Phy 201: General Physics I
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Transcript of Phy 201: General Physics I
Phy 201: General Physics I
Chapter 4: Forces & Newton’s Laws of Motion
Lecture Notes
Newton’s 1st Law
• 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
• Stated a simpler way: Nature is lazy! {i.e. matter resists changes in motion}
F=0 a = 0 {v = constant}
Every object continues in its state of rest, or of motion unless compelled to change that state by forces impressed upon it.
Newton’s 2nd Law• When a net force is exerted on an object its velocity will
change:
• 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
or
• The direction of will always correspond to the direction of
ˆ ˆx y
F 1a= = F x + F y
m m
ˆ ˆ
x yF = ma= m a x + a y
...1 2 3F=F F F dv
dt
a
F
Newton’s 3rd LawWhen an object exerts a force on a second object, the second
object exerts an equal but oppositely directed force on the first object
where:
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
1 on 2FBody 1 Body 2
2 on 1F
2 on 1 1 on 2F F
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
W
Joey in “Free Fall”
Joey
W
floorF
Joey standing on a floor
Joey
W
floorF
Joey getting slapped while standing on a floor
slapF
Types of Forces
Non-Contact:• Gravitational• Electric• Magnetic
Contact:• Normal• Frictional• Tension
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:
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:
• On the surface of the Earth, the gravitational force is referred to as weight:
• 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
ˆG G G G G G GF =ma =ma y F =m a F =ma
ˆG GF = W = (-mg)y F = W = mg
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 contactExample: 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. At rest2. Constant velocity3. Accelerating upward4. 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 ( ) 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:
Where:– is the coefficient (maximum) of static friction– FN is the normal force
max maxs s Nf =μ F
sf
maxsμ
Kinetic Friction• Kinetic frictional force ( ) 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
Where:– k 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
k k Nf =μ F
kf
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
• With Pulley (flat surface):
• Inclined Plane:
• Atwood Machine:
M1
M2
M1
M2
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.”