# Chapter 4- Newton�s laws of Motion by 594F8exy

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```									     Chapter 4-
Newton’s laws of Motion
• Kinematics
– the study of how objects move
• Dynamics
– the study of why objects move
• Force
– a push or a pull; symbol is F; SI unit is the
Newton, or N
– One Newton is the force necessary to cause a
one kilogram mass to accelerate at the rate of
1 m/s2
– 1 N = 1 kg m/s2
• Statics
– Statics is the study of the forces acting on and within
structures that are in equilibrium. Statics means that
the body is at rest.
• Conditions for static equilibrium
– The sum of the forces acting on the body must add up
to zero. (Remember, if a force component points in
the negative x, y, or z direction, it is assigned a
negative value.
 SFx = 0
 SFy = 0
 SFz = 0
– The sum of all the torques acting on the object
(calculated along any axis) must be zero. St = 0
• Four basic forces:
– Gravitational force -an attractive force that exists
between all objects with mass; an object with mass
attracts another object with mass; the magnitude of
the force is directly proportional to the masses of the
two objects and inversely proportional to the square
of the distance between the two objects. Stated
mathematically:
– Where G is the universal gravitational constant
(meaning it has the same value throughout the
universe), m1 and m2 are the masses of the objects
in kilograms, and d is the distance between them in
meters
– G = 6.67 x 10-11 N m2 / kg2
– Cavendish found the universal gravitation constant,
allowing the earth to be "weighed."
– Check out Black Holes, Gravitational Waves, and
Newton’s Laws of Motion:
• Newton’s First Law – an object in motion remains in
motion at constant speed and moving in a straight line
and an object at rest remains at rest unless acted upon
by an outside force; called the law of inertia.
• You do not need a force to keep a body moving at a
constant velocity. Also, a body at rest in one frame of
reference could be moving at constant speed relative to
another frame of reference.
– Equilibrium
an object is in equilibrium when its velocity is zero or its
velocity is constant
– Inertia
a measure of how an object resists changes in motion; it is a
measure of an object’s mass
Electromagnetic force
an attractive or a repulsive force between
charged particles; when charged particles
are in motion, they produce magnetic
forces on each other; the magnitude of the
force is directly proportional to the
magnitudes of the charges and inversely
proportional to the square of the distance
between the two charges
Strong nuclear force
an attractive force between the particles in
the nucleus; it is the strongest of the four
forces, but only acts over very small
distances (does not obey inverse square
law for distances)
Weak nuclear force
a force involved in the radioactive decay of
some nuclei (in the 1960’s, Weinberg
theorized the existence of the electroweak
force, combing the electromagnetic and
the weak nuclear force)
• Newton’s Second Law – An unbalanced force
(or net force, S) causes an object to accelerate;
this acceleration is directly proportional to the
unbalanced force and inversely proportional to
the object’s mass; called the law of acceleration
– a = SF / m or S F = m a
– Equilibrium
• an object is in equilibrium when no unbalanced force (or net
force) acts on it
– Mass
• A measure of the inertia of a body. (SI unit is the kilogram);
Mass is a property of a body itself. It should not be confused
with weight, which is a force (the force of gravity acting on an
object).
– An excellent Newton's Second Law Applet that allows
you to conduct a simulated Second Law experiment.
• Newton’s Third Law – When one object
exerts a force on another object, the
second object exerts a force on the first
object that is equal in magnitude, but
opposite in direction; for every action,
there is an equal, but opposite reaction;
called the law of action-reaction
• A good site that tests your understanding
of action/reaction pairs of forces
Advanced Look at the 3rd Law
• Where do forces come from? A force is exerted
on an object and is exerted by another object.
The "action" force acts on a different body than a
"reaction" force. To experience the 3rd law, push
distorted, showing that a force is acting on it.
You can feel the force that the desk exerts on
your hand. The harder that you push on the
desk, the harder that the desk pushes back on
your hand. You only feel the forces exerted on
you; you do not feel the forces that you exert on
something else.
