as the “Law of Inertia”
• Key Points:
– When an object is moving in uniform linear motion it has no net force
acting on it
– When there is no net force acting on an object, it will stay at rest or
maintain its constant speed in a straight line
• This property of matter to maintain uniform motion is called
inertia
F=0  a = 0 {v = constant}
• Stated a simpler way: Nature is lazy!
{i.e. matter resists changes in motion}
Newton’s 2nd Law
•
•
When a net force is exerted on an object its velocity will
change:
dv
F=F

F

F

...

 1 2 3
dt
The time rate of change of motion (acceleration) is related
to:
– Proportional to the size of the net force
– Inversely proportional to the mass of the object (i.e. its inertia)
•
The relationship between them is
F 1

a=
=
Fx xˆ + Fy yˆ or  F = ma= m  ax xˆ + ay yˆ 

m m

•

The direction of a will always correspond to the direction
of  F
Newton’s 3rd Law
When an object exerts a force on a second object, the second object
exerts an equal but oppositely directed force on the first object
Body 1
where:
F2 on 1
F1 on 2
Body 2
F2 on 1  F1 on 2
Consequences:
•
Forces always occur in action-reaction pairs (never by themselves)
•
Each force in an action-reaction pair acts on a different object
Important:
•
Newton’s 3rd law identifies the forces produced by interactions
between bodies
•
Newton’s 2nd law defines the accelerations that each object
undergoes
Free-Body Diagrams
• Simplified drawing of a body with only the forces acting on
it specified
• The forces are drawn as vectors
• Free-Body diagrams facilitate the application of Newton’s
2nd Law
Examples:
Joey getting slapped
Joey standing on a floor
while standing on a floor
Joey in “Free Fall”
Joey
W
Ffloor
Joey
W
Ffloor
Joey
W
Fslap
Types of Forces
In our world, forces can be categorized as one of 2 types:
• Non-Contact: force is exerted over a distance of space with
out direct contact (a.k.a. “action-at-a-distance” forces)
• Contact: forces is exerted due to direct contact
(Note: at the microscopic level, ALL forces are non-contact)
• In either case, Newton’s 3rd law still applies to the
forces present
Examples of each type of force:
Non-Contact:
• Gravitational
• Electric
• Magnetic
Contact:
• Normal
• Frictional
• Tension
Mass vs. Weight
•
The “weight” of an object is the gravitational force
exerted on it by the gravitational attraction between
the object and its environment:
FG=maG=maGyˆ  FG =m aG  FG=maG
•
On the surface of the Earth, the gravitational force
is referred to as weight:
FG = W = (-mg)yˆ  FG = W = mg
•
Mass is a measure of an object’s inertia (measured
in kg)
– Independent of object location
•
Weight is the effect of gravity on an object’s mass
(measured in N)
– Determined by the local gravitational acceleration
surrounding the object
Notes:
• Mass is a measure of an object’s inertia (measured in kg)
– Independent of object location
•
Weight is the effect of gravity on an object’s mass (measured in N)
– Determined by the local gravitational acceleration surrounding the object
Normal Force
• The “support” force between 2 surfaces in contact
• Direction is always perpendicular (or normal) to the plane of
the area of contact
Example: the force of floor that supports your weight
Consider standing on a scale on the floor of an elevator.
The reading of the scale is equal to the normal force it exerts
on you:
Task: Construct free body diagrams for the scale:
1.
2.
3.
4.
At rest
Constant velocity
Accelerating upward
Accelerating downward
Examples of Normal Force
Surface Frictional Forces
• When an object moves or tends to move along a surface, there
is an interaction between the microscopic contact points on the
2 surfaces. This interaction results in a frictional force, that is
– parallel to the surface
– opposite to the direction of the motion
• There are 2 types of surface friction:
– Static (sticking)
– Kinetic (sliding)
Static Friction
• Static (or sticking) friction ( fs ) is the frictional force
exerted when the object tends to move, but the external
force is not yet strong enough to actually move the object.
• Increasing the applied force, the static frictional force
increases as well (so the net force is zero) . The force just
before breakaway is the maximum static frictional force.
• The direction of the static friction force is always in
opposition to the external forces(s) acting on the body
• The magnitude of the maximum static friction force is:
fsmax =μmax
FN
s
Where:
– μmax
is the coefficient (maximum) of static friction
s
– FN is the normal force
Kinetic Friction
• Kinetic frictional force ( fk ) is the frictional force exerted by the
surface on an object that is moving along the surface
• Kinetic frictional force:
– always opposes the direction of the motion
– the direction is along the surface (parallel to the surface)
• The magnitude of the kinetic frictional force depends only on
the normal force and the properties of the 2 surfaces in
contact
fk =μk FN
Where:
– mk is the coefficient of kinetic friction
– FN is the normal force
Notes:
– Kinetic friction is independent to the rate of travel of the sliding body
– Kinetic friction is independent to the surface area of contact
Tension Force
• Force applied through a rope or cable
• When the rope or cable is mass-less (negligible
compared to the bodies it is attached to) it can be
treated as a connection between 2 bodies
– No mass means no force needed to accelerate rope
– Force of pull transfers unchanged along the rope
– Action force at one end is the same as the Reaction
force at the other end
• When attached to a pulley the tension force can
be used to change the direction of force acting
on a body
• Calculation of a tension force is usually an
intermediate step to connecting the free-body
diagrams between 2 attached objects
Tension Applications
M2
• With Pulley (flat surface):
M1
• Inclined Plane:
q
M1
• Atwood Machine:
M1
M2
Sir Isaac Newton (1642-1727)
• Greatest scientific mind of the late 17th century
• Invented the “calculus” (independently but
simultaneously with Gottfried Wilhelm Leibnitz)
• Among his accomplishments included:
– A Particle Theory Light & Optics
– A Theory of Heat & Cooling
• Established 3 Laws of Motion
• Proposed the Law of Universal Gravitation (to
settle a parlor bet proposed by Christopher Wren!!)
– The competition was actually between Edward
Haley & Robert Hooke
– This theory successfully explained planetary motion
and elliptical orbits
“If I have seen further it
is by standing on the
shoulders of giants.”