Transcript 5-4 Forces and Circular Motion

Lecture Powerpoints
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 5
Applications of Newton’s
Laws
Main points of Chapter 5
• Gravity, tension, normal force revisited
• Friction, static and kinetic
• Drag forces
• Circular motion
• Fundamental forces
5-1 Common Forces Revisited
Gravity
The acceleration is the
gravitational force divided by
the inertial mass:
(5-1)
The force is the acceleration of
gravity multiplied by the
gravitational mass:
(5-2)
Therefore, the inertial and
gravitational masses are equal:
(5-3)
5-1 Common Forces Revisited
Tension
Tension always pulls, never pushes.
For light (negligible-mass) ropes, the magnitude
of the tension is the same everywhere along the
rope.
5-1 Common Forces Revisited
The Normal Force
Normal force is always perpendicular to surface:
5-1 Common Forces Revisited
Applying Newton’s Laws with Constant Forces
If force is constant, acceleration is constant:
(5-8)
(5-9)
These equations apply to each component.
5-2 Friction
Static and kinetic friction
Static friction applies when object is not
moving along surface; kinetic applies
when it is moving
Both types of friction depend on the
normal force
5-2 Friction
Static and kinetic friction
The friction force is always opposite to
the direction of motion (or the direction
motion would occur, in the case of
static friction)
5-2 Friction
• Static frictional force starts at zero (if no
opposing horizontal force components) and
increases linearly with the force up to its
maximum value.
5-2 Friction
•Kinetic frictional force is somewhat smaller
than static, so that when object begins to
move it accelerates if force stays constant.
• Otherwise can lessen force to maintain
constant speed.
• In either case, force of kinetic friction does
not depend on speed.
5-2 Friction
Forces when pushing box from dead start:
5-2 Friction
Static friction:
(5-21)
Kinetic friction:
(5-22)
Here, μ is the
coefficient of
friction, and FN is
the normal force.
5-3 Drag Forces
• Drag forces come from fluids – gas or liquid
– and are generally proportional to the
square of the speed of the object
• So, as falling object accelerates, drag force
gets bigger and bigger, until it is equal to
accelerating force
• At this point, the net force on the object is
zero, and it moves at a constant velocity from
then on; this is called the terminal velocity
5-3 Drag Forces
(5-30)
Here,
FD is the drag force;
ρ the density of the
medium;
A the cross-sectional
area of the object;
CD the drag
coefficient.
5-4 Forces and Circular Motion
We already know that objects in circular
motion move with a centripetal acceleration:
(5-33)
Therefore, there must be a centripetal force:
(5-34)
5-4 Forces and Circular Motion
In this diagram, the centripetal force is supplied
by the rope:
5-4 Forces and Circular Motion
Circular Motion with Changing Speed
If speed is changing, there must be a component
of the force parallel to the velocity; this means
that the acceleration has both tangential and
radial components.
5-4 Forces and Circular Motion
Circular Motion with Changing Speed
Look at a pendulum:
The gravitational force
on it points straight
down, and therefore
has a tangential
component.
5-4 Forces and Circular Motion
Circular Motion with Changing Speed
Force
diagram:
Components
of gravitational
force:
Radial component of
acceleration:
Tangential component:
5-4 Forces and Circular Motion
Circular Motion and Noninertial Frames
• In this example,
centripetal force is
provided by normal force
• Astronaut is in
noninertial reference frame
• Centrifugal force that she
feels is not a true force
5-5 Fundamental Forces
• Universal gravitation: gravitational force
between any two masses
• Electroweak force: includes electric, magnetic,
and weak nuclear forces (responsible for
radioactive decay)
• Strong (nuclear) force: binds protons and
neutrons together in nucleus
All will be discussed at greater
length in subsequent chapters.
Summary of Chapter 5
• Force of gravity:
(5-2)
• Tension: always a pulling force; if rope’s
mass is negligible, tension is constant
throughout
• Normal force: perpendicular to surface;
equal to force towards surface
• Static friction is variable, depending on
applied force:
(5-21)
• Kinetic friction is constant:
(5-22)
• Frictional force always opposes direction
of motion
Summary of Chapter 5, cont.
• Drag force arises when object travels
through fluid:
(5-30)
• In uniform circular motion, the force is
centripetal:
(5-34)
• Fundamental forces: gravitation,
electroweak, strong nuclear