Applications of Newton's Laws
• Free-body diagrams represent forces (their magnitudes
and their directions). In a free-body diagram, all forces
are represented using arrows. The direction of motion is
considered positive (usually assigned the right direction);
the direction opposite the motion is negative (typically
assigned the left direction); up is positive and down is
negative
• If the sum of all the horizontal forces acting on an object
is zero, then the object is in equilibrium horizontally. If
the sum of all the vertical forces acting on an object is
zero, then the object is in equilibrium vertically. If the
sum of the forces in a direction is not zero, then the
forces in that direction are not balanced. We say that an
unbalanced force acts in that direction. An object can be
in equilibrium in one direction and not in equilibrium in
another direction.
Forces that act horizontally are
independent of forces that act vertically.
To work free-body diagram problems:
• Draw the free-body diagram labeling all forces (their magnitudes and
directions). Remember to use the appropriate positive and negative
signs.
• Add all the forces in the vertical direction. If the sum is zero, the
forces are balanced, and there is no acceleration. If the sum is not
zero, the forces are unbalanced, and there is acceleration in the
vertical direction. This sum equals the product of mass times
acceleration.
• Add all the forces in the horizontal direction. If the sum is zero, the
forces are balanced, and there is no acceleration. If the sum is not
zero, the forces are unbalanced, and there is acceleration in the
horizontal direction. This sum equals the product of mass times
acceleration.
Common types of forces involved in motion:
1. Weight – a measure of the gravitational force
acting on an object; direction is down (toward
the earth’s center); symbol is Fg
– Fg = m g
– Where Fg is the weight of the object in Newtons, m is
the mass of the object in kilograms, and g is the
acceleration due to gravity.
– Letting the gravitational force equal represent the
weight of an object yields,
Fg = (G m1 m2) / d2
or m1 g = (G m1 M) / d2
or g = (G M) / d2
where M is the mass of the earth
It is easy to see that the force of gravity acts on an
object when it is falling. When an object is at rest
on a surface, the gravitational force still
continues to act. According to the second law,
only a net force would cause the motion of the
object to change. Since the object remains at
rest, the net force acting on it must be zero.
Another force (the normal force) balances the
gravitational force. This is not an example of an
action/reaction pair of forces! Both forces
(gravitational and normal) act on the same
object. Action/reaction pairs of forces act on
different objects.
2. Normal force
the force exerted by a surface to support an object; symbol
is FN; direction is always upward; when an object rests
on a horizontal surface, the normal force equals the
object’s weight; when an object is being pushed or pulled
by a horizontal force, the normal force equals the
object’s weight. When a push or a pull is something
other than horizontal, a free-body diagram is used to
determine the normal force (taking into account the
vertical component of the push or the pull). A normal
force is a "response" force. In other words, a surface
responds to a weight resting on it by acting to oppose it
to the extent necessary to "cancel out" these forces. For
our purposes, normal forces only exist on a surface (if
the object is in the air, there is no normal force). The
normal force is not an action/reaction pair of forces with
the weight.
Advanced Look at the Normal Force
Returning to our weight example ... An
upward force (the normal force) is exerted
by the table on the object. The reaction to
this is the downward force exerted by the
object on the table. Since these forces act
on different objects, they are
action/reaction forces described by
Newton's Third Law. What is the reaction
force acting in response to the
gravitational force? The object exerts a
gravitational force on the earth!
in terms of the third law
The object rests on the table and is in the Earth's
gravitational field. The Earth exerts a downward
gravitational force on the object equal to the object's
weight. The object exerts an equal gravitational force on
the Earth. The downward gravitational force exerted by
the Earth and the upward gravitational force exerted by
the object represent an action/reaction pair of forces.
The table exerts an upward force on the object. The
object exerts an equal downward force on the table.
These also represent an action/reaction pair of forces.
An action/reaction pair of forces never act on the same
object. Action/reaction pair of forces represent the mutal
interaction of two bodies.
Famous Physics Puzzle:
A man hitches a horse to a cart. The horse
refuses to pull the cart, telling the man,
"No matter how hard I pull, the cart pulls
back with an equal force, and it will be
impossible for me to ever pull the cart!"
• The horse exerts a force on the cart (action) and the cart
exerts an equal and opposite force on the horse
(reaction). The horse exerts a force on the ground
(action) and the ground exerts an equal and opposite
force back on the horse (reaction). There are two sets of
action forces acting (for the horse). If the reaction force
exerted by the ground on the horse is larger than the
reaction force exerted by the sled on the horse, the
horse will move forward. The cart will move forward
when the force exerted by it by the horse is greater than
the frictional force between the cart and the ground.
Remember, there are two sets of forces acting on the
cart: the force exerted by the horse on the cart
(action)/the force exerted by the cart on the horse
(reaction) and the force exerted by the cart on the
ground (action)/the frictional force exerted by the ground
on the cart (reaction).
Friction
• a force that usually opposes the motion of an
object; symbol is Ff; direction is negative; friction
is an electromagnetic force between surface
atoms
• Characteristics of friction:
– Friction acts parallel to the surfaces in contact
– Friction usually acts opposite the direction of the
motion. Friction opposes the applied force.
– Friction depends upon the types of surfaces in
contact (All surfaces are described by a coefficient of
friction, m , which is a characteristic of that surface. m
has no units.)
– Friction is independent of the surface area in
contact.(for hard surfaces)
3. Types of friction:
• Starting friction (Static Friction) opposes the
beginning of motion of an object; is always greater than
sliding friction
• Advanced Look at Static Friction If an object is resting
on a surface, there is no frictional force because there is
no horizontal force. A person now pushes horizontally on
the object, but not hard enough to make it move. The
force of static friction exerted by the surface on the
object prevents it from moving. The object does not
move until you push hard enough (Fmax)to overcome
static friction.
– Fmax = msFN where ms is the coefficient of static friction.
Sliding friction (Kinetic Friction)
– opposes the motion of an object
• Friction can be described mathematically:
– Ff = m FN
• Advanced Look at Kinetic Friction When a
body is in motion along a rough surface, the
force of kinetic friction acts opposite the direction
of the motion.
– Ff = mkFN In AP Physics, we will refer to a smooth
surface as one without friction and a rough surface as
one with friction.
– Interactive Frictional Force Site
4. Applied force – the push or pull that
"you" use to move an object; symbol is
Fapp
5. Unbalanced force (or net force ) – the
sum of all the forces in a direction; it is
what causes the acceleration of an
object
         SF=ma
6. Tension - a force usually associated
with a rope or a cable; it is a "response"
force. In other words, if one pulls on a
rope, the rope "fights back" by resisting
being stretched. If the rope has negligible
mass, the force exerted at one end is
piece of rope along its entire length to the
other end. Note: ropes, cords, and string
can only pull. They cannot push because
they bend.
• AP example
• Two boxes, mass 10 kg and mass 20 kg, are connected by a
massless string on a smooth surface. A horizontal force, Fapp pulls
the 20 kg box. How would you find the acceleration of each and the
tension in the cord? First, draw a free diagram for each box. Four
forces are involved in the free body diagram for the 20 kg box: Fapp
pulls the box horizontally to the right, the Tension (T)pulls to the left,
the normal force acts up, and the gravitational force (the weight)
acts down. Only the tension and the applied force act parallel to the
motion. Apply Newton's second law to the 20 kg box: SF = Fapp - T
= (20 kg)a. Draw a free body diagram for the 10 kg box. Three
forces are involved in the free body diagram for the 10 kg box: the
Tension (T)pulls to the right, the normal force acts up, and the
gravitational force (the weight) acts down. (Since we said the
surface was smooth, there is no friction). Only the tension acts
parallel to the motion. Apply Newton's second law to the 10 kg box:
SF = T = (10 kg)a. Since the boxes are connected, the two boxes
have the same acceleration. We "add" the two equations and get
Fapp =(30 kg)a. Once the acceleration is known, you can solve for
the tension.
7. Forces involved in springs: Most
mass/spring systems obey a simple
relationship between force and displacement
(x), known as Hooke's Law. The restoring
force (F) is proportional to the displacement
(x). The spring constant (k) is the
proportionality constant. Felastic = -kx
Forces on an Inclined Plane
– The normal force exerted by the incline to
support the weight, W. The parallel force is
the part of the object's weight that tends to
make it slide down the incline.
• FN = W cos q
• FP = W sin q
Inclined plane problems are easier to work if
one chooses the direction parallel to the
incline surface as your x-axis. The y-axis
is then perpendicular to the incline
surface. If an object slides down an
incline, three forces act on it: the normal
force, the frictional force, and the
gravitational force (or the object's weight).
• The gravitational force
can be resolved into its
x and y components.
Its x component is
called the parallel
force. Its y component
is equal in magnitude
and opposite in
direction to the normal
force exerted by the
surface on the object.

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